**4. Type-2: two direct contact with one non-contact fluids (TDCONF) exchanger**

Section 1, discussed about the DCHME that widely used in air conditioning industry, has categorized the exchangers into two groups. Mathematical model of the first type TFDC heat exchanger has been discussed in Section 3. The development of mathematical model for the second type of TDCONF exchanger will be discussed in detail in this section. The examples of TDCONF exchangers are the wet region of plate finned tube heat exchanger for the direct expansion (DX) evaporator coil, cooling coil unit working with chilled water or non-volatile refrigerant,

*Direct Contact Heat and Mass Exchanger for Heating, Cooling, Humidification… DOI: http://dx.doi.org/10.5772/intechopen.102353*

indirect evaporative cooler, and M-cycle dew point evaporative cooler, which are shown in **Figure 3**.

A discretized volume with distributed lump parameters model of TDCONF, shown in **Figure 8**, has three fluids, non-contact fluid, contact fluid, and wetted wick layer or thin water film. The product air of indirect evaporative cooler and volatile refrigerant or chilled water of the wetted plate finned tube cooling coil are the examples of non-contact fluid. These fluids are separated by the separator sheet or tube from thin water film and contact fluid air to prevent the transferring of mass and only to allow the transferring of heat between non-contact fluid and thin water film. Thermal resistance due to the conduction of separator sheet or metal tube is *Rmw*, and due to the convective heat transfer in the non-contact fluid is *Rl*. But, both heat and mass are transferring between the thin water film and contact fluid air. Heat and mass transfer circuit between from the symmetrical line of contact fluid air to the non-contact fluid with the coefficient of mass transfer, *KM*, and thermal resistances are shown in **Figure 8(c)**. Each discretized volume of all TDCONF exchanger is composed with three node points locating in line on the four layers of materials. The first node point, *Lavgj* is at the symmetrical line of noncontact fluid, *sj* is at the surface of saturated water film, and *aavgj* is at the symmetrical line of direct contact fluid air. This model assumed that the temperature difference between outer surface of separator sheet or copper tube and saturated surface of water film is negligible. TDCONF exchanger can be divided into three types of different numerical models: (1) Type-2.1.1 extended surface TDCONF exchanger working with non-volatile working fluid, (2) Type-2.1.2 extended surface TDCONF exchanger working with volatile refrigerant, and (3) Type-2.2 non-extended surface TDCONF exchangers, shown in **Figure 4**.

## **4.1 Type-2.1: Extended surface TDCONF exchanger**

In air conditioning process, plate finned tube heat exchange are widely used for cooling and dehumidification process in fan coil unit (FCU) and air handling unit (AHU). If there is no condensation on the outer surface of finned tube heat exchanger, it is a normal heat exchanger and can be calculated by using conventional heat exchanger equation, UA-LMTD or NTU-effectiveness method.

#### **Figure 8.**

*A discretized volume with distributed lump parameters model of a typical (a) indirect evaporative cooler, (b) wetted region of plate finned tube cooling coil, and (c) node numbering of non-contact fluid (product air, volatile refrigerant, and chilled water), water saturated surface layer, separator (sheet or tube), and contact fluid (air).*

However, if the surface temperature of heat exchanger is lower than the dew point temperature of the direct contact fluid air, the condensation process will be taken place and not only heat but also mass will be transferred between the air flow and the water condensate film. Hence, wet region of cooling heat exchanger can be assumed as a direct contact heat and mass exchanger.

#### **4.2 Fin efficiency of extended surface TDCONF heat exchanger**

In plate finned tube heat exchanger, fin efficiency is one of the critical parameters for the development of exchanger model, and that can be calculated from the physical dimensions of the heat exchanger. Equations (26)–(33) are the equations to calculate the physical parameters of heat exchanger; number of fins *Nf* [�], coil face or frontal area *Aa* [m2 ], external exposed prime surface area *Ap* [m2 ], external secondary surface area *As* [m2 ], internal surface area *Ai* [m2 ], total external surface area *Ao* [m2 ], the ratio of external to internal surface area Br [�], and coil core surface parameters *Fs* [�] from its dimensions, width *LW* [m], height *LH* [m], depth *LD* [m], fin gap *f <sup>g</sup>* [m], fin thickness *ft* [m], outside *do* [m], inside diameter *di* [m] of tube, longitudinal tube spacing *SL* [m], and transverse tube spacing *ST* [m]. This equations are based on heat exchanger with the continuous plate fin and tubes in stagger arrangement. For the other type of heat exchanger, their related equations are stated comprehensively in AHRI standard 410 [27], and that can be applied in the fin efficiency calculation.

