An Approximate Analysis for Convective Heat Transfer on Thermally Nonuniform Surfaces

This paper presents a new, simple, but powerful technique for nonsimilar natural and assisting mixed convection heat transfer problems in which thermal boundary conditions are specified arbitrarily even with step discontinuities. Temperature and velocity fields for natural convection over thermally nonuniform surfaces are formulated in terms of equivalent Grashof numbers defined by the superposition of surface heat fluxes and velocities obtained from similarity analyses for isoflux or isothermal surfaces. A local heat transfer rate for assisting mixed convection over thermally nonuniform surfaces is approximated using Nusselt numbers for pure forced and pure natural convection over such surfaces, which are obtained by the superposition method. Comparisons with existing similarity solutions, experimental results, and numerical solutions validate the use of this simple superposition method in many practical situations such as cooling configurations in electronic and manufacturing equipment.