Thermal transport in an inclined rough-membrane microchannel: impact of MHD on Ree-Eyring fluid flow

Heat transfer and entropy generation in microchannels are crucial to several industrial applications, particularly in device cooling and performance enhancement. These aspects are also significant in healthcare sectors, where microchannel-based systems are employed in processes such as dialysis and diagnostics. The current study investigates these phenomena in a microchannel with a non-uniform rough surface membrane attached to both walls, under the influence of a transverse magnetic field. Unlike conventional peristaltic or smooth-wall microchannel models, the present study focuses on a non-uniform rough-membrane configuration to simultaneously examine its influence on pumping performance, thermal transport, and entropy generation in a Ree-Eyring fluid. This combined analysis provides new insights into the interactions among wall roughness, membrane actuation, magnetic effects, and irreversibility, which have been poorly investigated in the existing literature. By employing a low Reynolds number and long-wavelength approximation, the governing equations are solved analytically to obtain the velocity profile, volumetric flow rate, temperature distribution and entropy generation analysis. Furthermore, the results of the present investigation are demonstrated and analyzed using MATLAB software. The results reveal that the rate of heat transfer is enhanced with the increase in key parameters, in conjunction with the membrane propagation. An increase in entropy generation is observed with rising Brinkman number and heat source parameter; however, this effect can be mitigated by adjusting the temperature difference.