The transfer of heat across a turbulent boundary layer at very high prandtl numbers

Abstract The paper considers a problem which was first treated mathematically by Lighthill in a different physical context. Solutions are provided for the limiting case of forced convection across a turbulent boundary layer when Pr →∞, i.e. when the thermal boundary layer is wholly confined within the laminar sublayer whose velocity profile is linear. The case of a flat plate with a uniform temperature or with one step in temperature is treated in great detail, and a convenient tabulation of formulae for a number of cases is provided. The case of a variable wall temperature is solved in two ways. First, the temperature distribution is replaced by a sequence of steps and superposition is used. Secondly, an exact analytic solution is given for the case when the temperature function consists of a step followed by a distribution given analytically. In the latter ease, closed-form equations are given for a polynomial temperature variation of which a linear temperature variation is a special case.