Heat Transfer Fundamentals Concerning Quenching Materials in Cold Fluids

*Nikolai Kobasko*

### **Abstract**

The current chapter discusses three principles of heat transfer related to transient nucleate boiling process when any film boiling during quenching is completely absent. They include the duration of nucleate boiling establishment, surface temperature behavior during self-regulated thermal process, and generalized fundamental equation for evaluation of transient nucleate boiling length. In fact, majority of authors in their analytical and experimental investigations always considered three classical heat transfer modes: film boiling, nucleate boiling, and convection. It is shown in the chapter that the absence of film boiling process simplifies numerical and analytical calculations. It is very important to know that mentioned principles can be used for calculation of temperature fields and stresses and development of new technologies without performing costly experiments. It is stated that universal correlation for heating and cooling time evaluation, modified by proposed principles, can be widely used for recipes development when exploring new intensive quenching technologies. Examples of calculations are provided.

**Keywords:** film boiling absence, three principles, heat transfer, new approach, recipes development, new technologies

### **1. Introduction**

This chapter considers recently discovered unusual characteristics of transient nucleate boiling process. It was possible to do that terminating any film boiling process during quenching. Since it was a widely distributed opinion on three stages of cooling (film boiling, nucleate boiling, and convection), scientists paid the main attention to studying film boiling processes. The results of investigation obtained by scientists are really very important and very interesting since they allowed to decrease distortion. Four types of heat transfer modes discovered [1, 2] were important for the practice. It was established that vapor film behavior depends on size and form of the

quenched steel part. These accurate investigations brought success and lifted the heat-treating technology to the next level in progressing scale. Nobody considered cooling curves during quenching without considering the film boiling process because existing theory and accurately performed experiments in many cases showed vapor films during quenching in liquid media. Engineers used this concept in practice. Even thermal scientists were sure that film boiling during hardening steel in cold fluids always exists. However, accurate experiments of French [3], which were performed in cold 5% water slow agitated solution of sodium hydroxide (NaOH), clearly displayed the absence of film boiling process when quenching spherical steel samples of different diameters from 875°C in the mentioned fluid. Accurate experiments of French were published in many papers and books [3]. Scientists did not discuss them and did not use them for solving the inverse problem to investigate heat transfer when any film boiling process is completely absent during quenching. Probably, it was impossible to explain the absence of film boiling process during quenching probes from 875°C in a slow agitated cold fluid. The current short overview presents results of investigations which were obtained using long-lasting experiments of different authors including experiments of French. As a result, the three of the most important principles were formulated, which create the fundament for intensive quenching processes. These new principles are discussed in the current short chapter.

### **2. Incorrect heat transfer coefficient evaluation during transient nucleate boiling**

Historically in the heat-treating industry, the heat transfer coefficient (HTC) during transient nuclear boiling process is evaluated as αeff = q/(T – Tm), which is called the effective HTC. In fact, the real HTC is evaluated as αreal = q/(T – Ts). As known, the critical radius *Rcr* of a bubble growth depends on the overheat of a boundary layer Δ*TS* ¼ *Tsf* � *TS*, which is determined as [4]:

$$R\_{cr} = \frac{2\sigma T\_S}{r^\* \rho^\* \Delta T\_S},\tag{1}$$

Note that *Rcr* is critical radius of a bubble that is capable of growing and functioning; *σ* is surface tension (N/m); *TS* is saturation (boiling) temperature; r\* is latent heat of evaporation (J/kg); *ρ*} is vapor density (kg/m3 ); and Δ*TS* ¼ *Tsf* � *TS* is wall overheat. HTC related to difference Δ*TS* ¼ *Tsf* � *TS* is known as a real HTC and it is called unreal (effective) if it is related to Δ*Tm* ¼ *Tsf* � *Tm:* Here,*Tsf* is wall temperature and *Tm* is bath temperature. Effective HTC is used only for approximate core cooling rate and core cooling time evaluation and cannot be used for correct temperature field calculation. There is a big difference between the real and effective HTCs. **Table 1** shows the difference between real and effective HTCs depending on bath temperatures *Tm.*

As seen from **Table 1**, effective HTC is decreased up to 700%, as compared with the real HTC. That is why the cooling process during transient nucleate boiling was considered as the slow cooling that requires the use of powerful pumps or powerful rotating propellers to make the cooling process more intensive via strong agitation of the quenchant.

*Heat Transfer Fundamentals Concerning Quenching Materials in Cold Fluids DOI: http://dx.doi.org/10.5772/intechopen.113240*


**Table 1.**

*Ratio of real HTC to effective HTC versus temperature of water.*

### **3. Finite initial heat flux density to be compared with its critical value qcr1**

It was accepted by worldwide community that during quenching steel from high temperatures in cold fluid, three stages of cooling are always present: film boiling, transient nucleate boiling, and convection. It is supported by the conventional law of Fourier (2):

$$q = -\lambda \frac{\partial T}{\partial r} \tag{2}$$

During immersion of a heated steel part into cold liquid, at the very beginning of cooling *q* ! ∞*:* It means that at the very beginning, initial heat flux density always accedes to the first critical heat flux density qcr1, resulting in developed film boiling process. However, Lykov [5] considered modified law of Fourier (3) resulting in finite heat flux density:

$$q = -\lambda \frac{\partial T}{\partial r} - \pi\_r \frac{\partial T}{\partial \tau} \tag{3}$$

It was shown by him that modified law of Fourier generates hyperbolic heat conductivity eq. (4) [5]:

$$\frac{\partial T}{\partial \tau} + \tau\_r \frac{\partial^2 T}{\partial \tau^2} = adiiv(gradT) \tag{4}$$

Here, *λ* is thermal conductivity of solid material in W/mK and *τ* <sup>r</sup> is relaxation time.

For the first time, hyperbolic heat conductivity Eq. (4) with the appropriate boundary and initial conditions was solved analytically by authors [6] and it was shown that initial heat flux density is finite value which can be far below the first critical heat flux density qcr1. It means that the film boiling process is absent completely when quenching steel parts from high temperatures in cold fluids. Such conclusion was formulated from the point of view of mathematics. One can formulate the same conclusion from the point of view of physics. Really, at the very beginning of cooling the cold fluid must be heated to the boiling point of a liquid and then overheated to initiate the nucleate boiling process. During this period of time, the surface of the steel part decreases, thereby creating a temperature gradient that results in finite initial heat flux density. At that moment of time, heat flux density is compared with the first critical heat flux density. If it is below qcr1, any film boiling process is completely absent. To support such conclusion, it makes sense to consider experiments of French [3] presented by **Table 2**.

As seen from **Table 2**, surface cooling curves for spherical probes of sizes such as 6.35 mm, 12.7 mm, and 120 mm are practically similar and cooling short time for all of them is almost the same.


#### **Table 2.**

*Time required for the surface of steel spheres of different sizes to cool to different temperatures when quenched from 875°C in 5% water solution of NaOH at 20°C agitated with 0.914 m/s [3].*

Similar results on drastic decrease of surface temperature, which drops within short time almost to the boiling point of a quenchant, were obtained by different authors (see **Figures 1**–**3**).

In **Figures 1**–**3**, the surface temperature of probes after initial drastic decrease maintains at the level of boiling point of a liquid and is called the self-regulated thermal process (SRTP).

**Figure 4** presents a comparison of experimental core cooling curve with core cooling curve obtained for constant surface temperature during self -regulated thermal process.

