2. History and basics of offset strip fin

Offset strip fin is one of the most preferred fin geometry in compact heat exchangers, which has a rectangular cross section cut into small strips of length, l and displaced by about 50% of the fin pitch in the transverse direction. The scheme of a typical strip fin is presented in Figure 1. The most significant variables of fin geometry are the fin thickness and strip length in the flow direction that leads to higher heat transfer coefficient and higher friction factors than plain fin geometries. The main reason of this improvement relies on developing laminar boundary layers (Figure 2). The enhancement is provided by the interruption of the flow

Figure 1. Offset strip fin schematic representation [2].

Comprehensive Study of Compact Heat Exchangers with Offset Strip Fin http://dx.doi.org/10.5772/66749 33

Figure 2. Flow patterns observed in the visualization experiments [3].

studies about the compact heat exchangers is to produce more efficient ones by reducing the physical sizes of the equipment for a given duty, which leads to use less coolant as well. There is not much possibility in order to get this goal, but one of these options is to have a higher heat transfer rate for particular conditions and the other one is to create a higher surface area and the last one is increasing both. The typical way to increase heat transfer surface area is using fins on the heat exchangers, which provide a higher surface area per unit volume ratio. The researchers endeavor to develop more efficient heat exchangers but small passage dimensions, nonuniformities and geometrical changes make it hard to characterize the heat transfer surface. The applications of the compact heat exchangers can be widely found in industry such as

In this particular chapter, it is aimed to inform and address the offset strip fins, which have been studied by the researchers in detail for decades and still getting the attention due to its superior advantages. In the following sections, the history and fundamentals of this structure will be given first and in the following parts, the investigations will be summarized by considering their objectives, which are handled in the communications such as parametric effect of the structure, experimental and numerical research of the fin under varying flow regimes and conditions and the evolution of heat transfer and friction factors under different flow conditions by the change of the regime. The chapter will be concluded with the remarks

Offset strip fin is one of the most preferred fin geometry in compact heat exchangers, which has a rectangular cross section cut into small strips of length, l and displaced by about 50% of the fin pitch in the transverse direction. The scheme of a typical strip fin is presented in Figure 1. The most significant variables of fin geometry are the fin thickness and strip length in the flow direction that leads to higher heat transfer coefficient and higher friction factors than plain fin geometries. The main reason of this improvement relies on developing laminar boundary layers (Figure 2). The enhancement is provided by the interruption of the flow

air conditioning, refrigeration, automotive and aerospace.

32 Heat Exchangers– Advanced Features and Applications

that will outline the findings and will guide to the future studies.

2. History and basics of offset strip fin

Figure 1. Offset strip fin schematic representation [2].

periodically, which does not only create fresh boundary layers but also generate greater viscous pressure drop due to higher friction factor (Figure 2).

The surface geometry in the given representation is described as follows: the fin length is l, height is h, transverse spacing is s and thickness is t. Even though nonuniform spacing is applicable and possible, generally the fin offset is the half-fin spacing and uniform. Furthermore, there are some other parameters that have influence on the flow and heat transfer like manufacturing irregularities (such as burred edges, bonding imperfections, etc.) [4].

Even though offset strip fins have been studied for decades by numerous researchers, Kays and London [5] and London and Shah [6] could be easily called as the pioneers of the offset strip fin researches by their valuable reports of their experiments about offset strip fins. The roots of their investigations rely on a test program at Stanford University in 1947 [5]. Since then, they have published their outcomes in several reports and papers, which still keep their importance to enlighten the path of researchers working in this field. In their study, they have examined several types of fins with regard to their varying parameters and operating conditions in order to explain and uncover blurry parts of the compact heat exchangers. In one of their very valuable publications [6], they shared their outcomes on the offset strip fins. The schematic representation of the fin structure is presented in Figure 3.

In that particular study, they have examined eight different fins, which differ from each by their fin numbers per inch, type of flow section, fin height, distance between plates, flow length, fin thickness and the material used in the study. Due to diverse fin type used in their studies, Kays and London [5] and London and Shah [6] have developed a coding method (explanation of the code is given in Table 1) in order to differentiate the fins from each other. An example of that coding might be given as in the following,

$$\begin{array}{ccccccccc} \text{25.01.R(S)} - 0.201/0.200 - 1/9(\text{O}) - 0.004(\text{A1}) \\ \text{1} \quad \text{2} \quad \text{3} \quad \text{4} \quad \text{5} & \text{6} \quad \text{7} & \text{8} & \text{9} \\ \end{array}$$

The numbers given underneath the code stands for, number of fins per inch, type of fin flow cross section (R= rectangular, T = triangular, U =U shape), fin sandwich construction

Figure 3. General features of the fin core material [6].


