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This work studies the flow of a non-Newtonian power-law fluid with viscous dissipation through a pipe with a variable expand ratio (B).The influence of the power law index (n), expand ratio (B), Darcy number (Da) and  Brinkman number(Br) on heat transfer and thermodynamics irreversibility is investigated. Equations of the problem are solved numerically using COMSOL software. Results show that heat transfer and entropy generation are deeply affected by selected governing parameters. Both thermal entropy generation and average Nusselt number are maximal at low power index and at high medium permeability. Power index effect is insignificant at relatively low Darcy number. Considering viscous dissipation with high Brinkman number, heat transfer direction can be reversed at moderate Darcy number and high power index.

This paper reports a numerical study about the viscous dissipation effect on steady sate of mixed convection in lid-driven porous square cavity. The analysis is performed using Darcy–Brinkman formulation with the Boussinesq approximation. The set of coupled equations of conservation of mass, momentum and energy are solved using the Control Volume Finite Element numerical method (CVFEM). The viscous dissipation model of Al-Hadhrami is used in this investigation and its expression is injected in the energy equation as a source term. Effects of viscous dissipation on thermal and Darcy viscous entropies generations are investigated. It was found that the heating effect, by viscous dissipation, significantly affects the thermodynamics irreversibility in the porous medium. Mainly more, results reveal that heat transfer irreversibility dominates for all Darcy number when viscous dissipation effect is taken into account.