In this article, the problem of combined forced and natural convection in a vertical porous channel for both regular fluids and nanofluids has been solved by perturbation and numerical methods, taking into account the influences of viscous heating and inertial force. In this regard, various types of viscous dissipation models, including the Darcy model, the power of drag force model, and the clear fluid compatible model, were considered to account for viscous heating. In addition, the mass flux of nanoparticles was also considered in terms of Brownian and thermophoresis mechanisms. The velocity and temperature distributions of both the regular fluid and nanofluid and the Nusselt number values were determined by considering isothermal boundary conditions in terms of Grashof, Reynolds, Forchheimer, Brinkman, and Darcy numbers. Moreover, the results of the numerical method were validated against those predicted by the perturbation method for small values of the Forchheimer drag term and the Brinkman number. In addition, the results obtained for both the nanofluid and the regular fluid were compared in terms of dimensionless parameters such as Brinkman number, Forchheimer drag term, pressure drop, Grashof-to-Reynolds-number ratio, Darcy number, and nanoparticle mass flux. The predicted results clearly indicate that the presence of nanoparticles enhances the Nusselt number values significantly.