Abstract This paper aims to numerically analyze the melting effect on transient mixed convective heat transfer from a vertical plate in a liquid saturated porous medium. The Darcy’s flow with the Boussinesq approximation and energy equations for this study is transformed into the non-dimensional equations by using pseudo-similarity coordinate ( ζ) and dimensionless time ( ξ). The resulting the boundary value problem is solved by the method of lines (MOLs) with central finite difference and Newton’s iteration to completely obtain the solutions for the whole transient mixed convective heat transfer from transient heat conduction to steady mixed convection in porous medium with melting effect in the presence of aiding and opposing external flows. As shown in the results, it is both found that the rate of dynamic heat transfer is reduced with increasing melting strength and the response time from transient heat conduction to steady mixed convection in porous medium for aiding external flow is shorter than that for opposing external flow in the presence of melting effect. Additionally, the melting effect may be reduced with increasing mixed convective strength Gr/ Re 1/2 during transient mixed convective heat transfer in porous medium with aiding external flow.