Numerical study of non-darcy natural convection from two discrete heat sources in a vertical annulus

Abstract

A numerical investigation of natural convection heat transfer induced by two discrete heat sources placed on the inner wall of a vertical porous annulus has been carried out in this article. The outer wall is maintained at a lower temperature, while top and bottom walls and unheated portions of inner wall are kept adiabatic. The porous medium is modeled by using the Brinkman-extended Darcy equation. An implicit and stable finite difference technique has been used to solve the nonlinear and coupled governing equations of the flow system. For a wide range of modified Rayleigh and Darcy numbers and aspect and radius ratios, the analysis is carried out to understand the effect of discrete heating on the streamlines, isotherms, and the average Nusselt number. The qualitative changes in the flow patterns and isotherms due to discrete heating caused by two heat sources are successfully captured in the present analysis. It was observed that the heat transfer can be enhanced by increasing the radius ratio, modified Rayleigh number, and Darcy number, while it decreases with an increase in aspect ratio. Among the two heat sources, the bottom heater is found to dissipate higher heat transfer compared to top heater. The maximum temperature at the heat sources is also determined. We discuss many issues of the maximum temperature for different values of the modified Rayleigh and Darcy numbers, radius, and aspect ratios.