Conjugate Natural Convection: A Study of Optimum Fluid Flow and Heat Transfer in Eccentric Annular Channels

Abstract

Laminar natural convection-conduction heat transfer in vertically positioned annular channels with inherent eccentricity is investigated for optimum solid-fluid thermal conductivity ratio and optimum cylinder walls thicknesses allowing maximum induced fluid flow rate and heat transfer under varying geometry parameters, i.e., annulus eccentricity and radius ratio. A finite-difference technique is employed to solve the coupled momentum and energy equations for the cylindrical annulus walls and the annular fluid with Prandtl number 0.7. As part of the results, fluctuations in the induced fluid flow rate and heat transfer in the eccentric annular channel due to the conjugate effect, governed by the ratios of the solid and fluid thermal conductivities and thicknesses of outer and inner circular cylinder walls, are obtained for the boundary conditions of one wall heated isothermally and the other kept adiabatic. Commonly encountered ratios of the solid and fluid thermal conductivities and cylinder walls thicknesses are utilized in the present analysis. Results reveal that the optimum conductivity ratio and cylinder walls thicknesses increase nonlinearly with eccentricity and radius ratio. Such results can be very useful in effectively designing the heat transfer equipment for optimum performance.