**Table 3** presents initial temperature *TI* and temperature *TII* at the end of selfregulated thermal process (SRTP) versus thickness of the stainless probes.

#### **Figure 1.**

*Surface (1) and core (2) temperature curves versus time during quenching cylindrical probe 20 mm in diameter in low concentration of water polymer solution at 20°C [7].*

*Heat Transfer Fundamentals Concerning Quenching Materials in Cold Fluids DOI: http://dx.doi.org/10.5772/intechopen.113240*

#### **Figure 2.**

*Cooling curves obtained in Idemitsu Kosan Co., Ltd. Lab (Japan) for cylindrical specimen of 28 mm diameter and 112 mm length when quenching in water flow of 1.5 m/s at 20°C [8].*

**Figure 3.**

*Cooling curves versus time during quenching cylindrical probe 50 mm diameter in 14% NaCl water solution at 23°C [9].*

The average surface temperature for a probe 50 mm in diameter during numerical calculation within the self-regulated thermal process was approximately equal to 114°C (see **Figure 3** and **Table 3**). Error due to averaging of surface temperature is rather small and is equal to 0.47% (see **Table 4**).

Based on unusual characteristics of SRTP, intensive quenching processes IQ-2 and IQ-3 were developed. The IQ-2 technological process explores transient nucleate boiling (see **Figure 5a**), while transient nucleate boiling process is absent while performing IQ-3 technology (see **Figure 5b**). It is very important to know how much technological process IQ-3 differs from technological process IQ-2, which is essentially cheaper.

#### **Figure 4.**

*A comparison of experimental cooling curve with calculated cooling curve when surface temperature during quenching 50 mm probe in water salt solution is constant.*


#### **Table 3.**

*Initial temperature* TI *and temperature* TII *at the end of self-regulated thermal process (SRTP) versus thickness of the stainless probes.*


*Heat Transfer Fundamentals Concerning Quenching Materials in Cold Fluids DOI: http://dx.doi.org/10.5772/intechopen.113240*


#### **Table 4.**

*Errors at the core of a cylindrical probe 50 mm diameter generated by replacing the real surface temperature during SRTP with average constant surface temperature.*

#### **Figure 5.**

*The temperature difference between IQ-2 and IQ-3 processes when quenching a cylindrical steel probe 50 mm in diameter in an agitated water solution at 20°C and in condition when HTC is infinity: a) it is an IQ-2 process and b) it is a IQ-3 process.*


**Table 5.**

*Core cooling time difference between IQ-2 and IQ-3 processes when transient nucleate boiling and direct convection occur during quenching.*

#### **Figure 6.**

*Real Knnb and effective Knconv Kondrat'ev numbers versus time when quenching a 50 mm cylindrical sample in a low concentration of water salt solution at 20°C.*

As one can see from **Figure 5**, the temperature difference between IQ-2 and IQ-3 processes in core cooling curve change is insignificant (see **Table 5**).

This fact opens the possibility of approximate core cooling time calculation of different steel parts using average values of Kondrta'ev numbers Kn (see **Figure 6**).

**Figure 6** presents real Knnb and effective Knconv Kondrat'ev numbers as a result of the calculation of core cooling curves for a cylindrical probe 50 mm diameter quenched in still fluid with convective HTC 548 W/m<sup>2</sup> K. Convective biot number for such condition is equal to 0.6 and duration of transient nucleate boiling, according to [10], is equal to 72.6 s. Kondrat'ev numbers Knnb and Knconv were calculated by the well-known equation presented in [10, 11] on the basis of solving the inverse problem for calculating HTCs as α<sup>r</sup> = q/(T – Ts) and as αeff = q/(T – Tm). Note that effective HTC is used only for core cooling time evaluation (see Eq. (5)):

$$\tau = \left[\frac{kBi\_V}{2.095 + 3.867Bi\_V} + \ln \frac{T\_o - T\_m}{T - T\_m}\right] \cdot \frac{K}{aKn} \tag{5}$$

Here,

*τ* is cooling time in seconds; k = 1, 2, 3 for plate, cylinder accordingly; BiV is generalized Biot number; To is initial temperature; Tm is bath temperature; K Kondrat'ev form factor; a is thermal diffusivity of steel; and Kn is dimensionless Kondrat'ev number.

*Heat Transfer Fundamentals Concerning Quenching Materials in Cold Fluids DOI: http://dx.doi.org/10.5772/intechopen.113240*

It is also used for cooling rate v evaluation (see Eq. (6)):

$$v = \frac{a \text{Kn}}{K}(T - T\_m) \tag{6}$$

According to **Figure 6**, the average effective Knconv = 0.625 while real Knnb = 0.93. It means that real generalized Biot number BiV = 10 [12].

There are many experimental data and databases related to effective HTCs, which are mainly used in the heat-treating industry for recipes development. That is why this issue is discussed here to be able to use cost-effective HTCs obtained by different authors. The real HTCs and real Kondrat'ev numbers are used for calculation of temperature field and residual stresses. In the last decade, it was possible due to the absence of film boiling process. The problem of elimination of film boiling process is solved effectively by the next three main approaches:


$$q\_{in} = \frac{q\_o}{\left(1 + 2\frac{\delta}{R}\frac{\lambda}{\lambda\_{\rm cut}}\right)}\tag{7}$$

Here, qin is initial heat flux density of cylindrical probe covered by polymeric layer; qo is initial heat flux density of cylindrical probe free of polymeric layer; *δ* is thickness of polymeric layer; R is radius of cylindrical probe; *λ* is thermal conductivity of steel; and *λcoat* is thermal conductivity of insulating layer.

• The use of resonance effect generated by hydrodynamic emitters to destroy any film boiling process during quenching steel in cold fluids [13].

### **4. Fundamentals of transient nucleate boiling processes**

When any film boiling is completely absent due to qin < qcr1, one can formulate three very important for the practice characteristics of the transient nucleate boiling process. They are:

a. For a given condition of cooling in cold fluid, the duration of establishing developed nucleate boiling is almost the same, independently of the form and size of the steel part. It can be explained by an extremely high heat exchange during shock boiling which lasts for a very short time, thereby creating a huge temperature gradient in a very thin surface layer. Core temperature during this time is not affected by shock boiling at all and cooling process at the very beginning is considered as a cooling of semi-infinity domain. It is happening because the speed of heat distribution is a finite value and during this short time of cooling, the heat does not reach layers located at the core of steel parts (it follows from Eq. 3 and Eq. 4).

b. The surface temperature of a steel part, beginning from the start of full nucleate boiling establishing, maintains at the level of boiling point of the fluid insignificantly differing from it. The so-called self-regulated thermal process is established. The initial temperature of self-regulated thermal process *TI* can be evaluated as:

$$T\_I = T\_\mathcal{S} + \mathfrak{A}\_I \mathcal{C} \tag{8}$$

where

$$\mathfrak{H}\_{I} = \mathbf{0}.2\mathfrak{P}\mathbf{3} \cdot \left[\frac{\mathbf{2}\lambda(\mathfrak{H}\_{o} - \mathfrak{H}\_{I})}{R}\right]^{0.3} \tag{9}$$

The temperature of self-regulated thermal process *TII* at the end of nucleate boiling is evaluated as:

$$T\_{\rm II} = T\_{\rm S} + \mathfrak{g}\_{\rm II}, \, ^\rho \mathbf{C} \tag{10}$$

where

$$\mathfrak{H}\_{\mathrm{II}} = \mathbf{0}.2 \mathfrak{P} \mathbf{3} \cdot \left[ a\_{\mathrm{conv}} (\mathfrak{H}\_{\mathrm{II}} + \mathfrak{H}\_{\mathrm{u}h}) \right]^{0.3} \tag{11}$$

*ϑI*, *oC* is overheat of a boundary layer at the beginning of SRTP; *ϑII* is overheat of a boundary layer at the end of SRTP.