$$N\_f = \frac{L\_W}{f\_g} \tag{26}$$

$$A\_d = \frac{L\_H L\_W}{1000000} \tag{27}$$

$$A\_t = N\_f \left[ \frac{L\_H L\_D}{500000} - \frac{d\_o^2 N\_t}{636688} \right] \tag{28}$$

$$A\_p = \frac{d\_o L\_W N\_t - d\_o t\_f N\_t N\_f}{\text{318344}} \tag{29}$$

$$A\_i = \frac{d\_i N\_t L\_W}{\text{318344}}\tag{30}$$

$$A\_o = A\_s + A\_p \tag{31}$$

$$Br = \frac{A\_i}{A\_o} \tag{32}$$

$$F\_s = \frac{A\_o}{A\_f N\_r} \tag{33}$$

Fins can increase heat transfer from a prime surface of heat exchanger. Fin efficiency can be define with the ratio of the actual heat transferred from the fin to the heat that would be transferred if the entire fin were at its root or base temperature [20]. Fin efficiency equation can be written as follows:

$$\mathcal{D}\_f = \frac{\int a\_a (T\_f - T\_a) dA}{\int a\_a (T\_{fr} - T\_a) dA} \tag{34}$$

where ∅*<sup>f</sup>* is the fin efficiency, *Ta* is the temperature of the surrounding environment, and *Tfr* is the temperature at the fin root. *T <sup>f</sup>* is the temperature along the *Direct Contact Heat and Mass Exchanger for Heating, Cooling, Humidification… DOI: http://dx.doi.org/10.5772/intechopen.102353*

fin. Fin efficiency decreases as the heat transfer coefficient increases because of the increased heat flow. Total heat transfer from a finned tube heat exchanger is sum of heat transfer from finned surface or secondary area *As* and un-finned or prime area *Ap*. It can write in equation as follows:

$$Q = \left(a\_p A\_p + \mathcal{Q}\_f a\_s A\_s\right) \left(T\_{fr} - T\_a\right) \tag{35}$$

Assuming the heat transfer coefficients for the finned surface *α<sup>s</sup>* and prime surface *α<sup>p</sup>* are equal and note as *α<sup>a</sup>* air side heat transfer coefficient, Eq. (35) can be rearranged as follows:

$$\mathfrak{Q}\_{\mathfrak{s}} = \left( \mathbf{1} - \left( \mathbf{1} - \mathfrak{Q}\_{f} \right) \frac{A\_{\mathfrak{s}}}{A\_{\mathfrak{o}}} \right) = \frac{A\_{\mathfrak{p}} + \mathfrak{Q}\_{f} A\_{\mathfrak{s}}}{A\_{\mathfrak{o}}} \tag{36}$$

where *Ao* is total surface area of (*As* þ *Ap*). ∅*<sup>s</sup>* is fin effectiveness. Schmidt [28] presents empirical equation of fin surface efficiency for circular, rectangular, and hexagonal fins using an equivalent circular fin radius.

$$\mathcal{D}\_f = \frac{\tanh\left(m\_p r\_o \rho\right)}{m\_p r\_o \rho} \tag{37}$$

$$m\_p = \sqrt{\frac{2\,a\_d}{k\_a t\_f}}\tag{38}$$

$$\boldsymbol{\rho} = \left[ \left( \frac{r\_{\epsilon}}{r\_{o}} \right) - \mathbf{1} \right] \left[ \mathbf{1} + \mathbf{0}.35 \ln \left( \frac{r\_{\epsilon}}{r\_{o}} \right) \right] \tag{39}$$

where *ro* is the outside tube radius, *re* is the equivalent circular fin radius, *mp* is the standard extended surface parameter, *φ* is dimensionless thermal resistance. *α<sup>a</sup>* is convective heat transfer coefficient of air. *ka* is the thermal conductivity of the fin and *tfin* is the fin thickness. Plate finned tube heat exchanger for stagger tube array can be considered as the integration of hexagonal fins. For hexagonal fins:

#### **Figure 9.**

*Staggering arrangement of tube in plate finned tube heat exchanger (a) a half of transverse distance is lesser than longitudinal distance and (b) longitudinal distance is lesser than half of transverse distance.*

$$\frac{r\_\epsilon}{r\_0} = 1.27 \text{ } \mu \sqrt{\beta - 0.3} \tag{40}$$

where *Ψ* and *β* are defined as; *ψ* ¼ *B=ro* and *β* ¼ *H=B*, *β* must be greater than 1. Depending on the *ST* (the transverse vertical tube spacing) and *SL* (the longitudinal horizontal tube spacing), shown in **Figure 9**, *B* and *H* can be defined as follows: If *SL* > *ST*/2, then *B* = *ST*/2. If *SL* < *ST*/2, then *B* = *SL*.

$$H = \frac{1}{2}\sqrt{\left(\frac{\mathbf{S}\_T}{2}\right)^2 + \mathbf{S}\_L}^2\tag{41}$$

However, Schmidt's empirical equation of fin surface efficiency is limited to the situations of where *β* > 1.

When calculating the overall area of Type-2.1 extended surface TDCONF exchanger, the fin effectiveness term, ∅*s*, can used to simplify the thermal resistance equation of heat and mass transfer from air to working fluid.

### **4.3 Type-2.1.1 extended surface TDCONF exchanger operating with non-volatile working fluid**

Type-2.1.1 extended surface TDCONF exchanger is widely used as a cooling coil of air conditioning unit that operating with non-volatile working fluid such as chilled water or ethylene/propylene glycol. The air entering to the first part of the cooling coil is start decreasing its temperature but without moisture removing, this is called sensible heat removing part or dry coil region. When the air temperature is decreasing and reaching the dew point temperature of the entering air, moisture in the air stream start condensing on the surface of the coil called sensible and latent heat removing part or wet coil region.

