Second-Law Analysis of Mini/Micro Counterflow Parallel-Plate Heat Exchangers: Optimizing Effectiveness by Minimizing Wall Entropy Production

We present an analytical and numerical study of the entropy production rate in laminar counterflow parallel-plate heat exchangers, aiming to investigate the interplay between multidimensional wall conduction, entropy production, and the optimum wall conductivity that leads to maximum effectiveness. The analysis assumes that the Peclet number is sufficiently large to neglect axial conduction in the fluids, while multidimensional wall conduction is retained as the main ingredient of this work. A parametric study is conducted to examine the influence of the two parameters that govern multidimensional wall conduction: the dimensionless wall thickness and the dimensionless wall thermal resistance. The overall entropy balance leads to an approximate relationship between the heat exchanger effectiveness and the rate of entropy production, reflecting the so-called entropy generation paradox. For moderately long heat exchangers with effectiveness above those of coflow systems, it is observed that the maximum effectiveness is correlated to a minimum in overall entropy production, but this result does not hold for shorter heat exchangers with smaller effectiveness. However, the analysis reveals a universal connection between maximum effectiveness and minimum wall entropy production not previously established in the literature, indicating that wall-related factors dominate over fluid-related entropy production in determining optimal heat exchanger operation. These findings are particularly relevant for the design and optimization of compact thermal systems in applications such as microelectronics cooling and aerospace thermal management.