Effects of Darcy and Viscous Dissipation on Natural Convection Flow in a Vertical Tube Partially Filled with Porous Material under Convective Boundary Condition

Abstract

In this paper, a study is presented considering the effects of Darcy and Viscous dissipation in a steady natural convection incompressible fluid through a vertical composite tube partially filled with a porous material. The fluid motion in the vertical composite tube is caused by a temperature gradient due to heat applied to the wall of the tube. The Brinkman Darcy extended model was used to stimulate the fluid flow under the working fluids of water and air. The Homotopy pertubation method was used to solve the temperature and velocity equations in both the clear and porous fluids. An increase in the Brinkman number increases the temperature and velocity profiles of both working fluids. An increase in the thickness of the porous material can be used to increase the velocity of the fluid in the composite vertical tube. An increase in the internal conductive resistance leads to a decrease in the buoyancy force and, as a result, the fluid thickness, which leads to a decrease in the velocity of the fluid.