Heat transfer from a permeable square cylinder to a flowing fluid

Abstract

Flow and heat transfer from an isolated square cylinder maintained at a constant temperature is considered. The cylinder is porous with constant permeability and porosity. The cylinder is placed horizontally and is subjected to an uniform flow of air. Forced convection heat transfer from the cylinder is analyzed for different values of Darcy numbers (10 −6–10 −2) at low Reynolds numbers. Brinkman model with an additional Forchheimer term has been used to model the flow in the porous media. The effect of Darcy number and porosity on the drag coefficient, length of the wake behind the cylinder, Nusselt number at each face of the cylinder and the overall Nusselt number of the cylinder have been analyzed for Reynolds numbers 1–40. The important results of the study can be summarised as follows: • The flow is steady for the range of Reynolds and Darcy numbers considered here. The flow pattern through and around the porous cylinder depends much on the Darcy number of the porous medium. At small Darcy numbers (=10 −6), the permeable cylinder behaves like a solid cylinder with no fluid penetrating the surface. With increasing Darcy numbers the fluid starts penetrating the surface with ease. • The drag coefficient, mean Nusselt number and wake length of the permeable square cylinder approaches the corresponding case of a impermeable cylinder placed in an unbounded domain for very low Darcy number, typically at Darcy numbers 10 −6. With increasing Darcy number the drag coefficient and wake length decreases. Flow separation from the cylinder is delayed with increasing Darcy number. • Fluid impinging the front surface carries away more heat than any other surface resulting in a high local Nusselt number along the front surface which increases with increase in Darcy number while it decreases along the other three faces. But the mean Nusselt number of the cylinder shows an enhancement in heat transfer rates with increasing Darcy numbers and Reynolds number.