Table 1. Explanation of codes.

(SD=single-double, S=single, D=double, T= triple), fin height before brazing, fin height after brazing, uninterrupted fin length, type of surface (L=louvered, O=offset, P=plain, S =strip), fin metal thickness, fin material (Al=aluminium, SS=stainless steel, Ni=nickel, etc.) respectively. Since their experiments are the basics of the OSF heat exchanger researches, it would be better to understand their terminology to distinct the varying geometries and structures in their investigations.

## 3. Data reduction of offset strip fins

The aim of the thermohydraulic analysis of the offset strip fins is to determine the pressure drop data and overall heat transfer coefficients of the structure. The pressure drop could be directly obtained from experiments, while the heat transfer rate could be found from experimental measurements by applying energy balance equations on either hot or cold streams. The typical equations used in data reduction could be derived as in the following.

In order to determine the heat transfer rate, the effectiveness-NTU method is used, which would be the ultimate purpose of the analysis.

The average heat transfer rate can be calculated by using Eq. (1)

$$
\dot{Q} = (\dot{Q}\_c + \dot{Q}\_h)/2 \tag{1}
$$

where Q\_ <sup>c</sup> and Q\_ <sup>h</sup> are the heat transfer rates of cold and hot stream, respectively. The heat transfer rates of each fluid can be calculated with Eq. (2) and Eq. (3)

$$
\dot{Q}\_c = \dot{m}\_c c\_{p,c} (T\_{c,o} - T\_{c,i}) \tag{2}
$$

$$
\dot{Q}\_h = \dot{m}\_h \mathcal{c}\_{p,h} (T\_{h,i} - T\_{h,o}) \tag{3}
$$

The effectiveness for both unmixed fluid,

$$\varepsilon = 1 - \exp\left[\frac{NT\mathcal{U}^{0.22}}{\mathcal{C}\_r} \{\exp(-\mathcal{C}\_r NT\mathcal{U}^{0.78}) - 1\}\right] \tag{4}$$

where

$$
\varepsilon = \dot{\mathbb{Q}} / \dot{\mathbb{Q}}\_{\text{max}} \tag{5}
$$

$$\mathbf{C}\_{\mathbf{r}} = \frac{(\dot{m}c\_p)\_{\text{min}}}{(\dot{m}c\_p)\_{\text{max}}} \tag{6}$$

With regard to these, the overall heat transfer coefficient (UA) can be obtained for the heat exchanger as,

$$
\mathcal{U}A = (\dot{m}c\_p)\_{\text{min}} \text{NTU} \tag{7}
$$

where

(SD=single-double, S=single, D=double, T= triple), fin height before brazing, fin height after brazing, uninterrupted fin length, type of surface (L=louvered, O=offset, P=plain, S =strip), fin metal thickness, fin material (Al=aluminium, SS=stainless steel, Ni=nickel, etc.) respectively. Since their experiments are the basics of the OSF heat exchanger researches, it would be better to understand their terminology to distinct the varying geometries and

The aim of the thermohydraulic analysis of the offset strip fins is to determine the pressure drop data and overall heat transfer coefficients of the structure. The pressure drop could be directly obtained from experiments, while the heat transfer rate could be found from experimental measurements by applying energy balance equations on either hot or cold streams. The

typical equations used in data reduction could be derived as in the following.

structures in their investigations.

Table 1. Explanation of codes.

3. Data reduction of offset strip fins

No Explanation of the code Number of fins per inch Type of fin flow cross section Fin sandwich construction Fin height before brazing (inch) Fin height after brazing (inch) Uninterrupted fin length (inch)

Figure 3. General features of the fin core material [6].

