Functions for the resistance to heat and momentum transfer in the region near the wall have been defined for flows with various geometries, and correlations from available literature on rough wall friction and heat transfer have been made for these functions. The functions may then be used in the expressions for velocity and temperature profiles to solve the turbulent boundary-layer equations for flows over rough surfaces. Roughnesses such as those formed by machined grooves, piston-rings, wires, and three-dimensional elements have been included in the correlations.

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