It is possible to use average temperature ð Þ *TI* þ *TII =*2 for approximately calculating temperature fields and residual stresses during quenching of steel parts in fluids when film boiling is completely absent with the accuracy <1% .

c. As a result of long-lasting accurate experiments and appropriate analytical solutions, for the fixed initial temperatures To and Tm, the author [14] has formulated very important for the practice the main characteristic of the transient nucleate boiling process. It says that duration of transient nucleate boiling is directly proportional to squared thickness of steel part, inversely proportional to thermal diffusivity of material, depends on the form of steel part, and convective Biot number Bi. The generalized equation for such statement can be mathematically formulated as [14]:

$$
\pi\_{nb} = \Omega k\_F \frac{D^2}{a} \tag{12}
$$

Here, *τnb* can be considered as a width of noise generated by vapor bubbles, which is equal to its duration measured in seconds; Ω is dimensionless parameter depending on convective HTC; *kF* is dimensionless form coefficient; D is thickness of steel part in m; and a is thermal diffusivity of steel in m<sup>2</sup> s �1 .

For the fixed To = 850°C and Tm = 20°C, the dimensionless coefficient Ω, presented by **Figure 7**, depends only on convective Biot number Bi (**Table 6**).

The heat transfer coefficients (HTCs) during transient nucleate boiling process were evaluated using Tolubinsky's equation [4]:

*Heat Transfer Fundamentals Concerning Quenching Materials in Cold Fluids DOI: http://dx.doi.org/10.5772/intechopen.113240*

#### **Figure 7.**

*Value Ω versus convective Biot number Bi [15].*


#### **Table 6.**

*Dimensionless form coefficients kF for different forms of steel parts.*

$$\frac{a}{\lambda} \sqrt{\frac{\sigma}{\mathbf{g}(\rho - \rho^{\cdot})}} = 75 \cdot \left(\frac{q}{r^{\bullet} \rho^{\cdot} W^{\cdot}}\right)^{0.7} \cdot \left(\frac{\nu}{a}\right)^{-0.2} . \tag{13}$$

According to Tolubinsky equation [4], the real HTC during nucleate boiling is calculated from the rewritten Eq. (14):

$$a = 75\lambda \left[ \frac{\mathbf{g} (\rho' - \rho'')}{\sigma} \right]^{0.5} \left( \frac{a}{v} \right)^{0.2} \left( \frac{1}{r^\* \rho'' w''} \right)^{0.7} \cdot q^{0.7} \tag{14}$$

or

$$a = cq^{0.7} \tag{15}$$

where.

$$\mathcal{L} = 75 \lambda' \left[ \frac{\text{g} \left( \rho' - \rho'' \right)}{\sigma} \right]^{0.5} \cdot \left( \frac{a}{\nu} \right)^{0.2} \left( \frac{1}{r^\* \rho' w''} \right)^{0.7}; \text{ } W \text{ }^{\circ} = d\_{\text{q}} f \text{ }.$$

Here, *α* is the real HTC during nucleate boiling process in W/m<sup>2</sup> K; *λ* is thermal conductivity of liquid in W/mK; g is gravitational acceleration in m/s<sup>2</sup> ; *ρ* is liquid density in kg/m<sup>3</sup> ; *ρ*" is vapor density in kg/m<sup>3</sup> ; q is heat flux density in W/m2 ; *W*} is vapor bubble growth rate in m/s; is kinematic viscosity in m<sup>2</sup> /s; *a* is thermal

diffusivity of liquid in m<sup>2</sup> /s; *do* is diameter of a bubble in m; and *f* is frequency of a bubble departure in Hz.

Calculations of HTCs were made for maximal critical heat flux density of water salt solution which was equal to 15 MW/m<sup>2</sup> . Dimensionless correlations of Tolubinsky and Shekriladze [4, 16] were used for evaluation of HTCs, which are presented in **Table 7**.

According to Tolubisky equation, cooling during transient nucleate boiling process is very intensive, even in still fluid if any film boiling is completely absent (see **Table 7**).

Heat flux density during initial time of quenching in cold fluids reaches almost 20 MW/m<sup>2</sup> when film boiling is absent (see **Figure 8a** and **b**). It is comparable with the first critical heat flux density of cold water when qcr2/qcr1 = 0.05.

Heat transfer coefficients during transient nucleate boiling process can be easily evaluated if heat flux density during nucleate boiling is known (see **Figure 8a** and **b**).

According to the investigation of the author [4], during the extremely fast cooling produced by shock boiling, the first critical heat flux density *qcr*<sup>1</sup> is very large, because the ratio (16):

$$\frac{q\_{cr2}}{q\_{cr1}} = 0.05\tag{16}$$

which during conventional cooling is five times larger (see Eq. (17) published in [4, 17]:

$$\frac{q\_{cr2}}{q\_{cr1}} = 0.2\tag{17}$$

According to authors [4, 17], the first critical heat flux density qcr1 for water at 20°C is equal to 5.9 MW/m<sup>2</sup> and for water at 10°C is equal to 6.5 MW/m2.. During shock boiling, the mentioned critical heat flux densities reach values 29.5 MW/m<sup>2</sup> and 32.5 MW/m<sup>2</sup> that follow from comparing Eq. (16) and Eq. (17). It means that any film boiling is completely absent during quenching in slow agitated cold water at 10–20°C. The conclusion made is in good agreement with the experimental data (see **Figures 1**–**3**). Since any film boiling process in many cases is completely absent, one can consider fundamental characteristics of transient nucleate boiling process as the main factors during quenching process in cold fluids. The transient nucleate boiling process exists independently of the will of people. It is happening when meteorites fall into oceans. They produce noise generated by tiny vapor bubbles. The same is happening during volcanos' activity located in oceans and near seas. Transient nucleate boiling can be:


**Table 7.**

*Real HTCs in W/m<sup>2</sup> K during nucleate boiling process depending on the temperature of water solution when heat flux density is 15 MW/m2 .*

*Heat Transfer Fundamentals Concerning Quenching Materials in Cold Fluids DOI: http://dx.doi.org/10.5772/intechopen.113240*

#### **Figure 8.**

*Heat flux density variation versus time during quenching cylindrical specimens 25 band 50 mm in water salt solution of optimal concentration at 20°C: a – diameter 25 mm.*


Discovered characteristics of transient nucleate boiling process create a stable basis for:

• Making intensive quenching process into a mass production since there is no need to design costly quench tanks equipped with the powerful propellers and tanks.