34 Heat Exchangers– Advanced Features and Applications

7 Type of surface

9 Fin material

8 Fin metal thickness (inch)

$$
\Delta UA = \dot{\mathbf{Q}} / \Delta T\_m \tag{8}
$$

ΔTm is the logarithmic mean temperature difference, which can be defined as,

$$
\Delta T\_m = \frac{(T\_{h,i} - T\_{c,o}) - (T\_{h,o} - T\_{c,i})}{\ln \left( (T\_{h,i} - T\_{c,o}) / (T\_{h,o} - T\_{c,i}) \right)} \tag{9}
$$

The heat transfer coefficient (hc) for the cold stream can be written as in the following,

$$\frac{1}{\eta\_c A\_t h\_c} = \frac{1}{\text{U}A} - \frac{\delta\_t}{k\_t A\_t} - \frac{1}{A\_h h\_h} \tag{10}$$

In this equation, hh is the heat transfer coefficient of the hot stream. One of the other parameters in the given equation is the surface effectiveness (ηc) for a dry surface,

$$\eta\_c = 1 - \frac{A\_f}{A\_c} (1 - \eta\_f) \tag{11}$$

where η<sup>f</sup> is,

$$\eta\_f = \frac{\tanh(ml)}{ml} \tag{12}$$

where

$$m = \sqrt{h\_c P\_f / k A\_{c,f}} \tag{13}$$

The flow regime is the crucial parameter of the thermohydraulic analysis of the heat exchanger studies since it has a big impact on the performance of the fin structure. Even though Reynolds number has a unique definition, it may be interpreted by the researchers from various aspects and could be written in different ways with regard to defined hydraulic diameter,

$$Re = \frac{\mu \ D\_e}{\upsilon} \tag{14}$$

where hydraulic diameter De is,

$$D\_e = \frac{2sh}{s+h} \tag{15}$$

As noted before, the major difference between the Re number relies on the definition of the hydraulic diameter and in order to provide a better look, some of the reported diameters and the corresponding Re numbers will be summarized in the following Table 2.


Table 2. Hydraulic diameter described in offset strip fin investigations from literature.

#### 3.1. Heat transfer and pressure drop characteristics of offset strip fins

Like all other systems and devices, there are some nondimensional factors to evaluate the performance of the offset strip fins. The most common parameters used to decide the benefits of the structure are Colburn j-factor and friction factor (f), which corresponds to the heat transfer and pressure drop, respectively. These two parameters could be defined as in the following,

η<sup>c</sup> ¼ 1−

m ¼

and could be written in different ways with regard to defined hydraulic diameter,

the corresponding Re numbers will be summarized in the following Table 2.

3.1. Heat transfer and pressure drop characteristics of offset strip fins

Table 2. Hydraulic diameter described in offset strip fin investigations from literature.

q

where η<sup>f</sup> is,

where hydraulic diameter De is,

36 Heat Exchangers– Advanced Features and Applications

[4] De <sup>¼</sup> <sup>2</sup> • <sup>ð</sup>s−tÞ<sup>h</sup>

[7] De <sup>¼</sup> <sup>2</sup> • <sup>ð</sup>Hf <sup>−</sup>tf ÞðPf <sup>−</sup>tf <sup>Þ</sup>

[8] De <sup>¼</sup> <sup>4</sup> • <sup>s</sup> • hf • <sup>l</sup>

[9] De <sup>¼</sup> <sup>2</sup> • <sup>w</sup> • <sup>L</sup>ðFp <sup>−</sup>t<sup>Þ</sup>

[10] De <sup>¼</sup> <sup>4</sup> • <sup>s</sup> • <sup>h</sup> • <sup>l</sup>

[11] De <sup>¼</sup> <sup>2</sup> • <sup>ð</sup>s−bÞ<sup>l</sup>

where

Af Ac

<sup>η</sup><sup>f</sup> <sup>¼</sup> tanhðml<sup>Þ</sup>

The flow regime is the crucial parameter of the thermohydraulic analysis of the heat exchanger studies since it has a big impact on the performance of the fin structure. Even though Reynolds number has a unique definition, it may be interpreted by the researchers from various aspects

Re <sup>¼</sup> u De

De <sup>¼</sup> <sup>2</sup>sh

As noted before, the major difference between the Re number relies on the definition of the hydraulic diameter and in order to provide a better look, some of the reported diameters and

Reference Hydraulic diameter Reynolds number

2 • ðs • lþhf • lþhf • tÞþs • t

w • ðLþtÞþL•ðFp −tÞ

Like all other systems and devices, there are some nondimensional factors to evaluate the performance of the offset strip fins. The most common parameters used to decide the benefits of the structure are Colburn j-factor and friction factor (f), which corresponds to the heat

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi hcPf =kAc,<sup>f</sup>

ð1−ηfÞ (11)

ml (12)

<sup>υ</sup> (14)

<sup>s</sup> <sup>þ</sup> <sup>h</sup> (15)

