Simultaneous effects of viscous and Darcy dissipation on mixed convection flow in an annulus partially filled with porous material: Analytical approach

Abstract

The effect of thermal dissipation on a steady, fully developed, mixed convection viscous, incompressible fluid in an annulus partially filled with porous materials has been thoroughly examined in this work. Fluid flow begins within the annulus when a pressure gradient is applied abruptly in the flow direction. The fluid flow in the porous zone is characterized by the Brinkmann‐extended Darcy model. The fluid is divided into transparent and porous parts by a minimal interface. By matching their velocities and considering the shear stress jump conditions at the interface, the clear fluid and the porous region are connected. Additionally, the viscous dissipation effect is considered while determining the energy equation in the clear fluid zone. However, in the porous area, the Darcy dissipation effects are considered in addition to the viscous dissipation influence. In the model, the results of various fluid parameters in the problem were addressed using line graphs and the homotopy perturbation method. The study found that when the porous region's thickness grows, heat transmission on the annular surface enclosing the clear fluid region increases while it decreases on the border surface close to the porous region. In addition, a thicker porous region requires a greater pressure gradient to propel the flow.