**4. Performance evaluation of the wire and tube heat exchanger with varying wire-tube configuration**

Heat transfer process and its efficiency in the wire and tube heat exchanger are strongly dependent on the geometrical architecture between the wire and tube. In this section, the effect of wire-tube configuration, including inline, staggered, and woven matrix wire and tube, and the operating condition will be discussed based on the experimental investigation and numerical modeling using computational fluiddynamics (CFD).

### **4.1 The empirical efficiency formulation of the inline wire and tube heat exchanger**

To have a starting point for further geometrical optimization, here the simple inline wire and tube heat exchanger is discussed. An experimental investigation using different wire geometries, that is, wire pitch to wire length ratio (pw/Lw), under different operating conditions, that is, inlet fluid temperature of 40–80°C with 10°C intervals, has been carried out [28]. As the heat exchanger has been tested in an isolated and air-conditioned room, the heat exchanger can be assessed employing the relevant parameters and the dimensional analysis to generate a dimensionless equation following the π-Buckingham theory. Thus, the heat exchanger efficiency follows:

$$\eta\_o = \frac{q\_t}{q\_{\text{max}}} = \frac{h.s\_w(T\_w - T\_\text{\textinfty}) + h.s\_t(T\_t - T\_\text{\textinfty})}{h.s\_{\text{tot}}(T\_t - T\_\text{\textinfty})} \tag{22}$$

$$q\_t = f\left[q\_{\text{max}}, \mathbf{g}, \beta, a, v, \Delta T, pw, dw, Lw, pt, dt\right] \tag{23}$$

The above function can be grouped into several dimensionless parameters: *π***<sup>1</sup>** ¼ *q***1** *qmax* <sup>¼</sup> *<sup>η</sup><sup>o</sup>* is the heat exchanger efficiency, *<sup>π</sup>***<sup>2</sup>** <sup>¼</sup> *<sup>g</sup>:Lw***<sup>3</sup>** *<sup>υ</sup>***<sup>2</sup>** and *π***<sup>3</sup>** ¼ *ΔT:β* are the Grashof number parameters, *<sup>π</sup>***<sup>4</sup>** <sup>¼</sup> *<sup>α</sup> <sup>υ</sup>* is the reciprocal of Prandtl number, *<sup>π</sup>***<sup>5</sup>** <sup>¼</sup> *pw Lw* is the dimensionless wire pitch, *<sup>π</sup>***<sup>6</sup>** <sup>¼</sup> *dw Lw* is the dimensionless wire diameter, *<sup>π</sup>***<sup>7</sup>** <sup>¼</sup> *pt Lw* is the dimensionless tube pitch, and *<sup>π</sup>***<sup>8</sup>** <sup>¼</sup> *dt Lw* is the dimensionless tube diameter. The equation can then be reformulated as follows:

$$
\pi\_1 = f\left[\frac{\pi\_2.\pi\_3}{\pi\_4}\pi\_5, \pi\_6, \pi\_7, \pi\_8\right] \tag{24}
$$

Considering that the wire diameter (dw), the tube diameter (dt), and the tube pitch (pt) are constant, the general mathematical expression of the heat exchanger efficiency can be written:

$$\eta\_o = f\left[\frac{\mathbf{g}\cdot\boldsymbol{\beta}\cdot\Delta T\cdot Lw^3}{v\cdot a}, \frac{pw}{Lw}\right] \tag{25}$$

The above function suggests that the heat exchanger efficiency is a function of Rayleigh number (Ra) and the dimensionless wire pitch (or the wire pitch to wire length ratio (pw/Lw)).

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

#### **Figure 4.**

*Contour plot of the heat exchanger efficiency (log y) as a function of Rayleigh number (log x1) and wire geometry (log x2, where x2 = pw/Lw). Figures from Ref. [28] used with permission.*

**Figure 4** shows the contour plot of the heat exchanger efficiency (y) as function of Ra (x1) and the wire pitch to wire length ratio (pw/Lw) (x2). Fitting the experimental data using multivariable logarithmic regression results in the best fitting parameter (R2 = 0.897) with the resulting function as follows:

$$\begin{split} \log \eta\_o &= -8.650 + 2.161 \log R\_a + 0.259 \log \left( \frac{pw}{lw} \right) - 0.041 (\log R\_a)^2 \\ &- 0.146 \left( \log \left( \frac{pw}{lw} \right) \right)^2 - 0.084 \left( \log R\_a \times \log \left( \frac{pw}{lw} \right) \right) \end{split} \tag{26}$$

The above empirical formulation is considered a helpful finding to assist the heat exchanger optimization by taking into account both geometrical aspects of the wiretube configuration and the operating condition, which is limited by the optimum Ra value (log�<sup>1</sup> (x1) at which the log y is maximum).

As above discussed quantitatively, the Ra is dependent on the Prandtl number and Grashof number, and hence, the inlet mass flow inlet as well as the inlet fluid temperature plays role in determining the heat exchange efficiency. To gain its qualitative and quantitative correlation between these operating conditions to the wire and tube heat exchanger efficiency, **Table 2** summarizes the heat exchanger capacity (Q) and heat exchanger efficiency (η) upon varying the inlet mass flow and temperature [22, 23]. In this investigation, the wire and tube heat exchanger possess the following specifications: wire length of 445 mm, wire pitch of 7 mm, wire diameter of 1.2 mm, tube diameter of 5 mm, tube pitch of 476 mm, and tube turn of 12.

