The problem of electro-kinetically free convective heat flow in a slit micro-channel was studied, the non-dimensional quantities were utilized to change the governing equation from dimensional to dimensionless, the steady and unsteady solution were derived using theory of simultaneous ordinary differential equations and implicit finite difference scheme method respectively. The analytical solution is differentiated to derive the rate of heat transfer and shear stress. Graphical representations are provided for a number of important flow-controlling factors, including the Debye–Hückel parameter ( \(\kappa\) ), Non-linearity Density with Temperature (NDT), MHD, and Heat generating/absorbing parameter for velocity and temperature. The rate of heat transfer and shear stress were also depicted with aid of line graph and discuss in detail. The outcomes of the findings revealed that a slight increase in the Hartman number causes the Lorentz force, which streamlines the velocity boundary layer and slows the flow. However, as time (t) passed, both the slip case and the no slip scenario experienced an improvement in the velocity profile. The effect of NDT on velocity profile showed that the temperature of the fluid flow increased with increasing non-linearity factor with respect to time (t). As result that N magnifies the temperature, which increases kinetic energy furthermore, since only temperature can affect velocity when the parameter is present. It was also depicted that Debye–Hückel parameter ( \(\kappa\) ) tends to reduce the EDL effect, leading to a reduction in the EDL boundary layer but an increase in the electric potential in the micro-channel. However, as time (t) goes on, the fluid seen in the no-slip wall rises above the super-hydrophobic surface.
