Microchannel heat exchangers have become the preferred choice in contemporary technologies like electronics, refrigeration, and thermal management systems. Their popularity stems from their compact design and exceptional efficiency, which outperform traditional heat exchangers (HE). Despite ongoing efforts, the optimal microchannels for enhancing heat management, minimizing pressure drop, and boosting overall performance have yet to be identified. This study seeks to deepen our understanding of heat transmission and fluid dynamics within a cross-flow microchannel heat exchanger (CFMCHE). Utilizing numerical modeling, it examines how various physical aspects—such as channel geometry, spacing between channels, the number of channels, and the velocity at the inlet—affect key performance indicators like pressure drop, effectiveness, Nusselt number, and overall efficiency. To enhance the design, we analyze six unique shapes of crossflow microchannel heat exchangers: circular, hexagonal, trapezoidal, square, triangular, and rectangular. We employ the Galerkin-developed weighted residual finite element method to numerically address the governing three-dimensional conjugate partial differential coupled equations. The numerical results for each shape are presented, focusing on the surface temperature, pressure drop, and temperature contours. Additionally, calculations include the efficacy, the heat transfer rate in relation to pumping power, and the overall performance index. The findings reveal that while circular shapes achieve the highest heat transfer rates, they underperform compared to square-shaped CFMCHEs. This underperformance is largely due to the increased pressure drop in circular channels, which also exhibit a 1.03% greater reduction in effectiveness rate than their square-shaped counterparts. Consequently, square-shaped channels, boasting a performance index growth rate of 53.57%, emerge as the most effective design among the six shapes evaluated. Additionally, for the square-shaped CFMCHE, we include residual error plots and present a multiple-variable linear regression equation that boasts a correlation coefficient of 0.8026.
