**2. Experimental approach**

To explore the effect of geometrical design on the wire-tube configuration, three different configurations including inline, single-staggered, and woven matrix wire and tube heat exchanger were fabricated [20]. The design of wire and tube heat exchanger considered various geometrical aspects that include the width (W) of the wire cross, the wire length (Lw), the wire pitch (pw), the wire diameter (Dw), the tube pitch (pt) or tube spacing (st), and the tube diameter (Dt). The wire pitch then defined the number of wires used in a certain width of tube coil width (W). As shown in **Figure 1** (top and side view), the wire-tube connections were different among these three configurations and this difference was expected to affect the heat exchanger performance.

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

#### **Figure 1.**

*The wire and tube heat exchanger fabricated and tested in this study with (a) inline, (b) single-staggered, and (c) woven matrix wire-tube configuration. Figure was adapted from Ref. [20] with permission.*

The evaluation of heat exchanger capacity and efficiency employed the custom-built heat exchanger testing apparatus as shown in **Figure 2a** [20, 21]. Hot fluid was pumped through the wire and tube heat exchanger, on which the surface temperature was monitored at nine different selected positions. The mass flow rate, pressure, and temperature before and after passing through heat exchangers were monitored as well. Details on the components of the heat exchanger testing apparatus are described in **Figure 2b**, and the specification is summarized in **Table 1**.

### **2.1 Experimental test for evaluating the wire and tube heat exchanger performance**

Running the experiment was started by soaking the working fluid, that is, oil Thermo 22, into the thermostatic vessel. It is worth noting that the apparatus was placed at constant room temperature (T∞). Afterward, the pump was turned on allowing for the cold fluid to flow in the piping and tubing system. At this juncture, if there was no leakage, the pump was then turned back off. To manipulate the inlet fluid temperature, the working fluid was heated by the installed electric heater inside the vessel, and the temperature was controlled at the desired value. The pump again was turned on to circulate the heated working fluid. In addition, the inlet mass flow could be tuned by adjusting the opening of valves in the apparatus

#### **Figure 2.**

*(a) The visual appearance of the heat exchanger testing apparatus, and (b) schematic of heat exchanger apparatus, which consists of thermostatic vessel embedded with electric heater, pump, pressure gauge, instrumentation box, flow meter, valves, and thermometer. Figure was adapted from Refs. [20,21] with permission.*


#### **Table 1.**

*The specification and operating conditions of each component in the home-built heat exchanger testing apparatus [20–24].*

and checked at the flow meter, which has an accuracy of 0.1 kg cm<sup>3</sup> . During the experiment, wire-tube temperatures at nine different points (Tw1 – Tw9 shown in **Figure 2b**), the inlet (Tin), and outlet (Tout) fluid temperature were recorded [22, 23].

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

## **2.2 Equations of convection**

To evaluate the resulting experimental data, the air properties including density (ρ), kinematic viscosity (υ), Prandtl number (Pr), conduction coefficient (k), thermal diffusivity (α) were interpolated for every Tout. These properties were then used to determine the Grashof number (Gr), Rayleigh number (Ra), and Nusselt number (Nu) using the following equation:

$$Gr = \frac{\text{g} \cdot \beta \cdot (T\_s - T\_\infty) \cdot L^3}{v^2} \tag{1}$$

$$Ra = \frac{\text{g} \cdot \beta \cdot (T\_s - T\_\infty) \cdot L^3}{va} \tag{2}$$

$$Nu = \frac{4}{3} \left(\frac{Gr}{4}\right)^{0.25} \cdot f(\text{Pr})\tag{3}$$

$$f(Pr) = \frac{0.75\sqrt{Pr}}{\left(0.609 + 1.221\sqrt{Pr} + 1.238Pr\right)^{0.25}}\tag{4}$$

The heat transfer coefficient was then calculated as follows:

$$h = \frac{Nu \cdot k}{L} \tag{5}$$

The heat exchanger capacity (Q) was then calculated based on the heat transfer coefficient in Eq. (5) using the following formula:

$$Q = h \cdot A \cdot (T\_s - T\_\infty) \tag{6}$$

where A is the total effective area of the wire and tube heat exchanger.
