Microscale heat transfer is essential in advanced thermal systems such as microchannel heat sinks, micro-heat pipes, and bio-microfluidic devices, where passive pumping mechanisms drive biological fluid transport. This study presents a novel bio-thermal pumping model for Casson fluid flow through a rough-walled vertical microchannel under the influence of a magnetic field. The governing equations are derived from mass, momentum, and energy conservation principles. Using dimensionless analysis and lubrication theory, analytical solutions are obtained and validated numerically via the Collocation method (implemented in MATLAB using bvp5c). The model examines the effects of surface roughness, thermal gradients, and buoyancy forces on velocity profiles, pressure distribution, volumetric flow rate, and streamline patterns. Additionally, entropy generation and the Bejan number are evaluated to assess thermodynamic efficiency. Quantitative results show that increasing wall roughness reduces the volumetric flow rate by 16.90%, whereas thermal buoyancy enhances it by 51.02%. The heat source parameter and Casson rheology further augment the pumping capacity by 31.20% and 68.49%, respectively. In contrast, magnetic field effects strongly suppress fluid transport, decreasing the flow rate by 70.56%. Key findings reveal that wall roughness dampens near-wall velocity while enhancing central flow, and that the Brinkmann number critically governs entropy production. These insights contribute to the optimization of microscale thermal-fluidic systems, particularly in biomedical applications where membrane-based heat transfer is pivotal.
Vaidya et al. (Thu,) studied this question.