PRESSURE-GRADIENT EFFECTS ON REYNOLDS ANALOGY FOR CONSTANT PROPERTY EQUILIBRIUM TURBULENT BOUNDARY-LAYERS

The effects of pressure gradient on turbulent heat transfer to or from planar surfaces are examined. Only incompressible, equilibrium therma l boundary layers are investigated. The equilibrium condition is chara cterised by the Clauser parameter beta. Temperature profiles which are parametric in beta and the turbulent Prandtl number, Pr(t) have been calculated for the range -0.54 less-than-or-equal-to beta less-than-or -equal-to infinity; corresponding in one end to a favorable pressure g radient flow beyond which no equilibrium boundary layer is possible an d in the other end to turbulent flow at incipient separation, respecti vely. It is found that an overlap exists between the temperature law o f the wall region and the outer defect law region for all values of be ta and Pr(t), except when beta --> infinity. The existence of this ove rlap region gives rise to an expression for the Stanton number which i s shown to be a function of beta and Pr(t). At incipient separation, t he skin friction coefficient goes to zero while the wall heat flux rem ains finite. However, the wall heat flux and the Stanton number in thi s limit cannot be determined because of the neglect of viscous effects in the present analysis. A modified Reynolds analogy that accounts fo r the effects of beta and Pr(t) is deduced and the classical Reynolds analogy is shown to be valid only in the limit of beta goes to zero, P r(t) goes to 1 and the Reynolds number based on the displacement thick ness approaches infinity.