**5. Numerical model for heat exchanger performance prediction and optimization**

As previously motivated in the introduction, a numerical model of the heat exchanger in general is developed to guide the future optimized design of the heat exchanger. Here, an example of a finite element model has been developed for a

**Figure 6.**

*An exemplified of heat transfer coefficient* h *for the inline, single-staggered, and woven matrix wire and tube heat exchanger bearing pitch wire of (a) 7 mm and (b) 14 mm.*

single-staggered wire and tube heat exchanger [24, 25]. In this case, the model was developed to aid the optimum design, which is limited by two variables including wire pitch (pw) and wire diameter (Dw). Experimental validation was carried out for the heat exchanger with wire pitch of 7 mm and 14 mm to assess the accuracy of the finite element model.

**Figure 7** highlights the results of the finite element model on the singlestaggered wire and tube heat exchanger using a wire pitch of 7 mm. The data verification reveals that the average error of modeling data compared to the measurement data is lower than 5%. In comparison, the earlier finding of the numerical simulation reported by Basal and Chin [16] that employed the heat load validation method yields an average error of up to 10%. This indicates that the simple finite element model developed in this work is considered reliable and accurate.

As the model is experimentally validated and reliable, this model was used to assess the heat exchanger capacity of the wire-tube configuration with the wire pitch spanning from 5 to 12 mm and the wire diameter spanning from 0.8 to 1.5 mm. The contour plot in **Figure 7b** displays the dependency of the heat exchanger capacity (Q tot) to the wire pitch and diameter. For optimization procedure, an optimization factor ( *f* ) was defined:

$$f = \frac{Q/W}{Q\_0/W\_0} \tag{27}$$

where Q is the capacity of the optimized heat exchanger, W is the mass of the heat exchanger, and Q0 and W0 are the capacity and mass of the basis designed heat exchanger, respectively.

In this case, the basis designed heat exchanger possess the following specifications: exchanger height of 445 mm; width of heat exchanger (wire) of 431 mm; width of heat exchanger (tube) of 476 mm; the tube length of 6416 mm; the outside tube diameter of 4.8 mm; the inside tube diameter of 3.2 mm; and the wire diameter of 1.2 mm. Using this consideration, the optimum condition is obtained if the optimization factor is maximum. In this regard, the optimum condition is obtained for Q tot of 119.9214 W using a wire pitch of 11 mm and wire diameter of 0.9 mm. The contour plot in **Figure 7b** indicates that the smaller the wire pitch the bigger Q tot. In addition, increasing the wire diameter tends to enhance the Q tot. Nonetheless, if pw ≤ dw, the system will merely be considered as tube, where the fins form of plate structure, and this condition yields lower Q tot.

*Design, Performance, and Optimization of the Wire and Tube Heat Exchanger DOI: http://dx.doi.org/10.5772/intechopen.100817*

**Figure 7.**

*(a) Temperature validation of each element for heat exchanger with wire pitch of 7 mm representing the wire temperature measured at nine measurement points. (b) Contour plot of the total heat exchanger capacity as a function of wire diameter and wire pitch. Figures from Ref. [24] used with permission.*

Having optimized for the design of single-staggered wire and tube heat exchanger, the performance of inline and single-staggered wire-tube configuration is compared experimentally. The experimental data indicate that the inline configuration allows for 110 W heat release, while the single-staggered wire and tube heat exchanger exhibits a heat exchanger capacity of 107.3 W [24]. The difference is not that significant, and this result shows that changing the wire-tube geometry from inline to single-staggered already provides more efficient conditions. It is considered efficient as the single-staggered design reduces the number of wires used for manufacturing, and hence, it cuts the mass of construction materials and costs. Reducing the number of wires also leads to higher convective airflow since the flow is not blocked by the wall geometry as indicated from the velocity contour plot in **Figure 8**.

**Figure 9a** and **b** displays that air velocity distribution on the array of wire between inline and staggered heat exchanger. The results clearly indicate that the average velocity amplitude of the airflow around the wire tube is higher for a single-staggered one than that of the inline configuration. With velocity amplitude

**Figure 8.**

*(Left) Velocity and (right) temperature contour of (a) inline and (b) single-staggered wire and tube heat exchanger bearing wire pitch of 7 mm. Figures from Ref. [24] used with permission.*

of 4 times higher and more homogeneously distributed, the single-staggered wiretube heat exchanger also shows a slightly larger temperature difference between the outer surface of the wire-tube and the near-surface air. The more distributed airflow in the vicinity of the staggered wire-tube configuration supports the argument that this configuration minimizes the airflow blocking by geometry wall. As the convective heat transfer coefficient is proportional to the air velocity, this leads to a higher rate of heat release by convection from the surface to the surrounding air.

It is already discussed that the numerical model is helpful to assist the optimization of a single-staggered wire and tube heat exchanger. Here, we further present the numerical study using CFD of single-staggered wire and tube heat exchanger with varying wire pitch (7, 9, and 11 mm) and inlet fluid temperature (40, 60, and 80°C) [26]. In this case, the inlet mass flow was set to 2 <sup>10</sup><sup>3</sup> kg s<sup>1</sup> . The simulation results show that the temperature difference ΔT (Tin – Tout) is exceptionally low and almost similar for the heat exchanger operated in the lowest inlet fluid temperature (**Figure 9a**–**c**). Thus, the inlet temperature of 40°C yields very low heat exchanger capacity irrespective of the wire pitch. **Figure 9d**–**f** exhibits quite significant ΔT upon increasing the inlet temperature to 60°C. For wire pitch of 7 mm, a ΔT = 26°C is reached, while wire pitch of 9 and 11 mm shows ΔT of 24 and 22°C, respectively. This simulation is consistent with the experimental results that single-staggered wire and tube heat exchanger bearing 7 mm wire pitch shows ΔT = 26°C [25, 26].

