An Approximate Second-Order Multiscale Method for Calculating Temperature Distributions in Compact Heat Exchanger Structures with Constant Fluid Properties

An efficient performance evaluation method is important for designing compact heat exchangers (CHEs). Low-order calculations based on heat transfer correlations cannot provide detailed temperature fields, while three-dimensional simulations require substantial computational resources. In order to overcome these problems, a multiscale method for heat transfer in CHE structures is proposed in this paper. Homogenization analysis of the heat transfer equation with inner convective boundary conditions is conducted. The unit cell problems and homogenized heat transfer equations for the solid region are obtained. The effective thermal conductivity and other coefficients are related to the solutions of the unit cell problems. A one-dimensional heat transfer model for fluid channels is then coupled with the homogenized equations to solve for the average solid and fluid temperatures. Finally, the local temperature distributions around the flow channels can be obtained by combining average temperatures and unit cell solutions. The heat transfer in dual-channel structures with rectangular and semi-circular channels is used to validate the proposed multiscale method. The results demonstrate that although there are errors due to the simplifications in the multiscale model, the proposed method can be used to quickly evaluate the average temperature profiles for both the solid and fluid regions. The local temperature distributions around the flow channels can also be reconstructed.