<sup>ð</sup>sþtÞþht=<sup>l</sup> Re <sup>¼</sup> <sup>ρ</sup>vDe

<sup>ð</sup>Hf <sup>−</sup>tf ÞþðPf <sup>−</sup>tf <sup>Þ</sup> Re <sup>¼</sup> u De

<sup>2</sup> • <sup>ð</sup><sup>s</sup> • <sup>l</sup>þ<sup>h</sup> • <sup>l</sup>þ<sup>h</sup> • <sup>t</sup>Þþ<sup>s</sup> • <sup>t</sup> ReDe <sup>¼</sup> <sup>ρ</sup>uDe

<sup>ð</sup>lþb<sup>Þ</sup> Re <sup>¼</sup> <sup>u</sup> cDe

(13)

μ

υ

μ

υ

$$j = StPr^{2/3} \tag{16}$$

$$f = \left(\frac{A\_c}{A}\right) \left(\frac{2\Delta P}{\rho u^2} - k\_c - k\_e\right) \tag{17}$$

where Ac is the minimum free flow area for the external side and kc and ke are the coefficients of pressure loss at the inlet and the outlet of the heat exchanger. In addition to this, the Stanton number and the Prandtl number, which are used to define the Colburn j-factor, are,

$$St = \frac{h\_c}{\rho u c\_p} \tag{18}$$

$$Pr = \frac{\mu c\_p}{\lambda} \tag{19}$$

where hc is heat transfer coefficient, ρ is density, u velocity of the fluid, cp specific heat of the fluid, µ dynamic viscosity and λ thermal conductivity. Since these two parameters are commonly preferred by the researchers in order to observe the performance of the offset strip fins, the results received at the studies with regard to these two parameters will be summarized in the coming sections where the published papers will be addressed.

One of the first friction factor and Colburn factor investigations was performed by London and Shah [6] as they were the leading investigators in this field. In the study, the effect of blockages either in steam side (the side where the steam is introduced) or in the air side (the side where the air flows across the offset fin) is underlined. The reason for the first one is explained as the poor brazing, which tends to condensation and bridge flow passage, whereas the latter one is because of bent fin edges and results in lower Colburn j-factor and higher friction factor, f. Furthermore, the effect of nondimensional parameters on j and f for different cores (different fin structures with different fin numbers) is highlighted as well. It is worth to note that, with regard to their findings when the aspect ratio gets lower, the friction factor and heat transfer are affected less and while the number of fins per unit size gets higher, they are affected more. In addition, offset spacing length is illustrated in Figure 4. The importance of the effect is emphasized in Figure 4, where increasing the fin spacing lowers the friction factor and heat transfer and vice versa and lowering the spacing makes the performance of the fin structure higher.

In addition to these most common performance criterions, new approaches are also suggested by the researchers. Bhowmik and Lee [7] adopted the j/f, j/f 1/3 and JF in order to examine the performance of the offset strip fins instead of conventional methods. j/f is known as "area goodness factor" [7] and j/f 1/3 is known as "volume goodness factor" [7]. JF number, which is related with the volume goodness factor, can be obtained by the following equation [7].

$$JF = \frac{j/j\_R}{\left(f/f\_R\right)^{1/3}}\tag{20}$$

where jR and fR are the reference values of Colburn j-factor and friction factor, respectively.

Figure 4. Offset spacing length vs. Reynolds number comparisons for varying surfaces [6].

The analyses are performed by a commercial computerized fluid dynamics (CFD) software in three dimensions. Thermohydraulic performance is studied as well for laminar, transition and turbulent flow regions, which lead to a general correlation that fits to all three regions. Since varying fluids are investigated as well, a Nu correlation including the Prandtl effect is also presented. Firstly, the numerical computations are validated by Manglik and Bergles [4] and Joshi and Webb [3] correlations and seen how they have a good agreement with them and due to their continuity, the results are claimed as a good candidate for a single correlation that covers all three flow regions.

Unlike the earlier reports, the performance of the offset strip fins are examined by flow area goodness factor j/f, the ratio j/f 1/3 and thermohydraulic performance factor JF. In these performance characteristics, a high j/f factor provides a low frontal area for the heat exchangers. When the JF factor is high, it refers to a good thermohydraulic performance and finally, high j/f 1/3 factor leads to a good heat transfer and pressure loss performance.