#### *4.3.1 Resistance of heat and mass transfer and dry-wet boundary region*

Depending upon the dew point temperature of inlet air and working fluid temperature, the surface of the cooling coil can be fully dry, fully wet, or partially wet. The driving force for heat transfer in dry region is the temperature difference between air temperature *Ta* and working fluid temperature *Tl*, crossing the thermal resistance *Rad*, *Rmd*, and *Rl*. In the wet region, there are two types of heat and mass transfer processes synergy in series from the air to the working fluid. The first process is the exchange of heat and mass between the air and the saturated surface of water condensate layer due to their potential difference between *ha* and *hs*. The second process is transferring heat alone from the surface to the working fluid, and their driving force is the temperature difference between *Ts* and *Tl*. **Figure 10** shows a typical plate finned tube heat exchanger with counter flow process and thermal diagram of dry and wet region with their potential difference and resistances.

The capacity of the sensible heat *QD* that transferring in the dry region can be calculated by using the following equation:

$$Q\_{Td} = U\_D A\_{oD} \Delta T\_m = \frac{A\_{oD} \Delta T\_m}{R\_{TD}} \tag{42}$$

where *AoD* [m2 ] is total surface area of dry region, *RTD* [m<sup>2</sup> .K/W] is total thermal resistance of dry region, and Δ*Tm* is log mean temperature difference between air dry bulb temperature and working fluid temperature. In wet region, total heat

*Direct Contact Heat and Mass Exchanger for Heating, Cooling, Humidification… DOI: http://dx.doi.org/10.5772/intechopen.102353*

#### **Figure 10.**

*(a) A typical single circuit with four rows deep coil plate finned tube heat exchanger with counter flow arrangement between air and working fluid, (b) photo record of dry and wet region, and (c) thermal diagram of dry and wet region of extended surface TDCONF exchanger and their potential difference of heat and mass transfer process.*

capacity, *QW*, sensible heat and latent heat, transferred from air to saturated surface of condensate water can be calculated by using the following equation:

$$Q\_{Tw} = U\_W A\_{oW} \Delta h\_m = \frac{A\_{oW} \Delta h\_m}{\text{C} p\_m \, R\_{aW}} \tag{43}$$

where *AoW* [m2 ] is total surface area of wet region, *RaW* [m<sup>2</sup> .K/W] is thermal resistance of air side in wet region, and Δ*hm* is log mean enthalpy difference between air and saturated wetted surface layer. For the calculation of heat transfer from air to working fluid, total overall thermal resistance of finned tube heat exchanger is required to calculate from the heat exchanger parameters and heat transfer coefficient. Overall thermal resistance with clean non-fouled surfaces for dry and wet cooling coils is a combination of three individual thermal resistances: (1) *Ra* [m<sup>2</sup> .K/W] convective thermal resistance between air and external surface of the coil, (2) *Rm* [m2 .K/W] total conductance heat transfer of the metal fin, *Rf* , and tube, *Rt*, and (3) *Rl* [m2 .K/W] convective thermal resistance between the internal surface of the coil and the working fluid flowing inside the coil. Brown [29] derived thermal resistance of dry region, *Rmd*, and wet region, *Rmw*, based on the heat transfer concept, proposed by Ware-Hacha [30], as follows:

$$R\_{md} = R\_f + R\_t = \frac{(\mathbf{1} - \mathcal{Q}\_t)}{\mathcal{Q}\_t} R\_{ad} + \frac{\text{Br } \mathbf{D}\_i \text{ L} \pi \left( \mathbf{D}\_{\bigvee} \big|\_{\mathbf{D}\_i} \right)}{\mathbf{2} \ p\_t} \tag{44}$$

*Heat Exchangers*

$$R\_{mw} = R\_f + R\_l = \frac{(\mathbf{1} - \mathfrak{D}\_l)}{\mathfrak{D}\_l} \left( R\_{aw} \frac{\mathbf{C} p\_m}{m^\circ} \right) + \frac{\operatorname{Br} \operatorname{D}\_l \operatorname{L} \mathfrak{n} \left( \mathbf{1} \uprho\_{\operatorname{\mathcal{O}}\_l} \right)}{2 \operatorname{k}\_l}. \tag{45}$$

where *m"* is *dhs dTs* . The overall thermal resistance of dry *RTd* and wet *RTw* region can be calculated as follows:

$$R\_{Td} = R\_{ad} + R\_{md} + R\_l = \frac{\mathbf{1}}{\mathfrak{D}\_l \ a\_{ad}} + \frac{\operatorname{Br} \operatorname{D}\_l \operatorname{Ln} \left( \operatorname{D}\_{\sqrt{}} \right)\_{l\overleftarrow{\varepsilon}}}{\operatorname{2} \operatorname{k}\_l} + \frac{\operatorname{Br}}{a\_l}.\tag{46}$$

$$R\_{Tw} = R\_{aw} + R\_{mw} + R\_l = \frac{1}{a\_{aw}} + \frac{(1 - \mathcal{Q}\_l)}{\mathcal{Q}\_l} \left(\frac{1}{a\_{aw}} \frac{\mathcal{C}p\_m}{m^\circ}\right) + \frac{Br \, D\_i \, Ln \left(\mathcal{D}\_l \dot{\mathcal{D}}\_i\right)}{2 \, k\_l} + \frac{Br}{a\_l}.\tag{47}$$

where *Rad*, *Raw*[m<sup>2</sup> .K/W] are thermal resistance for convective heat transfer between air and external surface of the dry and wet coil, *Rt* [m<sup>2</sup> .K/W] is thermal resistance of the metal tube, and *Rl* [m2 .K/W] is thermal resistance between the internal surface of tube and the working fluid flowing inside the coil. Br [�] is the ratio of total external surface area *Ao* to internal surface area *Ai*.

