Coupled electroosmotic-electromagnetohydrodynamic transport in a vertical microchannel with suction/injection: Heat and mass transfer analysis for Lab-on-a-Chip cooling applications

Heat and mass transfer in vertical porous microchannels plays a crucial role in the design of micro heat exchangers and the cooling of micromechanical and microelectronic systems. When electroosmotic and electromagnetohydrodynamic (EO-EMHD) effects are incorporated, these channels enable active flow manipulation, mixing, and thermal regulation in Lab-on-a-Chip (LOC) devices, thereby broadening the scope of microscale cooling applications. This study investigates the effect of wall suction/injection on unsteady EMHD natural convection flow in a vertical microchannel, accounting for heat and mass transfer mechanisms. The dimensionless governing equations were formulated and solved analytically using appropriate initial and boundary conditions. Due to the coupled nature of the Soret and Dufour effects, a perturbation approach was employed to decouple the governing equations, which were then transformed from partial differential equations (PDEs) into ordinary differential equations (ODEs) using the Laplace Transform technique. Analytical expressions for velocity, temperature, and concentration were obtained in the Laplace domain, along with derived quantities such as skin friction, Nusselt number, and Sherwood number, evaluated through the Riemann-sum approximation. A MATLAB program was developed to examine the effects of key parameters including thermal radiation, Soret number, Dufour number, Grashof number, modified Grashof number, electric field strengths in the x and z directions, and the Hartmann number on the transport characteristics under suction and injection conditions. The results reveal that increasing the radiation parameter enhances the temperature and velocity but decreases the concentration. Similarly, higher Ez, Gr, and Gm values lead to higher velocities, while increases in Ex and M suppress fluid motion. The findings provide physical insight into electro-magnetically driven convective transport in microchannels, highlighting the influence of cross-diffusion, radiation, and field effects on flow and thermal performance, offering valuable guidance for the design and optimization of Lab-on-a-Chip cooling systems.