As we have noted previously that heat exchanger capacity tends to increase with increasing inlet fluid temperature, it is also obvious that at 80°C inlet temperature the ΔT becomes significantly higher. The ΔT magnitude for wire pitch of 7, 9, and 11 mm in heat exchanger operated at 80°C inlets are 30, 27, and 25°C, respectively. In brief, the CFD simulation allows for the prediction of the resulting ΔT and the

*Design, Performance, and Optimization of the Wire and Tube Heat Exchanger DOI: http://dx.doi.org/10.5772/intechopen.100817*

**Figure 9.**

*Temperature profile of the single-staggered wire and tube heat exchanger bearing wire pitch (pw) of (a,d,g) 7 mm, (b,e,h) 9 mm, and (c,f,i) 11 mm operated using inlet fluid temperature of (top) 313 K (40°C), (middle) 333 K (60°C), and (bottom) 353 K (80°C). Figures from Ref. [26] used with permission.*

average surface temperature of wire tube that can be used to evaluate heat exchanger capacity, wire efficiency as well as the heat exchanger efficiency.

Another set of examples benefitting the CFD approach for woven matrix wire and tube heat exchanger is shown in **Figure 10**. Previously, it is required for further optimization of woven matrix configuration with wire pitch below 14 mm. Thus, herein we discuss the performance of woven matrix wire and tube heat exchanger bearing wire pitch of 5, 7, and 9 mm and operated at different inlet mass flow, which was simulated using CFD [27]. In this case, the inlet temperature was set to 80°C. The general results show that lowering the mass flow rate from 1.10 <sup>10</sup><sup>3</sup> to 0.55 <sup>10</sup><sup>3</sup> kg s<sup>1</sup> increases the <sup>Δ</sup>T. For 5-mm wire pitch, a lower mass flow rate leads to outlet temperature as low as the ambient temperature (29.85°C). Similar results are obtained for heat exchanger bearing 7-mm wire pitch that can yield ΔT = 49.78°C and outlet temperature of 30.4°C under the operating condition of 0.55 <sup>10</sup><sup>3</sup> kg s<sup>1</sup> mass flow rate. Enlarging the wire pitch to 9 mm results in a lower heat transfer capacity as indicated by the higher outlet temperature even though the mass flow rate is set to the lowest. Considering that woven matrix wire and tube heat exchanger bearing wire pitch of 5 and 7 mm have no significant thermal performances, it can be deduced that 7-mm wire pitch is the optimum condition again from both practical and economical aspects.

Using the simulation results in **Figure 10**, the wire efficiency can also be calculated. Overall, increasing the inlet mass flow also improves the wire efficiency. Nonetheless, the maximum efficiency is reached for the inlet mass flow of 0.57 <sup>10</sup><sup>3</sup> kg s<sup>1</sup> irrespective of the wire pitch. The wire pitch in woven matrix configuration affects the wire efficiency, and it is found that 7-mm wire pitch yields the highest efficiency of 73% at the inlet mass flow of 0.57 <sup>10</sup><sup>3</sup> kg s<sup>1</sup> which is consistent with the above discussion.

#### **Figure 10.**

*Temperature profile of single woven matrix wire and tube heat exchanger bearing pitch wire of (a–c) 5 mm, (d–f) 7 mm, and (g–i) 9 mm operated using the inlet mass flow of (top) 1.10 <sup>10</sup><sup>3</sup> kg s<sup>1</sup> , (middle) 0.57 <sup>10</sup><sup>3</sup> kg s<sup>1</sup> , and (bottom) 0.55 <sup>10</sup><sup>3</sup> kg s<sup>1</sup> . Figures from Ref. [27] used with permission.*

#### **6. Conclusion**

In this chapter, we have discussed that geometrical design along with optimum operating condition substantially control the overall performance of wire and tube heat exchanger. It has been demonstrated that for the commonly used inline wire and tube heat exchanger the efficiency can be predicted using the empirical formula (logarithmic function), which depends merely on the geometrical aspect (wire pitch to wire length ratio) and the Rayleigh number. Consistent with the heat transfer theory in a practical heat exchanger increasing the inlet fluid temperature and slowing down the mass flow rate typically yield higher-heat exchanger capacity and efficiency irrespective of the wire-tube configuration, including the inline, single-staggered, and woven matrix. Nonetheless, among the three investigated wire-tube configurations the single-staggered wire and tube heat exchanger is promising as the most efficient heat exchanger by taking into account the overall thermal performance, material mass, and cost for manufacturing.

This chapter also presents a numerical model based on the finite element method (FEM) that has been developed to evaluate and optimize the geometrical design of a single-staggered wire and tube heat exchanger with the optimization constraints of wire pitch and wire diameter. The FEM has successfully modeled the thermal behavior of the heat exchanger, which is validated by the experimental data showing an average numerical error of less than 5%. To understand the underlying phenomena in the heat transfer process, computational fluid dynamics (CFD) analysis enables the discussion of the local and near-surface airflow affecting the natural convection mechanism, and the heat flux on the outer wire-tube surfaces, which is responsible for the radiation from the surface to the surrounding environment. In addition, CFD analysis alone also allows for a comprehensive analysis of wire and tube heat exchanger running at certain operating conditions, and eventually, the

*Design, Performance, and Optimization of the Wire and Tube Heat Exchanger DOI: http://dx.doi.org/10.5772/intechopen.100817*

heat exchanger capacity as well as the heat exchanger efficiency can be calculated based on the simulation results.