The ratio of wet and dry coil region is influenced by the characteristic of coil such as coil arrangement, refrigerant distribution, coil depth, entering air dew point and dry bulb temperatures, working fluid temperature, and their flowrates. Another parameter, *Y* [kg °C/kJ], the ratio of fluid temperature rise to air enthalpy drop, is also important parameter to calculate the boundary region. *Y* can be driven from the ratio of the heat that gained by working fluid to the heat that lost from the air stream. The equation is as follows:

$$\frac{dT\_l}{dh\_a} = \frac{m\_a}{m\_l \mathbf{C} p\_l} = Y \tag{48}$$

The total heat transferring from the air to the saturated water surface in wet region of TDCONF exchanger is similar with TFDC exchanger, Eq. (16). Mass transfer coefficient KM is substituted with Eq. (6), and it can be written as follows:

$$dq\_{Tw} = K\_M (h\_a - h\_s) \, dA\_{aw} = \frac{(h\_a - h\_s) \, dA\_{aw}}{C p\_m R\_{aw}} \tag{49}$$

Total heat transferred capacity *dqTw* in wet region also equals with the heat that transfer from the saturated wet surface layer to the working fluid that flowing inside the tube.

$$dq\_{Tw} = \frac{(T\_s - T\_l) \, dA\_{ow}}{R\_{mw} + R\_l} \tag{50}$$

After equating and rearranging of Eqs. (49) and (50), the following equation will be obtained, and can be denoted as the characteristic of the coil, *C* [2, 19, 20, 26].

$$\mathbf{C} = \frac{\mathbf{R}\_{mw} + \mathbf{R}\_{l}}{\mathbf{C}p\_{m}\mathbf{R}\_{aw}} = \frac{(T\_{s} - T\_{l})}{(h\_{a} - h\_{s})} \tag{51}$$

For the dry-wet boundary line, the coil characteristic *C* can be expressed as follows:

$$\mathbf{C} = \frac{\left(T\_{dpai} - T\_{lb}\right)}{\left(h\_{ab} - h\_{sb}\right)}\tag{52}$$

*Direct Contact Heat and Mass Exchanger for Heating, Cooling, Humidification… DOI: http://dx.doi.org/10.5772/intechopen.102353*

Enthalpy of air at dry-wet boundary line, *hab* [kJ/kg] can be derived from Eqs. (48) and (52) as follows:

$$h\_{ab} = \frac{T\_{dpai} - T\_{lo} + Y \, h\_{ai} + C \, h\_{sb}}{C + Y} \tag{53}$$

The exchanger coil can be determined whether it is fully wetted, fully dry, or partially wetted by comparing the values of *hab* with *hai*, and *hao*. If the value *hab* is higher than *hai*, all the surface of exchanger is fully wetted. If the value of *hab* is higher than *hao* but less than *hai*, the surface of exchanger is partially wetted. If the value of *hab* is less than *hao*, then the surface of exchanger is completely dry. The temperature of air at dry-wet boundary point,*Tab* [°C], can be calculated from the heat energy equation of the air stream that flowing in dry region.

$$T\_{ab} = T\_{ai} - \frac{(h\_{ai} - h\_{ab})}{C p\_m} \tag{54}$$

The working fluid temperature at dry-wet boundary line,*Tlb* [°C], cab be calculated from the energy balance equations between the air stream and working fluid in the dry region.

$$T\_{lb} = T\_{lo} - Y \, \text{Cp}\_m (T\_{ai} - T\_{ab}) \tag{55}$$

Air temperature, air enthalpy, and working fluid temperature of dry region can be calculated by using traditional heat exchanger equations. But for the wet region, a discretized volume with distributed lump parameters method, like TFDC model that explained detail in Section 3, can calculate the parameters of air stream, saturated surface, and working fluid.

### *4.3.2 Energy balance between two fluids of Type-2.1.1 exchanger (energy balance line, EBL)*

Energy balance line for the wet region of Type-2.1.1 exchanger can be derived by equating the energy lost from the air stream and the energy gained by the working fluid. EBL equation for each element with the numbering, *n*, of each node can be expressed as follows:

$$-m\_d dh\_d = -m\_l \, \mathrm{Cp}\_l dT\_l \tag{56}$$

$$\frac{h\_a^{n+1} - h\_a^n}{T\_l^{n+1} - T\_l^n} = \pm \frac{m\_l C p\_l}{m\_a} = EBL \tag{57}$$

A minus sign refers to a parallel flow between air stream and working fluid flow. A plus sign refers to a counter flow that working fluid is flowing in the opposite direction of airflow.

