Extended Lévêque solution for heat transfer to non-Newtonian fluids in pipes and flat ducts

Abstract

The problem of predicting the rate of heat transfer through the wall of a duct in which a nonNewtonian fluid is flowing in laminar regime is analyzed in the present contribution. The effect of heat generation by viscous dissipation is also considered. In this work an alternative route, to deduce an extension of the Lévêque solution, is presented up to terms including the effect of the Brinkman number. The results so obtained are compared with previous results showing that our final expression, valid for pipes as well as flat ducts, produces extremely good results within the range of validity of the variables which is specified.