The Reynolds Analogy is popularly known to relate turbulent momentum and heat transfer.
Experimental data for gas streams agree approximately with above equation if the Schmidt and Prandtl numbers are near 1.0 and only skin friction is present in flow past a flat plate or inside a pipe.
[1] In 2008, the qualitative form of validity of Reynolds' analogy was re-visited for laminar flow of incompressible fluid with variable dynamic viscosity (μ).
[2] It was shown that the inverse dependence of Reynolds number (Re) and skin friction coefficient(cf) is the basis for validity of the Reynolds’ analogy, in laminar convective flows with constant & variable μ.
Further, the validity of the Reynolds’ analogy is linked to the applicability of Prigogine's Theorem of Minimum Entropy Production.