Spectral Theory of Turbulent Heat Transfer in the Presence of a Rough Wall

Using the phenomenological theory of turbulence, a direct link between the Stanton number - a dimensionless number that represents the ratio of transferred heat to the thermal capacity of the fluid - and the scalar spectrum is established for both smooth wall and rough wall conditions. The effect of different scales of motion on heat transfer is demonstrated by investigating relevant limits of the scalar spectrum. It is shown that two important observations in literature - the lack of increase in heat transfer beyond a certain roughness size and the nonclassical Prandtl number scaling - are reproduced if only the viscous inertial and diffusive range of the scalar spectrum is accounted for.