Flow and Heat Transfer in Concentric and Eccentric Rotating Cylinders with a Porous Sleeve

Abstract

Analytical solutions are re ported for flow and heat transfer between two concentric and eccentric rotating cylinders with a porous sleeve attached to the outer cylinder. While the inner cylinder rotates with a constant angular velocity, the outer cylinder remains stationary. The flow in the annular gap is governed by Navier -Stokes equations and the flow inside the porous sleeve is governed by the Brinkman -extended Darcy law. The solutions are sought using the regular perturbation method. Solutions up to the second leading terms are presented. For comparison, the case with no porous sleeve is also studied. The effects of several parameters, such as the Darcy number, Brinkman number, eccentricity, and thickness of the porous sleeve, are investigated. Nomenclature a inner cylinde r radius, [m] Br Brinkman number, Br = �U 2 /�Cp(T H-TL) b porous sleeve inner radius, [m] Cp specific heat capacity, [J/kg·K] c outer cylinder radius, [m] Da Darcy number, Da = K/b 2