Modelling turbulent heat transfer in rough channels using phenomenological theory

Rough walls are often encountered in industrial heat transfer equipment. Even though it is well known that a rough wall affects velocity fields and thermal fields differently (and therefore also skin friction factors and Stanton or Nusselt numbers), predicting the effect of rough walls on turbulent heat transfer remains difficult. A relation between the scalar spectrum and the Stanton number is derived for channels with both smooth and rough walls. It is shown that the new relation agrees reasonably well with recent DNS experiments for wall roughness sizes of k⁺ < 150 and when Pr = 0.7 - 1.0. Under these conditions, a thermal analogue of Moody’s diagram can be created using the newly developed relation.