#### *4.3.3 Heat and mass transfer between two fluids of Type-2.1.1 model (tie-line slope)*

Tie-line slope is the ratio of enthalpy difference between air and saturated surface to the temperature difference between working fluid and saturated surface. Tie-line slope, Eq. (59) can be derived from the equating of the sensible heat, transferring from the working fluid to saturated surface, with the total sensible and latent heat that transferring from the saturated surface to the air stream, see in

**Figure 10**. Tie-line slope of Type-2.1.1 extended surface TDCONF exchanger is similar with the one of TFDC exchanger, Eq. (19), but the difference is an addition of thermal resistances of the metal wall and fins in the wet region, Rmw. Hence, Tie-line slope for Type-2.1.1 extended surface TDCONF exchanger can be expressed with the characteristic of coil, *C*, as follows:

$$K\_M(h\_s - h\_{avg})dA = U\_d(T\_{long} - T\_s)dA \tag{58}$$

$$\frac{h\_s - h\_{aug}}{T\_s - T\_{lavg}} = -\frac{U\_{sl}}{K\_M} = -\frac{\mathbf{C}p\_m R\_{aw}}{R\_{mw} + R\_l} = -\frac{\mathbf{1}}{\mathbf{C}} = -\mathbf{T} \mathbf{L} \mathbf{S} \tag{59}$$

The total heat which is transferring from the saturated surface node j, *T <sup>j</sup> <sup>s</sup>* to the average temperature of air stream, *T <sup>j</sup> lavg* which is the average of two adjacent nodes temperature *T<sup>n</sup> <sup>l</sup>* and similarly from the saturated surface to the air stream are shown in **Figure 11**. *TLS* equation, Eq. (59), has two unknown parameters, saturated temperature,*Ts*, and saturated enthalpy, *hs*. The third order polynomial regression equation, which is fitted with the saturation 100% RH line, shown in **Figure 7**, can be used as their relation equation Eq. (20) to the *TLS* equation Eq. (59), and rearranged with node number as follows:

$$\text{coef1}\left(\left.T\_{i}^{j}\right|^{3} + \text{coef2}\left(\left.T\_{i}^{j}\right)^{2} + \left(\text{coef3} + \text{TLS}\right)T\_{i}^{j} + \text{coef4} - \left(\frac{h\_{a}^{n} + h\_{a}^{n+1}}{2}\right) - \text{TLS}\left(\frac{T\_{l}^{n} + T\_{l}^{n+1}}{2}\right) = 0\right) \tag{60}$$

This third order polynomial *TLS* equation can be solved by using Newton Raphson iteration methods to finds its unknown root parameter,*Ts,* from the known parameters of tie line slope, enthalpy of air, and working fluid temperature.

#### **Figure 11.**

*Typical plate finned tube heat exchange with (a) a three circuit tube with four rows deep and staggered arrangement and, (b) its 3D view with dimensions' notation.*

*Direct Contact Heat and Mass Exchanger for Heating, Cooling, Humidification… DOI: http://dx.doi.org/10.5772/intechopen.102353*

#### *4.3.4 Dry bulb temperature of each node for Type-2.1.1 model*

Likewise the derivation of air temperature in Section 3.3, the air temperature of each node of TDCONF exchanger can be driven from the ratio of sensible heat that transfer from air to saturated surface to the total heat and mass transfer from the air to saturated surface. The ratio is as follows:

$$\frac{m\_a \mathcal{C}\_{pm} dT\_a}{m\_a dh\_a} = \frac{\alpha\_{aw} \left(T\_s - T\_{aavg}\right) dA}{K\_M \left(h\_s - h\_{aavg}\right) dA} \tag{61}$$

The value of *<sup>α</sup>aw KMCpm* can be assumed 1 for the Lewis number to the power of 2/3 is similar with 1, see the derivation in Section 3.2. For numerical calculation, the air temperature of each node, Eq. (61) is needed to be rearranged and rewritten with node number n and j as follows:

$$T\_a^{n+1} - T\_a^n = \frac{\frac{h\_a^{n+1} - h\_a^n}{\left(h\_i^{\prime} - h\_{\text{avg}}^{\prime}\right)} \left(T\_s^j - T\_a^n\right)}{\left(1 + \frac{h\_a^{n+1} - h\_a^n}{2\left(h\_i^{\prime} - h\_{\text{avg}}^{\prime}\right)}\right)}\tag{62}$$

From the above equation outlet air temperature of each node *T<sup>n</sup>*þ<sup>1</sup> *<sup>a</sup>* can be calculated from the known parameters of air inlet temperature, air enthalpy, and saturated air enthalpy of each node.

#### *4.3.5 Exchanger area calculation of Type-2.1.1*

The area of wet region, *Aw*, can be calculated by integration of the energy balance equation which is the total heat losing from the air stream is equal to the total heat and mass transferring from the air stream to the vapor saturated surface layer.

$$
\int m\_d dh\_a = \int K\_M (h\_s - h\_{a\text{avg}}) dA \tag{63}
$$

Mass transfer coefficient, *KM*, can be substituted with the parameters *<sup>α</sup>aw Cpm* , as the Lewis number to the power of 2/3 is similar with 1, see in Eq. (6). The integral equation Eq. (63) can be solved out with Sampson's rule or Trapezoidal method, and it can rewrite with node number *n* and *j* as follows:

$$A\_{ow} = \frac{m\_a \cdot \mathbf{C} p\_m}{a\_{aw}} \sum\_{j=1}^{j=N-1} \left[ \frac{\mathbf{1}}{\left(h\_s^j - h\_{aug}^j\right)} \times \left(h\_a^{n+1} - h\_a^n\right) \right] \tag{64}$$

The wet surface area of TDCONF exchanger can be calculated from the known parameters, air enthalpy *ha* and vapor saturated enthalpy *hs* of each element.

