In this study, we numerically investigated the transient steady state for the problem of double-diffusive convection in porous triangular enclosures with the effects of thin fin, various thermal and concentration boundary conditions in the presence of heat source. Finite difference method was employed to solve the dimensionless governing equations of the problem. The effects of governing parameters, namely heat generation parameter, buoyancy parameter and Lewis number on the streamlines, temperature and concentration contours as well as selected velocity component in the x-direction, Nusselt and Sherwood numbers and average Nusselt and Sherwood numbers at the enclosure bottom wall in the case of fixed boundary conditions and the case various boundary conditions were considered. The present results are validated by favorable comparisons with previously published results. All the results are presented in graphical and tabular forms and discussed.