Heat transfer from surfaces of non-uniform temperature

Abstract

The paper deals with the calculation of steady heat transfer from a surface of arbitrary temperature distribution to a laminar semi-infinite stream of arbitrary velocity distribution. Lighthill's method is improved by a correction which accounts for the departures from linearity of the velocity profile within the thermal boundary layer, and which comprehends the influences of Prandtl number, pressure gradient, body forces, and non-coincident start of velocity and thermal layers. Methods are given for evaluating the total heat flux directly, and for integrating the differential equations for the growth of the boundary layer thickness by means of quadratures.