Effects of vorticity, displacement speed and curvature on heat transfer with dissipation

Abstract

The method of matched asymptotic expansions has been used to analyze heat transfer with dissipation in forced convection, incompressible laminar flow on a surface with curvature. By using the well known solutions to the Falkner-Skan wedge flow and the corresponding energy equation with dissipation as the first order effects, the second order solutions to the energy equation including dissipation have been obtained. The calculated second order temperature profiles have been presented graphically as functions of the pressure gradient parameter and Prandtl number, to exhibit the effects of free-stream vorticity, displacement speed, longitudinal and transverse curvatures. The second order heat transfer, like the second order skin friction, becomes singular in adverse pressure gradients close to first order separation. Further, for the displacement speed problem and the curvature problems, other singularities occur at critical values of the pressure gradient parameter, just as for the second order skin friction. When there is no singularity, dissipation can affect heat transfer considerably, changing the Nusselt number from positive to negative, depending on the magnitude of the Eckert number. An increase of Prandtl number enhances the effects of dissipation.