### **5. Universal correlation for heating and cooling time evaluation during steel quenching**

There are numerous computer codes for numerical calculation of cooling time and cooling rate of any steel part's configuration. The author of this chapter proposed a generalized universal equation for heating and cooling time evaluation while heat treating steel parts [21], which has a very simple form:

$$
\pi\_{eq} = \overline{E}\_{eq} \frac{K}{aKn} \tag{18}
$$

Here, *Eeq* is specified if value N = (To – Tm)/(T – Tm) is known (see **Table 8**). **Table 8** provides *Eeq* value depending on N, which varies within 1.5–1000. Kondrat'ev form coefficients K (see **Table 9**) are provided by authors [11, 12, 22]. Kondrat'ev number Kn is calculated as:

$$Kn = \frac{Bi\_V}{\left(Bi\_V^{\cdot^2} + 1.437Bi\_V + 1\right)^{0.5}}\tag{19}$$

Here

$$Bi\_V = \frac{a}{\lambda} K \frac{\mathbb{S}}{V} \tag{20}$$



*Heat Transfer Fundamentals Concerning Quenching Materials in Cold Fluids DOI: http://dx.doi.org/10.5772/intechopen.113240*

#### **Table 8.**

*Coefficients Eeq depending on dimensionless value N that varies from 1.5 to 1000, taking into account different values of generalized Biot numbers BiV [19].*


#### **Table 9.**

*Kondrat'ev form factor K for different forms of steel parts.*

*Example 1:* Cylindrical sample 50 mm diameter, made of AISI (American Iron and steel institute) 1040 steel, is quenched from 860°C in low concentration of still water salt solution at 20°C [23, 24]. Maximal surface compression residual stress reaches its maximal value at the moment when core temperature of cylinder reaches 430°C. Calculate cooling time from 860–430°C to provide further self-tempering process of

surface layers and obtain high surface compression residual stress. For the given process, N = (860–100°C)/(430–100°C) = 2.3. According to **Table 7**, for BiV = 10 and N = 2.3, Eeq = 1.36. Kondrat'ev form factor K = R2 /5.783 = 108.1 <sup>10</sup><sup>6</sup> <sup>m</sup><sup>2</sup> . Average value of thermal diffusivity of AISI 1040 steel a = 5.4 <sup>10</sup><sup>6</sup> <sup>m</sup><sup>2</sup> /s. According to Eq. (18), *<sup>τ</sup>* = (1.3 108.1 <sup>10</sup><sup>6</sup> <sup>m</sup><sup>2</sup> )/(5.4 <sup>10</sup><sup>6</sup> <sup>m</sup><sup>2</sup> /s 0.93) = 29.3 s. Approximately *τ*= 30 s.

*Example 2:* Cylindrical forging 50 mm at its end, made of AISI 1040 steel, has a temperature 950°C. It is quenched intensively in spray water salt solution of low concentration creating condition when *BiV* tends to infinity. Of still water salt solution at 20°C. Calculate cooling time from 970–480°C to provide further self-tempering process of surface layers and obtain high surface compression residual stress and improved mechanical properties due to high temperature thermomechanical treatment. For given condition, N = (970–20°C)/(480–20°C) = 2. According to **Table 7**, for BiV equal infinity and N = 2, Eeq = 1.16. Kondrat'ev form factor K = R<sup>2</sup> / 5.783 = 108.1 <sup>10</sup><sup>6</sup> m2 . Average value of thermal diffusivity of AISI 1040 steel for interval temperatures from 500–950°C is a = 5.6 <sup>10</sup><sup>6</sup> <sup>m</sup><sup>2</sup> /s. According to Eq. (18), *<sup>τ</sup>* = (1.16 108.1 <sup>10</sup><sup>6</sup> <sup>m</sup><sup>2</sup> )/(5.6 <sup>10</sup><sup>6</sup> <sup>m</sup><sup>2</sup> /s 1) = 22.4 s.

Forging requires a shorter cooling time because it is sensitive to crack formation due to overheating.

### **6. Conclusions**


*Heat Transfer Fundamentals Concerning Quenching Materials in Cold Fluids DOI: http://dx.doi.org/10.5772/intechopen.113240*

## **Author details**

Nikolai Kobasko Intensive Technologies Ltd., Kyiv, Ukraine

\*Address all correspondence to: nkobasko@gmail.com

© 2023 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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[3] French HJ. The Quenching of Steels. Cleveland, Ohio, USA: American Society for Steel Treating; 1930

[4] Tolubinsky VI. Heat Transfer at Boiling. Kyiv: Naukova Dumka; 1980. p. 316

[5] Lykov AV. Theory of Heat Conductivity. Moscow: Vysshaya Shkola; 1967. p. 600

[6] Guseynov S, Buikis A, Kobasko N. Mathematical statement of the task with the hyperbolic equation of the thermal conductivity for the intensive quenching of steel and its solution. In: Proceedings of 7th International Conference "Equipment and Technologies for Heat Treatment of Metals and Alloys". Vol. II. Kharkov: KhTI; 2006. pp. 22-27

[7] Kobasko NI. Uniform and intense cooling during hardening steel in low concentration of water polymer solutions. American Journal of Modern Physics. 2019;**8**(6):76-85

[8] Kobasko NI, Aronov MA, Ichitani K, Nasegava M, Noguchi K. High compressive residual stresses in through hardened steel parts as a function of Biot number. In: Resent Advances in Fluid Mechanics, Heat &Mass Transfer and Biology. Harvard: WSEAS Press; 2012. pp. 36-40

[9] Kobasko NI. High Quality Steel Vs Surface Polymeric Layer Formed during Quenching. Germany: Lambert Academic Publishing; 2019. p. 98

[10] Kobasko NI. Basics of quench process hardening of powder materials and irons in liquid media. European Journal of Applied Physics. 2022a;**4**(3): 30-37

[11] Kobasko NI. Regular thermal process and Kondrat'ev form factors. In a book "Intensive Quenching Systems: Engineering and Design". USA: ASTM International; 2010. pp. 91-106

[12] Kondrat'ev GM. Thermal Measurements. Moscow: Mashgiz; 1957

[13] Kobasko NI. UA Patent No. 109572. Intensive hardening method for metal components. 2013

[14] Kobasko NI. Transient nucleate boiling as a law of nature and a basis for designing of IQ technologies. In: Proc of the 7th IASME/WSEAS International Conference on Heat Transfer, Thermal Engineering and Environment. Moscow: WSEAS; 2009. pp. 67-76

[15] Kobasko NI, Aronov MA, Powell JA. Intensive Quenching Processes, Quenchants and Quenching Technology. Vol. 4F. ASM International, USA: ASM Handbook; 2023

[16] Shekriladze IG. Boiling heat transfer: An overview of longstanding and new challenges. In: In a book "Film and Nucleate Boiling Processes". USA: ASTM International; 2010. pp. 229-284

[17] Kutateladze SS. Fundamentals of Heat Transfer. New York: Academic Press; 1963

*Heat Transfer Fundamentals Concerning Quenching Materials in Cold Fluids DOI: http://dx.doi.org/10.5772/intechopen.113240*

[18] Kobasko NI. Unexpected forced heat exchange phenomenon to be widely used for new quenching technologies development. Physics Letters. 2021;**9**(8): 179-191

[19] Kobasko NI. Self-regulated thermal process taking place during hardening of materials and its practical use. Theoretical Physics Letters. 2022;**10**(2): 273-287

[20] Kobasko NI, Moskalenko AA, Dobryvechir VV. UA Patent No. 119230. Method and apparatus for control quality of hardened in fluids metal components. 2019

[21] Kobasko NI. Thermal equilibrium and universal correlation for its heating – Cooling time evaluation. Theoretical Physics Letters. 2021;**9**(10):205-219

