Heat transfer analysis of mixed convection flow in a vertical microchannel with electrokinetic effect

In this article, the transient/steady mixed convective flow formation inside a vertical microchannel subjected to uneven wall zeta potentials in the presence of an electric body force is carried out theoretically. Employing the Navier–Stokes, Poisson–Boltzmann and energy equations, the velocity profile, electric potential and temperature distributions respectively governing flow formation and heat transfer in dimensional form are presented. Using appropriate dimensionless parameters, the corresponding dimensionless form of the governing equations are obtained. At the transient state, the Laplace transform technique is utilized while at the steady-state, direct integration as well as undetermined coefficients are employed to obtain solutions to governing equations. To justify solutions obtained, the steady state solution is found and compared with the implicit finite difference method at large time; this comparison gives an excellent agreement. Graphical simulations show that the skin-friction could have incurred an error of up to 19% if the buoyancy term in the momentum equation had been neglected. In addition, it is established that for a large electric double layer, the interval of no reverse flow at the microchannel walls is significantly extended.