Combined effects of Darcy and Viscous Dissipation on Steady Natural Convection flow in a Vertical Tube partially filled with Porous Material with asymmetric thermal boundary conditions

Abstract

This paper examines the impact of Darcy and Viscous dissipation on the hydrodynamic and thermal behavior of steady natural convection in a fully developed incompressible fluid flowing through a vertical composite tube with asymmetric thermal boundary conditions. The fluid motion in the tube is driven by a temperature gradient resulting from heat applied to the tube wall. The study employs the Brinkman-Darcy extended model to simulate fluid flow for both water and air working fluids. The homotopy perturbation method was chosen to solve the temperature and velocity equations for both clear and porous fluids. This method was selected because it systematically decouples the system and overcomes the limitations associated with small parameters in the commonly used perturbation method. Additionally, the homotopy perturbation approach highlights the interactions between parameters that are hidden in numerical methods. An increase in the Brinkman number enhances both the temperature and velocity profiles of the working fluids. Similarly, increasing the thickness of the porous material can boost the fluid's velocity in the composite vertical tube. A rise in the material's porosity also leads to an increase in fluid velocity.