On the Conjugate Problem of Laminar Combined Free and Forced Convection through Vertical Non-Circular Ducts

Abstract

The present analysis deals with the conjugate problem of combined free and forced convection through vertical non-circular ducts. The equations coupling heat conduction in the walls with the convection inside the fluid are solved to establish the influence of peripheral wall conduction, using variational technique. Fully developed laminar flow with uniform axial heat input and constant fluid properties, except for the small variation of density in the buoyancy term of the momentum equation, is assumed. The problem has been solved in a generalized way and the results have been presented for rectangular ducts. It is found that large values of the free convection effects and/or of the conduction parameter tend to minimize the asymmetries in circumferential wall temperature.

Combined forced and free laminar convection in horizontal tubes

“…"h -^-h--( Vl • " (4 2)where Pw * (hd^/kJ) (d^/t) is the tube wall parameter and s* = s/d^ is a dimenslonless circumferential coordinate. The tube wall parameter repre sents the ratio between the peripheral and radial thermal resistances and can be regarded as an extension of the nondimenslonal group proposed by both Iqbal et al[40] and Shah and London[41]. It can also be inter preted as the product of a Blot number and a two-dimensional geometrical ratio.…”