The Effect of Heat Exchanger Design on Heat Transfer Rate and Temperature Distribution

The heat exchanger (HE) is a device that is used to complete the process of heat transfer between different matters without direct mixing. Therefore, it is of great importance in the transfer of energy and the completion of various energy transition processes. In the processes of HE between different energy systems, many factors influence and play a major and important role in the efficiency of transformation and exchange in forms of energy, such as the length, the material type, the exchange fluid, the surrounding environment

As noted before, the heat transfer improvement in shell and tube HE is considered part of the improvement of the shell or tube side. The tube enhancement is not only for tubers that belong to shell-tube HE but also for the other HE. Relying on the design conditions for HE, a large transfer area means enhancing the heat transfer. The fins are one of the ideas to maximize the area of the transfer. Desai et al. [42] investigated the fluid vibrations inside the HE provided by fins. He found that the fine arrays are stable, which aids in the stability of the HE body. Deng et al. [43] presented a study about the thermal storage with the HE provided by fins, and he found that the fins play a major role in storing the thermal energy. Different HEs are used according to the requirements [44]. Guo et al. [45] provided a design module for the HEs aimed at reducing the volume of the exchanger, with the aim of reducing the cost of the fabrication. Wang et al. [46] present work regarding the pattern and optimization of the multi-layer exchangers. The exchanger provided with the fin is widely used with low-pressure exchangers [47].
The new circuit HE is made from several plates and connected by diffusion bonding. The operating conditions deal with the channel system of the plates. The new conditions lead to a complex design. An example of the diffusion-bonded process is copper-nickel, nickel alloys, and titanium [25]. Figley et al. [48] studied the structure of the HE using numerical simulation and found a major effect of the structure on the HE work. Zheng et al. [49] developed a new channel with a new shape of the HE to investigate the efficiency. A transient flow is detected by the new design. Ma et al. [50] study the inclination of a new design numerically of the HE and the drop in the pressure.
Simulation software is one of the most important engineering tools in investigating information about the work of engineering devices, as this software is based on simulating the virtual reality of working conditions and calculating expectations and the effects resulting from operating these various systems [49,51,52]. As a result of what simulation programs are doing, many industrial and engineering systems have been developed recently, as these programs reflect a clear picture of the work of the different systems and indicate potential faults and ways to address them during engineering design, even in some cases after implementing the design in reality [45,48]. The simulation programs give hope of modifying the realistic designs with the lowest effort, cost, and best possible performance [32,53,54]. In this study, the operational and design conditions of the HE are highlighted, such as the flow rate of the matter inside the HEs, the length of the HE, and the effect of these conditions on the efficiency of the HEs.

2-Heat Exchange Theory
Typically, HEs are classified according to the internal arrangement, flow profile, and internal structure. One of the most widespread HEs depends on the flow of fluids inside it, so hot and cold fluids flow in the same direction or in the opposite direction in what is known as the parallel-flow or counter-flow HE, respectively. Figure.   The heat exchange calculations inside the HEs start by calculating the value of the overall heat exchange coefficient as shown in the equations below. This is followed by the calculation of the heat transfer rates, taking into account the different temperatures of the hot inlet and the cold inlet and their exits as well, so that the effect of heat exchange can be properly studied along the length of the HE and then shows the effect of HE conditions on the heat exchange value.
Taking into the consideration the effects of the fouling factors " " where it can be extracted as a fixed value based on the system used such as steam, refrigeration liquid, and others as well as the temperature effectiveness of all surfaces. Then the above equation will be: Where; Table 1 shows the values of the overall heat transfer coefficients as well as the values of the fouling factors for the selected systems. To design the HE several factor taken into the consideration based on the temperature distribution. The log mean temperature difference approach is considered for the design as the following: and, The above equations can be rewritten in term of using the temperate difference as: Finally, the overall heat transfer expressed as the Equation 3; For the parallel and counter HE, the total heat exchange is based on the temperature difference as log mean difference which is deeply depend on the structure of the HE as it is clear from the Figure 2. The heat transfer is depending on the structure of the HE as the amount of the heat at each stage effected by the direction of the flow. As a part of the structure effect the length of the exchanger effect the amount of the heat transfer as well as it can reduce or increase the time of the heat exchange.

Figure 2. The temperature distribution in the (A) Parallel HE, (b) Counter HE
The log mean temperature is calculated based on the structure of the HE with an assumption of insulated HE from its surrounding, negligible axial conduction along the tube, constant fluid specific heat, and constant overall heat transfer coefficient. So the log mean temperature can be given as: Where, the parallel-flow exchanger temperature condition is: and, the counter-flow exchanger temperature condition is: Figure 3 shows the flowchart of the work which is started from the HE selection to be parallel or counter flow the simulation code is run with different input of the HE length to the final step which is the result extraction which reflect the best length as well as the highest efficiency of the investigated HEs.

