A phenomenological theory of heat transfer in turbulent shear flows

Based on the physics of heat transfer in turbulence, together with the use of dimensional analysis and several empirical facts, a rate equation was proposed to govern the variation of the effective turbulent thermal diffusivity. Effects of diffusion, convection, stress production, buoyant generation, and decay on n sub t are each modeled mathematically and represented by appropriate terms in the rate equation leaving only three universal constants to be determined by experiments. The formulation is intended to be general enough for turbulent shear flows with various thermal stratifications. Application was made to study a slightly heated turbulent wake behind the trailing edge of a flat plate. Solutions were carried out analytically by assuming local similarity and a far wake condition. It is shown that, under near neutral conditions, the Monin-Obukhov similarity hypothesis can be obtained as a limiting case of the present theory.