Irreversibilities and heat transfer in magnetohydrodynamic microchannel flow under differential heating

Abstract

This study investigates heat transfer and entropy generation in a microchannel subjected to differential heating, viscous dissipation, and Joule heating within a magnetohydrodynamic (MHD) fluid flow. A finite difference method with a fully implicit scheme is employed to accurately model temperature distribution and entropy generation. A comparison between the average Nusselt numbers (Nu) calculated using the classical method and the Bennett Formula reveals a notable discrepancy, particularly at the entry length (up to 14%). It has been found that when one plate is heated while the other is cooled and the Hartmann number (Ha) is low, the average Nu for both plates converges to 2. However, at high Ha values considering viscous dissipation and Joule heating, there is an 8% deviation between the Nu values of the two plates, with the higher Nu found on the cooling plate. Sensitivity analyses explore the impact of control parameters on entropy generation, emphasizing the significance of η as a key parameter that reflects the system's resistance to entropy generation. Increasing η from 0.1 to 0.5 results in a 32% reduction in entropy generation. In particular, for microchannels, substantial η high values imply reduced entropy generation, highlighting their efficiency in heat transfer.