Buoyancy Driven Flows and Heat Transfer Within a Vertical Porous Annulus Enclosed in a Cylinder

Abstract

Buoyancy driven flows and heat transfer within a vertical porous annulus enclosed in a cylinder are investigated. The inner wall of the annulus is maintained at an isothermal temperature Tc. The study is divided in two sections where the outer and bottom walls are subjected to a uniform heat flux separately. The fluid is assumed to obey the Darcy Law. Finite difference method is used to solve the partial differential equations governing the fluid flow and heat transfer behavior. The study is focused to investigate the effects of the convection, conduction, radiation, and geometry on the heat transfer within the annulus. Results are presented for different values of aspect ratio, Rayleigh number, Radiation parameter, and radius ratio. It is observed that variation in aspect ratio causes the flow to change from a highly conductive to convective regime. The Rayleigh number increases the convective effects in the cavity by increasing and decreasing the local Nusselt number for the top and bottom region of the inner wall respectively. The Radiation parameter increases the conductive effects causing uniformity in local Nusselt number throughout the inner wall. The radius ratio tends to scale the entire cavity causing the inner average Nusselt number to grow while keeping the bottom Nusselt number constant.

The radial heat flux on the outer wall keeps Nusselt number constant for all Ar, Ra and Rr values while increasing for Rd. The bottom heat flux on the other hand increases buoyancy effects in all conditions. The inner Nusselt number fluctuates based on Ar and Rd. while the bottom Nusselt number remains constant for all values.