### **4.4 Type-2.1.2 extended surface TDCONF exchanger operating with volatile working fluid**

The exchanger's geometrical structure of Type-2.1.2 is the same with the one of Type-2.1.1, for both are using plate finned tube heat exchanger having a similar thermal resistance for heat and mass transferring from air to working fluid. But the difference between them is that Type-2.1.1 exchanger is working with non-volatile fluid so that its fluid temperature *TL* is increasing along the area axis from *TLin* to *TLout*, shown in **Figure 10**, and Type-2.1.2 exchanger is operating with volatile refrigerant so that its working fluid temperature is constant along the coil depth, *dTL* is 0. As a result, the parameter *Y* become infinity. For coil characteristic *C* for Type-2.1.2 is similar with Type-2.1.1, the margin point, *hab*, of dry and wet region of Type-2.1.2 exchanger can be calculated from the coil characteristic equation Eq. (65). At boundary point, water saturated surface temperature of dry and wet region is same as dew point temperature of inlet air, *Ts* ¼ *Tdpai*. The enthalpy of air at boundary, *hab* can be expressed as follows:

$$h\_{ab} = h\_{sb} + \frac{\left(T\_{dpa i} - T\_l\right)}{\mathcal{C}}\tag{65}$$

Similarly with Type-2.1.1, temperature of air at dry-wet boundary point can be calculated from the equation, Eq. (65). As the working fluid temperature is constant in all coil depth, fluid temperature at boundary point *TLb* is same as with *TL*. Energy balance line for Type-2.1.2 is vertical for its refrigerant temperature is constant along the coil depth, *dTL* is 0. As a result, the refrigerant temperature of each node is constant, and the enthalpy of air outlet *hao* can be calculated from the energy balance equation between the total heat lost from the air stream and the vaporization heat of the refrigerant, and the equation is as follows:

$$m\_a dh\_a = -m\_l h\_{\text{fg}(T\_r)} \tag{66}$$

$$h\_{ao} = h\_{ai} - \frac{m\_l h\_{f\text{g}(T\_r)}}{m\_d} \tag{67}$$

The equations of tie-line slope, dry bulb air temperature, and contact area for Type-2.1.2 are the same with Eqs. (60), (62), and (64).

#### **4.5 Type-2.2: non-extended surface TDCONF heat exchanger**

Indirect evaporative cooler and M-cycle dew point evaporative cooler, Type-2.2 exchangers, are passive coolers and very efficient cooler for dry and hot region. The two fluids, a thin water film and working air, are directly contacting each other, and they do not contact with the third fluid, product air, by separating with aluminum or plastic film to prevent the moisture transferring and make sure allowing only heat transfer.

The phenomena of heat and mass transfer and its mathematical model is the same with a wet region of Type-2.1.1 exchanger, except the calculation of separator area. Tube is used as separator in Type-2.1.1 exchanger and flat sheet is used in Type-2.2 exchanger. Thus, total thermal resistance, RT, of non-extended surface TDCONF exchanger can be written with convective heat transfer coefficient of working air, *αaw*, and of product air, *αap*. *ksep* is the thermal conductivity of the separator and *tsep* is the separator thickness. The total resistance equation can be expressed as follows:

$$R\_T = R\_{aw} + R\_{mw} + R\_{ap} = \frac{\mathbf{1}}{a\_{aw}} + \left(\frac{\mathbf{1}}{a\_{aw}}\frac{Cp\_m}{m^\cdot}\right) + \frac{t\_{sep}}{k\_{sep}} + \frac{\mathbf{1}}{a\_{ap}}\tag{68}$$

The rest equations of energy balance line (EBL), tie-line slope (TLS), dry bulb air temperature *Ta*, and contact area for Type-2.2 exchanger are the same with Eqs. (57), (60), (62), and (64).

*Direct Contact Heat and Mass Exchanger for Heating, Cooling, Humidification… DOI: http://dx.doi.org/10.5772/intechopen.102353*

### **5. Effectiveness of heat and mass exchanger**

The effectiveness of heat and mass exchanger are defined in many different ways in many studies. The effectiveness of cooling tower, and direct evaporative cooler based on the temperature is the ratio of the range, the change of water temperature between the inlet, *TLin*, and the outlet, *TLout*, to the sum of the range and the approach which is the difference between water outlet temperature and the inlet air wet-bulb temperature, *TWBain* [31], expressed as follows:

$$
\varepsilon\_{\text{CoolingTorer}} = \frac{\text{Range}}{\text{Range} + \text{Approach}} = \frac{T\_{Lin} - T\_{\text{Lout}}}{T\_{Lin} - T\_{\text{WBain}}} \tag{69}
$$

Although Jaber and Webb [8] proposed a modified definition of cooling tower effectiveness with enthalpy, temperature based effectiveness, Eq. (69), is widely used in the cooling tower industry and this study also. Saturation effectiveness is a key factor in the determination of direct and indirect evaporative cooler performance. The saturation effectiveness of direct evaporative cooler is the ratio of the dry bulb temperature difference between inlet air, *TDBain*, and outlet air *TDBaout*, to the difference between inlet air dry bulb temperature and its wet bulb temperature, *TWBain* [2], expressed as follows:

$$
\varepsilon\_{\text{DirectEupPCoder}} = \frac{T\_{\text{DBain}} - T\_{\text{DBaout}}}{T\_{\text{DBain}} - T\_{\text{WBatin}}} \tag{70}
$$