[22] Kondrat'ev GM. Regular Thermal Mode. Moscow: Gostekhizdat; 1954

[23] Kobasko NI, Moskalenko AA, Logvynenko PN, Dobryvechir VV. New direction in liquid quenching media development. Thermophysics and Thermal Power Engineering. 2019;**41**(3): 33-40

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### **Chapter 3**

## A Brief Review of Techniques of Thermal Enhancement in Tubes

*Shamoon Jamshed*

### **Abstract**

Heat transfer enhancement in tubes is not a novel idea. These tubes are used in several engineering devices like heat exchangers, boilers, evaporators, refrigerators, and air conditioners, to name a few. To date, these tubes are undergoing an evolutionary period, since engineers are trying new ways to improve the heat transfer (or enhance the heat transfer). The main cause is the pressure loss that occurs due to friction and the limitation of the surface area of the tube. The passive techniques to overcome this loss are more common due to cost-effectiveness. Thus, common passive techniques include grooves inside the tube surface, grooves on both the inner and outer surface, or putting inserts within the tube. Modern techniques are utilizing nanofluids, that carry nano-materials inside the heat transfer fluid to enhance heat transfer. To quantitatively gauge the heat transfer enhancement, the heat transfer effectiveness is computed. This chapter deals with the study of the above-mentioned techniques in some detail and discusses minimizing entropy generation rate in groove tube(s). Also, a bird's-eye view of the nanofluids and their usage for heat transfer enhancement has been seen.

**Keywords:** heat transfer, groove tube, entropy generation, nanofluids, pressure loss, friction, effectiveness, nanofluids

### **1. Introduction**

Heat exchangers (HX)s are quite frequently used in industry. There are various types of heat exchangers available and their use depends upon the particular requirement. The most common type of heat exchanger is the indirect contact type where the fluids exchange heat employing a surface or surfaces lying between the two fluids. Thus, the name indirect applies. In indirect-contact type HXs, there are further classifications, such as tubular type, extended surface type, and plate-type heat exchangers. The extended type heat exchangers have been the subject of much research and this chapter focuses on techniques of optimization of these tube-type HX with reference to mechanical optimization in particular.

The work on tube-type heat transfer has been of much interest for about 50 years. After the late 1970s, the buzzing of global warming due to Chloro Floro Carbon (CFCs) and carbon footprints, engineers and scientists started to improve the devices that are majorly responsible for expelling carbon into the atmosphere. Mostly, among others such as gasoline and human waste, refrigeration devices were found to be responsible for emitting CFCs at a much higher rate. Several international conferences on heat transfer and symposia led the engineers to overcome this problem multifold by improving the device itself rather than the refrigerant. Hence, many research works were presented, attributed, and led to the design of tubes that have extended surfaces.

The works of Bergles, Ralph Webb, and Naryanamuruthy are highly recognized in the community. Arthur E. Bergles is a very well-known personality in the field of augmented heat transfer. He has written many papers and authored many books on enhanced heat transfer (**Figure 1**).

Ralph Webb was a Professor Emeritus of Mechanical Engineering at Penn State University. He wrote the book, Principles of Enhanced Heat Transfer. He performed research by discussing various heat transfer phenomena occurring in heat exchangers, and the design optimization of heat exchangers. He was a veteran consultant in more than 100 major companies and wrote 275 papers in international journals. He died in 2011.

Adrian Bejan is also a professional in the heat transfer field. He has done exacerbated work on entropy generation minimization. This topic has not been touched by any other for heat transfer surfaces. Adrian Bejan has written books on entropy minimization in heat exchange devices. He has also done work on a newer topic called Constructural Law but this is not in the scope of this book or chapter.

## **2. Methods of heat transfer enhancement**

There are many ways of heat transfer enhancement. Mainly, the classification is based on the mode of contact with the fluid and the surface. Two main classes are active and passive. Active methods involve the use of some external power or resource to generate heating. This energy will definitely increase the heat transfer rate. Nevertheless, the surface vibration or the fluid vibration is also used in active means of heat transfer enhancement. The electrostatic field is another technique for heat transfer. Jet impingement is frequently used for heat and cooling as well. It is used for cooling gasturbine blades where the cold fluid from various holes along the blade cross section is impinged on the surface, to make the blade surface cooler. This type of cooling is called film cooling. Film cooling is also used for cooling liquid rocket engines where

**Figure 1.** *Pioneers of the field of enhanced heat transfer.*

the cold fuel gets heated thereby cooling down the engine's heat and thus making the combustion effective.

The passive method involves direct heat transfer by modification in the hardware. By hardware, we mean the surface modification. This can be done by roughening the surface. By manufacturing, a good metal finish can be achieved. But the roughness, in fact, improves the heat transfer. A roughened surface increases the surface area and therefore improves the heat transfer rate. On the other hand, a poor surface finish should not be to such an extent to decrease material quality. The tube surface should also be capable of bearing high temperatures and pressure. If cost is of less issue, another method is the extended surface. This requires adding the fins on the outer or inner surface of the tube. Sometimes, the fins are welded on the outer surface. External surfaces are used if external heating is required. For inner surfaces, since welding a metal piece is not possible on the inner side, grooves are made. This is also sometimes done by making a rectangular sheet with inclined grooves etched into the sheet at a certain included angle (usually 45 or more). Then, the sheet is rolled and welded into forming a tube. Usually, the non-grooved part is now acting as an extended surface but on the inner side. The tubes used in air-conditioning condensers consist of 10 to 15 mm in diameter. This small diameter thus makes the grooving quite difficult. But, due to modern machining techniques (or the rolling technique as mentioned above), these groove-making processes are quite common now. The groove depth or the fin height on the inner side is classified as micro since h/D < 0.03 [1].

Sometimes the tube is itself rotated in the form of a coil. This also improves heat transfer. It does not necessarily increase the heat transfer area but (depending on the pumping power) the fluid now has heat stored in it for a long time, since the travel path is reduced due to coiling. This makes the heat transfer process effective. Coiled exchangers also offer not only a higher heat-transfer coefficient but also a more effective use of pressure drop due to large curvatures. Thus, the designs are used in cases where a large pressure drop is required besides the heating advantage. The coil design allows the management of high temperatures and extreme temperature differentials without high-induced stresses or costly expansion joints. High-pressure transmission capacity with the ability to fully clean the service-fluid flow area also adds a good characteristic to this type of design.

Adding additives nowadays is a very common technique. Additives are added in the form of nano-particles that increase the heat transfer properties of the mixture. **Table 1** shows these different modes of heat transfer enhancement.

The different types of geometrical formats for enhancing heat transfer are pictorially shown in **Figures 2** and **3**.

### **3. Literature on enhanced tubes**

### **3.1 Important terminologies**

There have been several works on enhanced heat transfer. The reason for this immense amount of research on this topic is obvious, that is the tubes with enhanced surfaces have proven to be a successful device in achieving the goal. Since nothing is perfect, there are methods and technologies still under discussion and debate to make tube-side heat transfer effective. Four terms are widely used in this regard.


A roughened surface with twisting tape insert

### **Table 1.**

*Different techniques of heat transfer enhancement.*

### **Figure 2.**

*Tube designs showing groove tube and insert in a tube.*


The entropy generation rate.

### *3.1.1 Friction factor*

The friction factor is the dimensionless pressure drop occurring along the length of the tube. Thus, it's directly related to the pumping power. The more the pumping power is, the lesser the pressure drop will be.

