In the present study, the unsteady magnetrohydrodynamic (MHD) flow of compressible fluid with variable thermal properties has been numerically investigated. The electrically conducting fluid flows through a porous media channel. The uniform magnetic field is applied perpendicular to the direction of the flow. The wall is assumed to be non-conducting and maintained at two different temperatures. The thermal conductivity and viscosity of the fluid change with temperature. Sixth - Order Accurate Compact Finite Difference scheme together with the Third-order Runge-Kutta method is used to solve a set of non-linear equations. The results of the calculation are expressed in the form of the velocity and temperature at different values of the magnetic field and porosity. The proposed mathematical model and numerical methods have been validated by comparing with the results of previously published studies that the compared results reveal the same trends. The difference is due to the compressibility and property variation effects. The results showed that the magnetic field and variable properties considerably influences the flows that is compressible thereby affecting the heat transfer as well as the wall shear stress
