2.3 Data acquisition

The main purpose of our experimental study is to construct the relationship among the heat transfer rate q, heat transfer surface area A, heat capacity rate c of each fluid, overall heat transfer coefficient U, and fluid terminal temperatures [10]. To conduct the heat transfer analysis of an exchanger, the basic relationships that are applied for this purpose are the energy balance based on the first law of thermodynamics, as outlined in Eq. (1).

$$Q = \dot{m} \ (i\_2 \dot{\imath}\_1) \tag{1}$$

where m\_ is the rate of mass flow, i1 and i2 represent the inlet and outlet enthalpies of the fluid, and Q is the heat transfer rate between hot fluid and cold fluid.

As shown in Figure 5, a two-fluid counterflow exchanger is considered to present variables relating to its thermal performance. Although flow arrangement may be different for different exchangers, the basic concept of modeling remains the same. The following analysis is intended to introduce important variables for heat exchanger.

If the fluids do not undergo a phase change and have constant specific heats with di = cp � dT, heat transfer rate released from the hot fluid (Q <sup>h</sup>) and absorbed by the cold air (Q <sup>c</sup>) can be expressed as

$$Q\_h = \dot{m}\_h C\_{p,h} (T\_{h\_1} - T\_{h\_2}) \tag{2}$$

and

$$Q\_{\mathcal{L}} = \dot{m}\_{\mathcal{c}} c\_{p,\mathcal{c}} (T\_{c\_2} - T\_{c\_1}) \tag{3}$$

The subscripts h and c refer to the hot and cold fluids, and the numbers 1 and 2 designate the fluid inlet and outlet conditions, respectively.

Thus, the average value of the heat transfer rate is calculated as

$$Q\_m = \frac{Q\_h + Q\_c}{2} \tag{4}$$

Eq. (5) reflects a convection-conduction heat transfer phenomenon in a twofluid heat exchanger. The temperature difference between the hot and cold fluids (ΔT = Th�Tc) constantly changes along with heat exchanger. Therefore, in order to conveniently analyze the heat transfer performance of heat exchanger, it is

Figure 5.

The energy balance for the hot and cold fluids of a two-fluid heat exchanger.

Heat and Mass Transfer in Outward Convex Corrugated Tube Heat Exchangers DOI: http://dx.doi.org/10.5772/intechopen.85494

important to establish an appropriate mean value of the temperature difference between the hot and cold fluids such that the total heat transfer rate Q between the fluids can be determined from

$$Q = UA\Delta T\_{\mathfrak{m}} \tag{5}$$

The heat transfer rate Q is proportional to the heat transfer area A, the average overall heat transfer coefficient based on the area U, and mean temperature difference ΔTmax ΔTm between the two fluids. This means that temperature difference is a log-mean temperature difference (for counterflow and parallel-flow exchangers).

$$
\Delta T\_{\rm m} = \frac{\Delta T\_{\rm max} - \Delta T\_{\rm min}}{\ln \frac{\Delta T\_{\rm max}}{\Delta T\_{\rm min}}} \tag{6}
$$

ΔTmax and ΔTmin, respectively, represent the maximum and minimum one between ΔT1 and ΔT2.

In the experiments, the tube-wall temperature was not measured directly. The heat transfer coefficient of the tube side (hi) is determined from:

$$\frac{\mathbf{1}}{U} = R\_t = \frac{\mathbf{1}}{h\_i} + \frac{A\_i \ln \left(r\_o/r\_i\right)}{2\pi kL} + \frac{A\_i}{A\_o h\_o} \tag{7}$$

where ri and ro are the inner radius and outer radius of the test tube, respectively. Ai and Ao are the inner and outer surface area of the tube, respectively. k is the thermal conductivity of tube material, L is the length of the heat exchange tube, and hi and ho are the heat transfer coefficients for inside and outside flows, respectively.

The Nusselt number can be calculated as

$$Nu = \frac{h\_i \cdot D\_i}{k} \tag{8}$$

where D is the characteristic diameter; the thermal conductivity k is calculated from the fluid properties at the local mean bulk fluid temperature.

The Reynolds number is based on the average flow rate of the test section.

$$Re = \frac{D \cdot u \cdot \rho}{\mu} \tag{9}$$

where μ is the dynamic viscosity of the working fluid, and u is the mean velocity. The friction factor (f) can be written as

$$f = \frac{\Delta p}{\frac{L}{D} \cdot \frac{\rho u^2}{2}}\tag{10}$$

where Δp is the pressure drop in the test section.

The performance evaluation criterion (PEC) is a dimensionless ratio, which is used for the evaluation of the overall performance of the enhanced tube and defined as follows:

$$\text{PEC} = (\text{Nu}\_c/\text{Nu}\_s) / \left(f\_c/f\_s\right)^{1/3} \tag{11}$$

When PEC > 1, it indicates that the enhanced tube has an advantage over the smooth tube; otherwise, the corrugated heat transfer component compares unfavorably with the smooth tube.

## 2.4 Heat and mass transfer performance

For the engineering applications and to design exchangers, the prediction of heat and mass transfer performance is important. We presented experimental data on the Nusselt numbers for turbulent regimes. In our experimental study, the hot fluid is at the tube side, and the cold fluid is at the shell side.

The heat transfer and resistance performance of corrugated tube are compared to smooth tube, aiming to reflect the superior of the corrugated tube. Ratio of Nu in the corrugated tube to that in the smooth tube (Nuc/Nus) and ratio of f in the corrugated tube to that in the smooth tube (fc/fs) are adopted to indicate the enhancement degree of heat transfer and flow resistance performance.

Figure 6 shows the effect of Rec (Re of the cold fluid) on Nuc/Nus, fc/fs, and PEC, along with the changing Re<sup>h</sup> (Re of the hot fluid). The figure exhibits that with the increase of Re, Nuc/Nus, fc/fs, and PEC decline. The decreasing rate of Nuc/Nus and PEC is almost linear, but fc/fs is decelerated.

Figure 6. Flow and mass transfer performance. (a) Nuc/Nus; (b) f/fs; (c) PEC.
