Computational Treatment of Unsteady Natural Convective and Mass Transfer Flow in a Vertical Microchannel Under Electroosmotic Effects

ABSTRACT In this article, the influence of heat and mass transfer on unsteady electromagnetohydrodynamic (EMHD) natural convection flow in a vertical microchannel with electroosmotic effects is examined. The dimensionless system of governing equations was solved analytically subject to appropriate initial and boundary conditions. The perturbation method was first adopted to decouple the system of equations arising from the coupled Soret and Dufour effects. Subsequently, with the aid of the Laplace transform technique, the governing energy, mass transfer, and momentum partial differential equations were reduced to ordinary differential equations to obtain analytical solutions for fluid temperature, concentration, and velocity in the Laplace domain. The semi‐analytical solutions for velocity, temperature, concentration, skin friction, and the Nusselt and Sherwood numbers were then derived using the Riemann sum approximation. A MATLAB program was developed to parametrically study the effects of the Dufour number, Soret number, radiation, heat source, Hartmann number, electric field strengths (in the x and z directions), Grashof number, and modified Grashof number on the fluid behavior. It is observed that an increase in the radiation parameter increases the temperature and velocity but decreases the concentration. Furthermore, an increase in time increases both the fluid concentration and velocity before they attain a steady state at large values of time. Likewise, an increase in the Debye–Hückel parameter and accelerates the velocity, while increases in and magnetic field parameter induce a deceleration. The velocity, temperature, and concentration profiles are presented graphically to demonstrate the impact of these arbitrary parameters.