where $\rho ,u\xaf,v\xaf,p\xaf,\mu ,$ and $Ex$ denote the fluid density, axial velocity, transverse velocity, pressure, fluid viscosity, and electrokinetic body force, and $g,\alpha ,T,cp,k$, $\phi $, $\sigma $, and $\Omega $ denote the acceleration due to gravity, coefficient of linear thermal expansion of fluid, temperature, specific heat at constant pressure, thermal conductivity, viscous dissipation, the electrical conductivity of the buffer fluid, and the heat absorption parameter. The first and second terms of Eq. (5) indicate the thermal energy transfer due to convection and thermal diffusion, respectively, while the third, fourth, and fifth terms show thermal energy generation in the system due to viscous dissipation, heat absorption, and Joule heating, respectively. The electric potential within the microchannel is given by according to well-known Poisson–Boltzmann equation as
Display Formula

(6)$\u22072\Phi \xaf=\u2212\rho \xafe\epsilon $