Figure 3. Research Methodology flowchart
The research methodology depends on testing the effect of the HEs lengths that start 10, 15, 20, and 25 m by using the simulation program code to re-work each time with a different length and comparing the effect of that length on the heat exchange and the temperature distribution and then testing the length that follows to finish the comparison and thus reach the result that It helps in choosing the most suitable HE with the best length for different engineering applications.

3-Results and Discussion
The results of this work are based on studying the effect of HE length for different types, including parallel and counter HE with a hot substance flowrate equal to 0.2 k and 0.3 kg/s for the cold substance. The effect of the HE length has been studied for several lengths, which are 10, 15, 20, and 25 m of the mentioned systems. Where it is found inside the parallel HE with liquid water medium, the heat transfer was increased by increasing the length of the heat transfer as it was 42.9 kW for the length of 10 m, 47.6 kW for the length of 15 m, 49.5 kW for the length of 20 m, and 50.2 kW for the length of 25 m. Figures 4A to 4D and Figures 5A to 5D show the temperature distribution inside the parallel HE with liquid medium between the hot and cold substances as it is clear that the temperature difference gap decreases by increasing the HE length as well as the heat transfer rate.  Figures 6A to 6D show the heat exchange process in the counter HE where it was found that by increasing the length of the HE the heat transfer is increasing as well where the heat transfer was 48.7 kW inside the HE with 10 m length, 58.6 kW inside the 15 m length HE, 65.1 kW inside the 20 HE length, and 69.6 kW inside the 25 m length HE. through the comparison between the parallel and counter HEs it was found that the counter HE is more efficient in the heat transfer as the values of the heat transfer rates is more in the counter HE compared to the parallel HE. Figure 7 A to D shows the temperature distribution inside the counter HE. It is clear that the temperature difference gap in the counter HE decreases with increasing the length of the HE as well as the heat transfer rate. The temperature profile for both HE parallel and counter shows two disadvantage which is the thermal stresses due to the large temperature difference at the end and the huge temperature difference gap which make the cold substance never reach the lowest temperature of the hot substance. The counter flow HE shows more advantages compared to the parallel heat flow exchanger which is a more uniform temperature difference distribution, the cold substance can reach the hot substance entrance temperature and more heat transfer homogenous distribution.
The results show the effect of the design conditions on the performance of the HEs, as we found that the length of the HE plays a major role in influencing the increase in heat exchange between the materials used in the HE (hot-cold). The heat exchange performance increases in the two types of HEs used, which are the parallel-flow exchanger and the counter-flow exchanger. The reason for the increase in the efficiency of the heat exchanges with increasing length is due to the increase in the surface area of the heat exchange and the increase in the time period to which the heat transfer materials are exposed between them. The results also show that the counter-flow HE has a higher efficiency than the parallel-flow HE because of the higher temperature difference in the counter-flow HE compared to the parallel-flow exchanger.
Many researchers studied the problems with HEs and ways to improve the quality of heat transfer in HEs. Here we found Wang et al. [46] who studied the increase in the heat exchange area, and they found that the efficiency of the HE increased, which is what was supported in this study. Zheng et al. [49] also studied the shape of the HE channels and found that by modifying the HE design internally, the efficiency of the HE is improved. Here we also found that this study supports this idea and develops the scientific content of that hypothesis.

4-Conclusion
Overall, this study is based on verifying the design conditions of parallel and counter-flow HEs, and in particular, studying the effect of increasing the length of the HEs on the efficiency of heat exchange. As it becomes clear from these results, the heat distribution within the HEs, whether in parallel or counter flow, is more homogeneous. The reason for the increase in the efficiency of HEs by increasing the length is due to the increase in the surface area of heat exchange and the increase in the time period for heat exchange processes inside the HEs. It was also found that by comparing the parallel and counter-flow HEs, the counter-flow HEs have a higher efficiency, and this is due to the reason of the temperature difference between the ends of the HE, which is higher than the temperature difference in the parallel-flow HE. In general, it is found that the change in the design conditions of HEs of different types often has an impact on increasing the efficiency of heat exchange. This is supported by previous research and scientific studies, and here it is recommended that studying the improvement of new design conditions is necessary to increase the efficiency of HEs in the future..

6-2-Data Availability Statement
The data presented in this study are available on request from the corresponding author.

6-3-Funding and Acknowledgements
I gratefully acknowledge the funding of the Project Number 428/2021, by the deanship of academic research -Mutah University, Jordan. This work is done by the researcher under Mutah University (Jordan) regulation and policy.

6-4-Conflicts of Interest
The authors declare that there is no conflict of interests regarding the publication of this manuscript. In addition, the ethical issues, including plagiarism, informed consent, misconduct, data fabrication and/or falsification, double publication and/or submission, and redundancies have been completely observed by the authors.