The saturation effectiveness of indirect evaporative cooler, wet-bulb depression efficiency, is the ratio of the dry bulb temperature difference between the product air inlet, *TDBpain*, and outlet, *TDBpaout*, to the difference between the product air inlet and inlet wet bulb temperature of working air, *TWBwain* [2], expressed as follows:

$$\varepsilon\_{IndirectExpCoer} = \frac{T\_{DBpain} - T\_{DBpaoout}}{T\_{DBpain} - T\_{WBoatin}} \tag{71}$$

The effectiveness of air washer chamber and wet part of cooling coil are based on the enthalpy, and can be defined as the ratio of enthalpy difference between air inlet and out let to the difference between inlet air enthalpy and saturation enthalpy associated with working fluid inlet temperature [8, 32], expressed as follows:

$$
\varepsilon\_{\text{Coil}/Airuaster} = \frac{h\_{\text{ain}} - h\_{\text{aout}}}{h\_{\text{ain}} - h s\_{\text{WFin}}} \tag{72}
$$

#### **6. Results and discussion**

This study has developed four types of numerical models for DCHME widely used in the air-conditioning industry. The first model explained in Section 3 is for Type-1 TFDC exchanger: air washer chamber, cooling tower, swamp cooler, or direct contact evaporative cooler, shown in **Figures 2**, **5**, and **6**. The second model derived in Section 5.2 is for Type-2.1.1 extended surface TDCONF exchanger working with non-volatile refrigerant (2.1.1. Extended Surface-Non Vol). An example of these exchanges is the wet region of plate finned tube heat exchanger used for cooling and dehumidification working with chilled water or ethylene/propylene glycol, shown in **Figures 3(a)**, **8(b)** and **(c)**, and **10**. The third model derived in Section 5.3 is for Type-2.1.2 extended surface TDCONF exchanger working with

volatile refrigerant (2.1.2. Extended Surface-Vol). Examples of these exchangers are the wet region of DX-coil for cooling and dehumidification working with R134a, R410, etc., shown in **Figures 3(a)** and **8(b)** and **(c)**. Finally, the fourth model, derived detail in Section 6, is for Type-2.2 non-extended surface TDCONF exchanger (2.2. Non-Extended Surface), which are indirect evaporative cooler and M-cycle dew point evaporative cooler, shown in **Figures 3(b)**, **8(a)** and **(c)**, and **12**.

There are two types of problems with known (given) parameters and parameters to calculate for DCHME, which are listed in **Table 1**. The first type of problem, Case 1a, and 1b, is the case for designing DCHME to solve the length or area of the exchanger to achieve the desired fluid outlet temp or air outlet condition. The second type of problem, Case 2, is the case for the model predictive control system to predict the effectiveness and output parameter of a given DCHME under the load's variation and different operational parameters. Model 1. TFDC and 2.1.1. Extended Surface-Non Volatile working fluids have three problem cases, but model 2.1.2. Extended Surface-Vol has only two problems excluded Case 1b because there is no temperature difference between the inlet and outlet of the volatile working fluid. Similarly, model Type-2.2. Non-Extended Surface has no Case 1a because the product air operating as a working fluid is the only parameter needed to design and develop the control model of the exchanger. The models with different types of problem cases are shown in **Figure 13**.

**Figure 14** shows the simulation result of temperature and enthalpy of the air, water, and saturated layer of each element of Type-1 TFDC exchanger, which are cooling tower or air washer chamber with Case 1 problem, calculation of exchanger

#### **Figure 12.**

*(a) A typical one unit cell of non-extended TDCONF exchanger with counter flow process between product air and working air, and (b) thermal diagram of non-extended surface TDCONF exchanger and their potential difference for heat and mass transfer process.*

*Direct Contact Heat and Mass Exchanger for Heating, Cooling, Humidification… DOI: http://dx.doi.org/10.5772/intechopen.102353*


**Table 1.**

*List of problem types with known and calculation parameters for DCHME.*

#### **Figure 13.**

*Four models with three different problem types of air conditioning exchanger.*

length or area. The numbering of nodes *i* and *j* for exchanger is shown in **Figure 5**, in which water is spraying into an (a) parallel or counter flow with airflow direction. The process is heating and humidifying airflow in the air washer chamber or cooling the water in the cooling tower. **Figure 14(a)** shows the result of parallel flow exchanger where the energy balance line is inclined to the left side due to its negative slope per Eq. (10), and similarly, the positive slope for counter flow, thus the line inclined to the right side as shown in **Figure 14(b)**. Both counter and parallel flow have the same negative tie line slope value, see Eq. (19), both tie lines are inclined into the left side. The outlet air temperature, green circle, of counter flow is 1.5°C higher than parallel flow under all the same condition. Thus, the counter flow has higher efficiency than the parallel flow.