### *3.1.2 Nusselt number*

Nusselt number is defined as the dimensionless heat transfer coefficient. It is usually given as.

**Figure 3.** *Different types of active heat transfer techniques.*

$$\mathbf{Nu} = \mathbf{hD}/\lambda. \tag{1}$$

Where 'h' is the heat transfer coefficient, D is the hydraulic diameter of the tube, and λ is the thermal conductivity of the heat transfer fluid. In the analysis of the heat transfer enhancement, the Nu and f are computed. These are computed for a plain tube (with no enhanced surface) and with an enhanced surface.

### *3.1.3 Thermal enhancement factor*

There is another term defined as thermal enhancement factor or thermal effectiveness which is given as,

$$\boldsymbol{\eta} = (\mathbf{N} \mathbf{u} / \mathbf{N} \mathbf{u}\_o) / (\mathbf{f} / \mathbf{f}\_o). \tag{2}$$

Where the subscript 'o' is for the plain tube. This term η is used for characterizing the thermal enhancement capacity of a tube. It should be >1, for obvious reasons, but if it is not, then it means that the friction factor term is dominating. This means that the tube surface is not effective in enhancing heat and pumping power is consumed in increasing the pressure to overcome the frictional loss. It will also depend upon the design that how much η can be afforded, but it is clear that it is required that it should be >1.

### *3.1.4 Entropy generation rate*

With this in view, a fourth term is needed to compute the overall heat transfer loss/gain. This (in a way) is a missing piece. This term is entropy generation rate. This is given as

$$\dot{S}\_{gen} = \frac{q\Delta T}{T^2} + \frac{\dot{m}\Delta p}{T\rho} \tag{3}$$

Where, *S* \_ *gen* is the rate of entropy generation**;** q is the heat flux; ΔT is the temperature difference across the tube ends; *m*\_ is the mass flow rate**;** Δp is the pressure drop along the tube length. T is the bulk temperature and ρ is the fluid density.

### **3.2 Experimental studies**

Most of the work on the enhanced-surface tube-heat transfer studies is experimental. There are notable works by Webb, Bergles, and Kakaç as referenced in [1, 2].

The work that has been done on enhanced-surface-tube research during the last century is mostly experimental-based. In these studies, there is a vast literature available revealing the notable works of Webb, Bergles, Sunden, and Sadik Kakaç, in the works of Webb et al. [1] and Kakaç [2]. Naryanamuruthy and Webb [1] discussed the heat transfer in helical groove tubes. He discussed the performance of tubes with respect to the Colburn j-factor (StPr2/3) and friction factor. It was concluded that the tubes (when compared with tubes with roughened surfaces) were equally good in depicting the heat transfer enhancement behavior. Jensen [3] discussed the fin dimensions, i.e., height and depth on the surface of the tube. He discussed in detail the effect of fin dimensions on the friction factor and Nusselt number. It was noticed that in the micro-fin tubes, the friction factor experiences a long delay for the flow to become fully turbulent. The flow becomes fully turbulent at Re = 20,000. Chen et al. [4] conducted a study on corrugated tubes. These tubes are not finned or grooved, rather they have a surface turned in the form of a wavy shape. Four-start (the number of grooves/fins/wavy shape seen at the start of the tube) tube was studied in detail. Results were compared with the study of Ravigururajan and Bergles [5], and Srinivasan and Christensen [6] This study concluded that, as far as the trend is concerned, Chen's results are not in agreement with Srinivasan's. Their trend is similar to that of Ravigururajan for heat transfer with a difference of 3000 W/m<sup>2</sup> K. Another researcher K. Gregory [7], investigated eight helical finned tubes and one smooth tube. Results of the heat transfer coefficient and friction factor were obtained and compared with the work of Webb et al. [8]. Results were comparable, in a good estimate, and within the prediction errors from 30 to 40%. Aroonrat et al. [8] determined the Nusselt number and the friction factor for the Reynolds number range of 4000 to 10,000. The tube with the largest helix angle predicted the highest Nusselt number. The helix angle in the tubes was varied from 0 to 90**°** with the highest Nu obtained in the case of 60<sup>O</sup> with 0.5**-**inch pitch. The same trend was followed for the friction factor.

### **3.3 Numerical studies**

Finned geometries were also examined from the numerical simulation perspective. Due to the advent of modern computers, performing complex flow simulations is no more a challenge. Therefore, there has been an increasing trend in Computational Fluid dynamics (CFD) based simulations over the past two decades. A study by Liu and Jensen [9] shows the work on several fin profile formations within a tube. Liu et al. [10] found that there is seldom variation in the fin profile if they were of rectangular or triangular shape. While the round profile under-predicted the friction

### *A Brief Review of Techniques of Thermal Enhancement in Tubes DOI: http://dx.doi.org/10.5772/intechopen.113134*

factor and Nusselt number which was figuratively 7–10% less than the rectangular-fin geometry. Kim et al. [11], utilized a Finite Element Method (FEM) based solver for predicting the flow and heat transfer effects and validated their results. Jasinski [11] and [12] used the CFX code. He determined the heat transfer and friction parameters for different helical angles in micro-finned tubes. This numerical study was a bit different from other researchers in the way that Jasinski determined the entropy generation rate in the tubes. The minimum entropy generation rate was found. The minimum rate of entropy (*S*\_ *gen*Þ was found for different helix angles, and it was predicted to be low for 700 tubes at Re = 60,000. Pirbastami et al. [13] predicted the results of Aroonrat et al. [8] using numerical simulations. Pirbastami modeled the complete three-dimensional geometry of the tube. However, the chapter did not take into account the solid region. This, in my view, is not correct. The chapter merely mentioned (by taking the point of Aroonrat) that the flux on the tube's inner wall was reduced to 30% from what was applied on the top outer wall. This approach, in the author's opinion, is not correct even though the results luckily matched the experimental data. This could be due to the reason that the wall was only 2 mm thick in comparison to the tube length, hence, flux variation did not affect the net results. Nevertheless, this study was a good approach in terms of validation but performed with many assumptions. H. R Kim et al. [14] and S. Kim et al. [14, 15] studied the fluid flow and flux in a twisted elliptical tube. Research work was similar to the works of Piotr, Jensen, and Pirbastami, as reported. This study, though, contained in-depth work since the effects of friction factor, Colburn j-actor, volume, and area were studied in this chapter.

Jamshed et al. [16] did an in-depth study on Aroonrat's geometry and also analyzed customized geometries of groove tubes. They studied different tubes with different pitch and helix angles. It was found that the tube with the lowest pitch gives better performance but at a bit lower Reynolds number of 5000. Also, the entropy generation rate is minimum with the tube with the lowest pitch.

### **4. Trends in the tube-side heat transfer research**

If we monitor the trends over the last two decades, most of the work has been done numerically. **Figure 4** shows the trends that have been occurring in the last 60– 70 years. This shows that significant studies have been done in the numerical domain. Now, the work is more inclined toward entropy minimization and optimization of Heat Transfer Fluid (HTF) with techniques like nanofluids. It should be noted that the scale of progress is just schematic and does not replicate the actual number of publications.

### **5. An example of the validation case**

A simple case was selected for validating the results of Aroonrat (through CFD) as mentioned in the literature review above. Jamshed et al. [16] have a detailed study on it. Here are some glimpses of the work done. This is mentioned to make the audience familiar with the validation process. The tubes selected were already described by Aroonrat [8]. The length of the tube was 2 m and the material was Steel. Thermocouples were mounted for temperature measurement on the tube. Constant heat flux condition was maintained at the wall with magnitude 3500 W/m<sup>2</sup> . The groove geometry is shown in **Figure 5**.

