In this article, the effects of viscous dissipation and inertial force on the velocity and temperature distributions of the mixed convection laminar flow in a vertical channel partly filled with a saturated porous medium have been studied. In this regard, the Brinkman–Forchheimer extended Darcy model was adopted for the fluid flow in the porous region. In addition, three different viscous dissipation models with isoflux-isothermal boundary conditions were applied. To determine the velocity and temperature distributions for both the regions, the coupled non-linear governing equations were solved using two parameter perturbation and numerical methods. Moreover, the results of the numerical method were validated against those predicted by the perturbation method for small values of the dimensionless perturbation parameters. Furthermore, the results obtained for both regions were compared in terms of Grashof, Reynolds, Forchheimer, and Brinkman numbers. The predicted results clearly indicate that the type of viscous dissipation model has a significant effect on the temperature and velocity distributions.
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