The effect of these three factors is observed for five Prandtl numbers (Pr =0.7, 7, 16, 33 and 50), which will enable to decide which are the right working fluid conditions as shown in Figure 5. The Pr effect is more significant for j/f factor at the turbulent region; j/f 1/3 factor increases when

Figure 5. Evolution of performance factors [7].

The analyses are performed by a commercial computerized fluid dynamics (CFD) software in three dimensions. Thermohydraulic performance is studied as well for laminar, transition and turbulent flow regions, which lead to a general correlation that fits to all three regions. Since varying fluids are investigated as well, a Nu correlation including the Prandtl effect is also presented. Firstly, the numerical computations are validated by Manglik and Bergles [4] and Joshi and Webb [3] correlations and seen how they have a good agreement with them and due to their continuity, the results are claimed as a good candidate for a single correlation that

Unlike the earlier reports, the performance of the offset strip fins are examined by flow area

performance characteristics, a high j/f factor provides a low frontal area for the heat exchangers. When the JF factor is high, it refers to a good thermohydraulic performance

The effect of these three factors is observed for five Prandtl numbers (Pr =0.7, 7, 16, 33 and 50), which will enable to decide which are the right working fluid conditions as shown in Figure 5.

The Pr effect is more significant for j/f factor at the turbulent region; j/f

Figure 4. Offset spacing length vs. Reynolds number comparisons for varying surfaces [6].

1/3 factor leads to a good heat transfer and pressure loss performance.

1/3 and thermohydraulic performance factor JF. In these

1/3 factor increases when

covers all three flow regions.

and finally, high j/f

goodness factor j/f, the ratio j/f

38 Heat Exchangers– Advanced Features and Applications

the Pr ascends on the other side; unlike the other two factors, Pr does not have a distinctive effect on JF. According to these, it is underlined that JF factor could be useful for the water, while j/f 1/3 is more convenient for gas-oil liquid. In contrary to the given two factors, j/f could not be considered as a good performance criterion for fluids.

Moreover, these performance criteria are employed to provide a better comparison between seven common configurations namely plain, perforated, offset strip, louvered, wavy, vortexgenerator and pin of plate-fin heat exchangers by Khoshvaght-Aliabadia et al. [8]. Water is used as the working fluid in Reynolds number range between 480 and 3770. The other purpose is to select an optimum plate-fin channel in which the best performance criteria evolution is observed. The significant enhancement is observed at the vortex-generator channel in the heat transfer coefficient and a proper reduction in the heat exchanger surface area (Figure 6). Moreover, the wavy channel displays an optimal performance at low Reynolds numbers, according to the referred criteria's. The offset strip fins, f factor, ascends by the increasing Re number as predicted but it is noted that the critical value for Re is 1800 and beyond that the friction factor rises 11.7%. As for the j/f 1/3, the offset strip fins got the highest values when the Re >1500, while wavy has the highest for the low Re range. Furthermore, it is observed that the JF factor curves show the larger increment by ascending Re number for offset strip and vortex generators.

Figure 6. j/f 1/3 ratio vs. Re for different plate channels [8].

A different performance evaluation aspect is employed to the OSF heat exchangers by considering second law of thermodynamics [9]. A new parameter that is called as relative entropy generation distribution factor is proposed by the researchers. This new parameter represents a ratio of relative changes of entropy generation. The effect of parameters, which are commonly used nondimensional parameters for the OSF studies, is discussed. Optimization for the investigated parameters is carried out, which could provide sufficient information about the conditions that could maximize the performance. The proposed performance evaluation parameter bases on the entropy generation number (Ns1) and can be written as in the following,

$$\psi^\* = \frac{(\mathcal{N}\_{s1,o,\varDelta T} - \mathcal{N}\_{s1,o,\varDelta T}) / \mathcal{N}\_{s1,o,\varDelta T}}{(\mathcal{N}\_{s1,o,\varDelta P} - \mathcal{N}\_{s1,o,\varDelta P}) / \mathcal{N}\_{s1,o,\varDelta P}} = \frac{1 - \mathcal{N}\_{s1,\varDelta T}^\*}{\mathcal{N}\_{s1,\varDelta P}^\* - 1}. \tag{21}$$

where 'a' and 'o' refer to the augmented (OSF) and reference (plain plate-fin) channel, respectively and 'ΔT' and 'ΔP' stand for entropy generation due to the temperature difference and pressure drop, respectively.

The given performance is examined for different geometrical parameters in order to estimate the effective ones, by considering varying relative temperature difference. According to the obtained data, smaller thickness at lower flow rates gives better results.
