Performance of a serpentine heat exchanger: Part II – Second-law efficiency
Introduction
Heat exchangers are widely used for heat transfer between a hot stream and a cold stream in thermal systems. In the heat exchanger industry, effectiveness is commonly used as a scale to evaluate the performance of a heat exchanger. The effectiveness of a heat exchanger is defined as the actual heat transfer rate divided by the maximum possible heat transfer rate [1], [2]. To some thermal systems, the main concern is the amount of thermal energy being transferred from a hot stream to a cold stream. In these systems, the effectiveness indeed reflects the performance of the heat exchangers in carrying out the mission. However, to some thermal systems, the main concern is the amount of exergy being transferred from a hot stream to a cold stream. The received exergy in the cold stream will be converted into work or cooling effect. The more the amount of exergy is received by the cold stream, the better the system performance is achieved. To evaluate the performance of the heat exchangers in these thermal systems, the effectiveness is no longer valid and an evaluation factor based on the second law of thermodynamics must be used.
Bejan [3], [4], [5], [6] presented the pioneer work on designing heat exchangers based on the second law of thermodynamics. The design strategy is to minimize the entropy generation in heat exchangers. He also made a clear review of the earlier work in this area [7]. San et al. [8] analyzed the second-law performance of a two-dimensional regenerator. The optimum channel length and operating period were obtained. San et al. [9] investigated the second-law performance of a wet cross-flow heat exchanger. Two optimum operations were found. Qureshi et al. [10] investigated the second-law efficiency of a counter-flow cooling tower and an evaporative cooler. The result shows that the variation in the dead state would not significantly affect the efficiency. Gupta et al. [11] performed a second-law analysis of a cross-flow heat exchanger in the presence of axial dispersion in one fluid. Wu et al. [12] defined an exergy transfer effectiveness for evaluating the performance of heat exchangers. The effects of Ntu, ratio of heat capacity rates and flow patterns on the exergy transfer effectiveness were investigated. Wang et al. [13] analyzed the exergy loss in a rotary air preheater. Saechan et al. [14] performed a second-law analysis to determine the optimal configuration of a finned-tube condenser. Gorla et al. [15] investigated the entropy generation in a phase-change microscale flow. Sahiti et al. [16] performed a second-law based optimization analysis for a double-pipe pin fin heat exchanger.
In the past two decades, much work relating to designing heat exchanger based on the second law of thermodynamics was performed by researchers. However, in the heat exchanger industry, this design technique is still not as popular as the LMTD method or the ε–Ntu method. Hence, developing a systematic procedure and providing useful data for this technique in order to facilitate heat exchanger designers to follow is an important task to researchers. This work intended to express the second-law efficiency of a cross-flow serpentine heat exchanger (Fig. 1) as a function of number of transfer units (Ntu), ratio of heat capacity rates and other relevant parameters. The acquired data will be useful to designing this heat exchanger for waste heat recovery.
Section snippets
Governing equation of heat transfer
The configuration of the serpentine heat exchanger is shown in Fig. 1. The upper-half surface of the first tube and the lower-half surface of the last tube were considered to be insulated. In the analysis, the y-coordinate was chosen to be along the path of the tube flow and the x coordinate was along the path of the flow outside the tubes (channel flow). In addition, the tube flow was mixed and the channel flow was unmixed. If so, the governing equations of the heat transfer for the tube flow
Results
Fig. 3 shows the second-law efficiency (ηII) and effectiveness (ε) of the serpentine heat exchanger at various Ntu and values. The N and ΔPc/Po values were fixed at 5 and 0.0001, respectively. The result shows that the ηII value increases with the Ntu value. However, the increasing rate decreases with an increase of the Ntu value.
As shown in Fig. 3, at a fixed Ntu value, the heat exchanger has a maximum ηII value (ηII,max). The optimum value corresponding to the ηII,max value slightly
Conclusions
For the considered waste heat recovery, the second-law efficiency (ηII) of the serpentine heat exchanger can be expressed as a function of Ntu, , θ∗, N and ΔPc/Po. The ηII value is weakly dependent on the number of rectangular tubes (N) in the serpentine heat exchanger. For a set of Ntu, θ∗, N and ΔPc/Po values, a maximum ηII value (ηII,max) was found. The optimum value corresponding to the ηII,max value is very close to 1.0. However, the result of the analysis also shows that the
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