**Figure 4.** *Progress in tube-side heat transfer enhancement research.*

#### **Figure 5.**

*Cutaway of the groove tube, from [9].*

The modeling was done in the software Gridgen v 15. This included the geometric modeling of the tube and the meshing of the fluid+solid region. Later, for the CFD analysis, ANSYS Fluent v16 was used. The turbulence model used was k-ω SST with default pressure-based solvers. Details are well explained in the papers by Jamshed et al. [16]. Due to the symmetric nature of the helical grooves and the flow, the modeling was simplified using the technique of Jensen [3]. This technique implied the modeling of 1/n the geometry where n is the number of grooves (start), then circumferentially modeling the segment from one groove to the other. After that, this geometry was extruded (lengthwise) over a single helical pitch length. The model is considered to be symmetric about the tube axis. Thus, this helically extruded geometry will be repeated until the tube length of 2 m is achieved. The geometrical shape of the tube that was modeled and meshed is shown in **Figure 6**. Flux is applied on the top wall with the solid portion shown in red color.

Other boundary conditions include the input of the velocity inlet on one side of the tube and the pressure outlet on the other side. Periodic symmetry was applied to the

cyan-colored region shown in the **Figure 6**. It should be noted that this symmetry boundary condition is of the rotational type where the rotational axis lies on the z-axis.

### **5.1 Friction factor**

The friction factor is computed from CFD simulations. The results for different tubes are plotted in **Figure 7**. These results are for GT\_02, GT\_04, GT\_06, and GT\_08.

*Modeled tube geometry with the flux applied on the top of the wall.*

The numbers in the nomenclature indicate the pitch value in inches. These values indicate that GT\_02 has the highest value in terms of pitch length. It is also indicated that all the tubes have a higher friction factor than the smooth tube which is expected. The trend is also logical, observing a decrease in value as a function of the Reynolds number. The Reynolds number is computed based on the hydraulic diameter of the smooth tube. GT\_02 being the highest is also logical since the smallest pitch length tube should reveal a greater resistance to fluid motion and significant pressure drop.

### **5.2 The Nusselt number**

The Nusselt number is computed based on the formula mentioned in Eq. (1) above. The heat transfer coefficient is computed as

$$h\_{\text{avg}} = \frac{q^{\text{\textdegree}}}{T\_{\text{avg},w} - T\_{\text{avg},f}} \tag{4}$$

Where *Tavg*,*<sup>w</sup>* is the average wall temperature and *Tavg*,*<sup>f</sup>* is the bulk fluid temperature obtained by averaging the inlet and outlet temperatures. This havg is used in the formula of Nu. **Figure 8** shows the behavior of the Nu as a function of the Reynolds number and brings the GT\_02 again in the lead. The increasing trend is due to the same physics as followed for the friction factor. However, the high friction also increases turbulence which increases the heat transfer rate. Since the flux is constant, and as the Reynolds number gets increased, the Nusselt number increases much faster. A high Reynolds number makes the boundary layer thin. This has a rapid temperature change from Twall to Tbulk and thus the difference minimizes. This increases *havg* , and thence the Nu. This increasing trend will be much more pronounced for very high Reynolds numbers, but here it is not as such due to lower values of Reynolds numbers. These trends can be seen in the paper of Piotr Jasinski [17].

**Figure 8.** *Effect of Nusselt number as a function of Reynolds number on the performance of different groove tubes.*

*A Brief Review of Techniques of Thermal Enhancement in Tubes DOI: http://dx.doi.org/10.5772/intechopen.113134*

**Figure 9.** *Thermal enhancement factor for different tubes.*

### **5.3 The thermal enhancement factor**

As described above, the Thermal Enhancement Factor (TEF) or (η) is a very important parameter in checking the performance of the enhanced surfaces. This parameter is the ratio of the Nusselt number ratio to the friction factor ratio. Each ratio is the ratio of the enhanced surface/tube to the plain surface/tube. **Figure 9** shows the TEF of the tubes discussed above. This graph shows that the tube with 2 inch pitch is at the lead. This is also expected since both the Nusselt and the friction factor were above the mark in comparison with the other tubes and the smooth tube. Overall, it can be concluded that the tube performance can be easily examined through numerical simulations. TEF can also be predicted by first computing the Nusselt number and the friction factor. The complete performance matrix will be established by determining the Entropy Generation rate which will be discussed next.

### **5.4 Entropy generation minimization**

Bejan [18] coined the concept of entropy generation minimization. It is not that the idea did not exist earlier. It existed there, but the concept was that an engineering system (or a device) working on the first principle, i.e., the thermodynamic principles, their performance must be evaluated on these principles as well. Earlier, before the works of Adrian, the problem of heat transfer enhancement was evaluated on the principle of the first law of thermodynamics, i.e., the energy is conserved. The problem was not seen from the viewpoint of the second law of thermodynamics. In terms of entropy, the second law states that entropy never decreases and it keeps on increasing. If you notice the title of this paragraph, it is written as entropy generation minimization. It never said, entropy minimization. Therefore, the system (enhanced tube) is discussed based on the way to minimize the generation rate of entropy. After all, a system with losses generates more entropy so in a way we are decreasing the losses (or trying to minimize the losses) thus increasing the availability as mentioned by Bejan in his texts [19*,* 20].

In exchangers, that is our focus, there is a trade-off between heat transfer irreversibility and friction work irreversibility. This can be easily understood by

describing the ratio of entropy ratio of the augmented tube to the entropy generated due to the plain tube [17, 21]. In respect of the enhanced tube, the numerical works done by Jasinski [11], and Bharat Kumar et al. [21] are notable. Works related to entropy by Majeed [22] and Zheng et al. [23] are on the axial groove tube.

Adrian Bejan mentions that the entropy generation ratio can be used to establish a design point for an augmented tube. A curve can be plotted showing the entropy ratio (*SR* <sup>¼</sup> \_ *Sgen S*\_ *gen*,*o* Þ as a function of the Reynolds number. In this curve, there must be a point at which the irreversibilities due to the friction of the fluid and the irreversibilities due to heat intersect. Therefore, a generalized curve can be generated. The right side of the intersection point shows the friction effect domination and the left side shows the thermal effects domination (**Figure 10**).

For the study of helical grooved tubes that are mentioned above, the same analogy was applied and the curve for SR was plotted. The entropy ratio curve depicts the optimized point for a tube giving the whole picture at various Reynolds numbers. The ratio is a function Reynolds number that looks like a v-shaped curve. This curve has a minimum point that lies at SR = 1. This shows that this is the point where the heat transfer effect and frictional losses have become equal. This curve is, in fact, a combo of two curves as shown in **Figure 11**.

### *5.4.1 Entropy generation minimization-practical example*

After some years of the publication of the above work, a very similar work was published. The work of Bharat et al. [21] was on the same theme of entropy minimization in internally made helical finned tubes. His finding on the design optimization using entropy-based work resembles the research work of Jamshed et al. [16, 24], whereas their work on the multi-objective optimization of the thermal and pressurebased entropy generation is similar to the paper by Jamshed [25] on multidisciplinary optimization.

