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Analytical solution for heat transfer problem in a cross-flow plate heat exchanger
International Journal of Heat and Mass Transfer ( IF 5.2 ) Pub Date : 2020-12-01 , DOI: 10.1016/j.ijheatmasstransfer.2020.120410
Mehdi Seddiq , Mehdi Maerefat

Abstract Cross-flow plate heat exchangers are used for plenty of applications in industrial and domestic sectors, and the analysis of heat transfer is a key for the evaluation of their performance. There are challenges for an analytical study because heat transfer in each channel is governed by a partial differential equation coupled with temperature fields in the adjacent channels representing a three-dimensional problem. The problem is even more complicated in the turbulent regime as the effective thermal diffusivity varies within the channel cross-section. In the present study, a separate set of governing equations and boundary conditions are considered for each part of the heat exchanger. Appropriate profiles for the flow velocity and thermal diffusivity are substituted into the governing equations of the channels. The resulting partial differential equations in the channels are solved using the separation of variables method. There remains an unknown boundary condition linked to the temperature field on the plate surface which is considered to be in the form of a two-variable series function whose coefficients are calculated by applying energy balance between the two sides of the plate. The obtained solution provides explicit expressions for the temperature fields in the plate and channels. A scaling analysis is conducted showing that the model is valid when Peclet numbers in both hot and cold channels are not small. The results are compared with empirical data and a numerical model, and the accuracy of the derived heat transfer coefficients is investigated. In harmony with the scaling analysis, a close agreement is observed in both laminar and turbulent flows for moderate and high Prandtl numbers and when Peclet number is greater than 1000 in the case of turbulent flow.

中文翻译:

错流板式换热器传热问题解析解

摘要 错流板式换热器在工业和家庭领域有着广泛的应用,传热分析是其性能评价的关键。分析研究存在挑战,因为每个通道中的热传递由偏微分方程控制,并且相邻通道中的温度场代表一个三维问题。由于有效热扩散率在通道横截面内变化,因此在湍流状态下问题更加复杂。在本研究中,换热器的每个部分都考虑了一组单独的控制方程和边界条件。流速和热扩散率的适当分布被代入通道的控制方程中。通道中产生的偏微分方程使用变量分离方法求解。仍然存在与板表面温度场相关的未知边界条件,该边界条件被认为是二变量级数函数的形式,其系数通过应用板两侧之间的能量平衡来计算。获得的解决方案为板和通道中的温度场提供了明确的表达式。标度分析表明,当热通道和冷通道中的 Peclet 数都不小时,该模型是有效的。结果与经验数据和数值模型进行了比较,并研究了导出的传热系数的准确性。与标度分析相一致,
更新日期:2020-12-01
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