Pressure loss and heat transfer in channels roughened on two opposed walls

In order to increase cooling effectivness selectively, coolant channels in gas turbine components are often only roughened on one or two walls of the channel. A model is presented for flow in rectangular channels having two opposed roughened walls and a theory is developed for both the pressure loss and heat transfer. The theory allows one to calculate the heat transfer coefficient on each wall separately in addition to the overall friction factor and heat transfer coefficient. Comparisons are made to data for similarly configured channels, tubes, and surfaces roughened by regularly spaced transverse ribs placed normal to the flow direction. Correlations for the displacement velocity in the logarithmic law and the roughness Stanton number in terms of the rib pitch-to-height ratio and roughness Reynolds number are also presented.