In the work of Bharat et al. [21], the entropy generation rate study was the entropy generation rate study was accompanied by the Pareto-optimal design technique. In

**Figure 10.** *Entropy generation ratio versus Reynolds number curve for a tube, Bejan [18].*

**Figure 11.** *Entropy ratio curve showing the effects of the pressure term and the temperature term.*

this technique, the height and pitch of the helical fin were chosen as design variables. The optimal solution (i.e. entropy rate minmization) is compared to the solution of multi-objective problem. This considers either minimization of pressure or the heat, but not both. However, the author also claimed that reducing pressure and heat transfer terms individually, may not be the right matrix to measure the performance of entropy. This is because entropy due to both terms is a strong function of the Reynolds number. Engineers can explore the optimal charts as per their design needs. In the study, Bharat et al. concluded that the entropy due to the pressure term is optimized at 25% of the heat transfer entropy generation. But this performance can be substantially different for other Reynolds numbers. This is shown in **Figure 12**.

Similar work was done using multi-disciplinary optimization of the grooved tubes by Jamshed et al. [25]. The Design of Experiments (DoE) technique was used with a D-optimal design taking the groove depth, helix angle, and the number of grooves as variables. The effect of the entropy generation rate was obtained at all of the design points. It was found that the tube with 1-inch of pitch length gave the maximum entropy. Now the optimum Reynolds number was computed, based on the same analogy described above, that the intersection of heat and pressure term will give the optimum Reynolds number. Thus, it was found to be 5000 for the 1-inch pitch tube as shown in **Figure 13**. A correlation was developed for the tube showing *SR = f(Re)*. This tube shows that the optimal point lies where *SR* = 1 and it lies at the optimum Re of 5000. The entropy ratio curve and the correlation are shown for the tube with Ns = 30, e = 0.5 mm, and pL = 25.4 mm (1-inch).

### **6. Nanofluids—a new avenue in the heat transfer enhancement domain**

Nanofluids are fluids with nanoparticles. As the name indicates, nanoparticles are very minute-sized particles of the order of 10�<sup>9</sup> m. Nanotechnology-based techniques

**Figure 12.** *Entropy generation rate minimization through Pareto-optimization, from Bharat et al. [21].*

#### **Figure 13.**

*The entropy ratio curve and the correlation shown for the tube with groove numbers = 30, groove depth = 0.5 mm, and pitch length = 25.4 mm (1-inch).*

could be used to produce these particles. These particles when added to a fluid of lower thermal conductivity, increase the heat transfer characteristics of the medium.

As mentioned by Mahmoud Salem [26], the nanofluid is a fluid in which nanosized particles are suspended in a base fluid. The solute thus forms a colloidal solution of particles in the base fluid. These particles are made up of metals, carbon nano-tubes, or oxides of metals. The base fluid is generally water, ethylene glycol, or oil. Research has been quite embryonic in understanding nano-particle physics thoroughly, but these particles have been found to possess great properties in enhancing heat transfer. Thus, these nanofluids have made a place in applications

like engines, domestic refrigerators, chillers, and even in flue gas temperaturereduction of a boiler.

### **6.1 Nanofluids for heat exchangers**

The thermal performance of a heat exchanger (HX) is greatly affected by several factors. As discussed above, the design or geometry is one of the factors that had been seen thoroughly. Fluid properties and the type of flow (turbulent or laminar) also affect the HX performance a lot. Since fluid properties have a major contribution in enhancing the performance of an HX, nanofluids second this thought. **Figure 14** shows the enhancement ways of thermal performance of an HX.

The effects of density, particle size, and concentration have been greatly discussed in a paper by Stephan et al. [27]. Nanoparticles, on the one hand, increase the heat transfer coefficient (HTC) but also increase the pressure drop. It was also found that the shape also matters in enhancing heat transfer such as the increase in thermal conductivity. Pressure drop is affected by the shape of the particles where it was found lower in the case of the spherically shaped particles. Stephan et al. studied the effect of TiO2 on the water and computed the result using mathematical modeling. It was found that all three properties, i.e., thermal conductivity, density, and viscosity were increased by 1.98, 2.61, and 2.03% respectively compared to the base fluid. With the constant flow rate, the heat transfer coefficient was also increased by 1.25% while the pressure drop was also increased by 2.03%.

The effect of flow rate with a constant concentration of 0.4% was also observed. In the variable flow rate, condition it was found that the HTC increased by 17.20%, and the pressure drop was found to be increased by 60%. This means that increasing the flow rate increases the heat transfer by a large magnitude but also increases the pressure drop. Thus, pumping power is increased. However, changing concentration, does not increase the HTC a lot, but can affect the overall performance of the heat exchangers since they need to run for longer durations. A small percentage amount can give larger volumes of benefits at a later time.

Stephan concluded and recommended that nanoparticles of high conductivity and small size may be selected. However, the concentration of the particles must be adjusted with the volumetric flow rate to elude huge pressure drops.

Thong Le Ba et al. [28] conducted a study of nanofluids in a circular tube. They have used CFD for the analysis of particles. The effect of SiO2-P25 particles in the solvent water/ethylene glycol was observed in a circular tube. Volume concentrations were 0.5, 1.0, and 1.5%. The Reynolds number in the flow was from 5000 to 17 k.

**Figure 14.** *Influencing factors on the thermal performance of heat exchanger, from [26].*

While the heat flux was 7955 W/m<sup>2</sup> . A constant heat flux condition was maintained. In the other case, a constant wall-temperature of 340.15 K was separately provided on the walls of the tube and results were obtained. The turbulent flow in the tube was monitored and it was concluded that constant heat flux gave similar results as that of a temperature-dependent case with lower cost. Nusselt number and pressure drop were increased with the increasing concentration and the flow rate of the nanofluid. This was also in good agreement with the experimental results.

With this literature, it can be concluded that nanofluids are an effective means of heat transfer enhancement. Proper effectiveness will be achieved through skills and dexterity in achieving the right proportions of concentration amount of the particles, their conductivity, and density, and this can be easily pre-analyzed through simulations. As the nanofluids technology is expensive, it is also difficult to conduct repeated experiments to see the effect of concentration, density, or thermal conductivity.

### **7. Conclusion**

Passive techniques mostly increase the surface area at the expense of the pumping power (which increases due to friction of the increased surface area). Thus, common passive techniques include grooves inside the tube surface, grooves on both the inner and outer surface, or putting inserts within the tube. First, in this chapter, mainly, the passive technique, such as groove, to enhance heat transfer is seen through a numerical study. CFD technique has been employed for validation of the friction factor results and the Nusselt number from published literature. The results were quite in good agreement with the experimental data. Secondly, the entropy generation rate minimization is also seen in these tubes which is a less-seen avenue of computing heat transfer enhancement in groove tube(s). It has been observed that a cut-off value of the pressure loss and the heat gain due to entropy describes the optimum point of the performance. Hence the optimum Reynolds number is defined. And lastly, a bird'seye view of the nanofluids and their usage for heat transfer enhancement has been seen since modern techniques (for heat transfer increase) are utilizing nanofluids, that carry nano-materials inside the heat transfer fluid to enhance heat transfer. To quantitatively gauge the heat transfer enhancement, the heat transfer effectiveness is computed in all the cases.

### **Author details**

Shamoon Jamshed Institute of Space Technology, Karachi Campus, Karachi, Pakistan

\*Address all correspondence to: shamoonjamshed@gmail.com

© 2023 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Section 2