**Figure 15** shows the simulation result of temperature and enthalpy of the air, water, and saturated layer of each element of Type-1 TFDC exchanger, air washer

#### **Figure 14.**

*Temperature and enthalpy of air, water and saturated layer of each element of Type-1 TFDC exchanger with Case 1 problem for the process of air heating and humidification in air washer chamber or cooling the water in cooling tower (a) parallel flow, and (b) counter flow.*

#### **Figure 15.**

*Temperature and enthalpy of air, water and saturated layer of each element of Type-1 TFDC and Type-2.1.1 exchanger with Case 1 problem for the process of air cooling and dehumidification in air washer chamber and cooling coil operating with non-volatile working fluid in a (a) parallel flow, and (b) counter flow.*

chamber, Type-2.1.1 exchanger, wet region of cooling coil working with nonvolatile fluid, for the process of air cooling and dehumidification. The behavior of the energy balance line and tie line is the same as the heating and humidification process, but the waterline, blue circle, is left side of the saturation line because the working fluid temperature is lower than the saturation temperature, red circle, at each node. At the same time, the water line is on the right side of the saturation line because the working fluid temperature is higher than the saturation temperature in the air heating and humidification process, see **Figure 14**.

**Figure 16** shows the effectiveness of the exchanger based on the water stream, Eq. (69), and based on the airflow stream Eq. (72) for cooling tower and air washer chamber under the same giving length with different liquid air ratio and inlet air enthalpy. At a low liquid-air flow ratio, the effectiveness of cooling tower based on water temperature stream is higher because the range, the temperature difference between water inlet and outlet, is higher due to the low water flow rate. However, for the air washer based on air stream, the effectiveness, Eq. (72), is lower than the higher liquid-air flow ratio because the temperature difference between the air inlet and outlet temperature is higher due to the high airflow rate. Therefore, this Type-1 exchanger with the Case 2 problem model can predict the effectiveness and outlet condition of water or air stream under the several of liquid-air flow ratio and inlet

*Direct Contact Heat and Mass Exchanger for Heating, Cooling, Humidification… DOI: http://dx.doi.org/10.5772/intechopen.102353*

#### **Figure 16.**

*Effectiveness of Type-1. TFDC exchanger based on the water stream for cooling tower and based on the air stream for air washer chamber: Type-1 exchanger with Case 2 problem model.*

**Figure 17.**

*Temperature and enthalpy of each element's (a) air, non-volatile working fluid and saturated layer of Type-2.1.1 exchanger (b) air, volatile working fluid and saturated layer of Type-2.1.2 exchanger with counter flow for the process of cooling and dehumidification.*

air condition. Thus this model can be applied as a sub-function of the model predictive control system.

**Figure 17** shows the simulation result of the temperature and enthalpy of each element. **Figure 17(a)** depicts the result of the model, Type-2.1.1 extended surface working with the non-volatile working fluid, and **Figure 17(b)** shows the result of the model, Type-2.1.2 extended surface working with volatile refrigerant for the process of cooling and dehumidification. Both models run at 6°C of working fluid temperature with the exact dimension of the plane finned tube heat exchanger and the same flow rate, flow rate ratio, and condition of the inlet air. Depending on the nature of the volatilization of the working fluid, the temperature of the non-volatile working fluid changes from inlet 6°C to outlet 10°C. The outlet air temperature is dropped from 31 to 24.1°C, as shown in **Figure 17(a)**, whereas, in the model of Type-2.1.2, the refrigerant temperature is constant at 6°C, but the outlet air temperature is dropped from 31 to 17°C, as shown in **Figure 17(b)**. Thus, the Type-2.1.2 exchanger has a better performance than the Type-2.1.1 exchanger.

#### **Figure 18.**

*Cooling and dehumidification process of Type-2.1.1 exchanger with same inlet air temperature but different humidity ratio.*

**Figure 18** shows the simulation result of model Type-2.1.1 exchanger running with the same plate finned tube heat exchanger and operating with the same volatile refrigerant at 5°C with the same refrigerant-air flow ratio. The result clearly shows that the model can estimate the dry and wet area and predict the outlet air temperature and moisture removing rate under different air inlet conditions (same inlet temperature but different humidity ratio). Thus, these models are suitable for use as a sub-function of the model predictive control system.

## **7. Conclusion**

This study has developed a mathematical model based on a discretized volume with distributed lumped-parameters method for two fluid direct contact (TFDC) exchangers and two direct contacts with one non-contact fluid (TDCONF) exchanger. Based on the flow system and structure, this study has developed four models; Type-1 TFDC exchanger model (air washer chamber, cooling tower, and swamp cooler or direct contact evaporative cooler), Type-2.1.1 extended surface TDCONF exchanger model working with non-volatile refrigerant (wet region of plate finned tube heat exchanger cooling coil working with chilled water or ethylene/propylene glycol), Type-2.1.2 extended surface TDCONF exchanger working with volatile refrigerant (wet region of plate finned tube DX-coil), and Type-2.2 non-extended surface TDCONF exchanger (indirect evaporative cooler and Mcycle dew point evaporative cooler). From the simulation result, these models can reflect both heat and mass transfer behavior in every spatially distributed physical system. Moreover, they can predict well the effectiveness and dependent parameters of DCHME under the different load conditions and its various input parameters. Hence, these models can be a valuable tool for designing the exchangers mentioned above and can be applied as a sub-function of the model predictive control system.

*Direct Contact Heat and Mass Exchanger for Heating, Cooling, Humidification… DOI: http://dx.doi.org/10.5772/intechopen.102353*