At a constant inlet mass flow of 5 � <sup>10</sup>�<sup>3</sup> kg s�<sup>1</sup> , the heat exchanger performance improves with increasing inlet fluid temperature. As the temperature increases, the outer surface temperature of wire and tube heat exchanger increases, and hence, the overall heat transfer rate is enhanced, that is, the internal forced convection and conduction from the fluid to the wire-tube elements, and the external radiation from the surface to surrounding and the free convection. Meanwhile, at the same fluid inlet temperature of 70°C increasing the mass flow from 4 � <sup>10</sup>�<sup>3</sup> kg s�<sup>1</sup> to


#### **Table 2.**

*Heat transfer capacity and heat exchanger efficiency for the inline wire and tube heat exchanger. Data are summarized from Refs. [22,23] upon permission.*

<sup>6</sup> <sup>10</sup><sup>3</sup> kg s<sup>1</sup> enhances the heat exchanger capacity by 24% and the efficiency also increases from 0.67 to 0.73. This increasing heat exchanger capacity is due to the higher mass flow in the tubes the higher the heat transfer rate to the surrounding colder air (at room temperature). This is simply reflected by the increasing inlet to outlet temperature difference ΔT, (Tin – Tout) which stems from the higher internal forced convection and external free convection as the mass flow increases.

#### **4.2 Inline vs. staggered vs***.* **woven matrix configuration**

It is already mentioned that the wire is designed as an extended surface (fin) that is capable to enlarge the heat transfer area in the wire and tube heat exchanger. In this section, this wire-tube configuration will be the focus of the discussion. It is already known that inline and staggered wire and tube heat exchanger have been utilized quite extensively. Nonetheless, some experimentations on the development of woven matrix wire-tube configuration have emerged as it likely combines both the inline and staggered wire-tube configuration.

To compare the heat exchanger capacity among these wire-tube configuration, inline, single-staggered, and woven matrix wire and tube heat exchanger have been fabricated with a variation of wire pitch, that is, 7, 14, and 21 mm [21]. To gain deeper insight, the inlet fluid temperature also varied from 50 to 80°C with 10°C intervals. The heat exchanger apparatus was run at 2 <sup>10</sup><sup>3</sup> kg s<sup>1</sup> inlet mass flow and the apparatus was placed in an air-conditioned room at 32°C. **Figure 5** displays the heat exchanger capacity of the wire and tube heat exchanger, which is affected by inlet fluid temperature, wire pitch, and the wire-tube configuration. In general, irrespective of the wire-tube configuration the heat exchanger capacity tends to increase with increasing inlet fluid temperature, whereas the heat exchanger capacity tends to decrease by enlarging the wire pitch irrespective of the wire-tube configuration. For 7 mm wire pitch (**Figure 5a**), inline configuration outperforms other configurations, which is plausible since for inline wire-tube configuration the number of wires used is larger than other configurations. This implies that the extended surface by the surface is enlarged, and thus, the heat transfer rate becomes more efficient.

It is interesting to note that the larger the wire pitch (see **Figure 5b** and **c**) the smaller the difference in heat exchanger capacity among three different wire-tube configurations. Particularly for 21 mm wire pitch, the heat exchanger capacity of a single-staggered configuration is on par with the inline configuration, in which the maximum heat exchanger capacity of 425 W is obtained at 80°C. The heat exchanger efficiency particularly for woven matrix wire and tube heat exchanger is shown in **Figure 5d**. An average of 69% heat exchanger efficiency is obtained

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

**Figure 5.**

*Different heat exchanger capacity of inline, single-staggered, and woven matrix wire and tube heat exchanger bearing pitch wire of (a) 7 mm, (b) 14 mm, and (c) 21 mm. (d) The efficiency of woven matrix wire and tube heat exchanger using different wire pitches and operated under varying inlet fluid temperature.*

for 7 mm wire pitch, while the efficiency drops 10% down by changing the wire pitch to either 14 or 21 mm. This reflects that there is a room for optimization by varying the wire pitch between 7 mm and 14 mm.

Digging into the heat transfer process inside the wire and tube heat exchanger the change in the heat transfer coefficient is shown in **Figure 6** for the utilization of heat exchanger with 7 mm and 14 mm wire pitch. Irrespective of the wire pitch, it is clear that the convection heat transfer coefficient tends to decrease with increasing inlet fluid temperature. While larger wire pitch results in a larger heat transfer coefficient, the inline wire-tube configuration consistently yields the lowest heat transfer coefficient compared to a single-staggered and woven matrix wire-tube configuration. As the convection drops down while the heat exchanger increases at higher inlet fluid temperature, this implies that the conduction from the inner wall to the outer surface of the tube as well as wire tube and the radiation from the surface of the tube to the surrounding dominates the heat transfer process at a higher temperature.
