A spectral relaxation method for linear and non-linear stratification effects on mixed convection in a porous medium

In this composition, we use a new spectral relaxation method (SRM) to investigate the effects of linear and non-linear stratification on mixed convective transport along a vertical surface embedded in a porous medium and it is viewed for the first time in both aiding and opposing buoyancy cases. The governing partial differential equations are transformed into ordinary differential equations using similarity transformation and then the resulting differential equations are solved numerically using SRM. A comparison is also made about the accuracy of SRM results in relation to the results obtained using the shooting method. We show that the proposed technique is an efficient numerical algorithm with assured convergence that serves as an alternative to common numerical methods for solving nonlinear boundary value problems. A parametric study of the physical parameters involved in the problem is conducted and a representative set of numerical results is illustrated, with accent on the comparison between linear and non-linear stratification. It is significant to notice that the separation of flow is found to be more in the absence of stratification whereas it is less in the presence of stratification. Finally, thermal and solutal stratifications significantly affect the heat and mass transfer rates, besides delay the boundary layer separation.