Surface roughness effects on heat transfer in Couette flow

Abstract

A cell theory for viscous flow with rough surfaces is applied to two basic illustrative heat transfer problems which occur in Couette flow. Couette flow between one adiabatic surface and one isothermal surface exhibits roughness effects on the adiabatic wall temperature. Two types of rough cell adiabatic surfaces are studied: (1) perfectly insulating (the temperature gradient vanishes at the boundary of each cell); (2) average insulating (each cell may gain or lose heat but the total heat flow at the wall is zero). The results for the roughness on a surface in motion are postulated to occur because of fluid entrainment in the asperities on the moving surface. The symmetry of the roughness effects on thermal-viscous dissipation is discussed in detail. Explicit effects of the roughness on each surface, including combinations of roughness values, are presented to enable the case where the two surfaces may be made from different materials to be studied. The fluid bulk temperature rise is also calculated for Couette flow with two ideal adiabatic surfaces. The effect of roughness on thermal-viscous dissipation concurs with the viscous hydrodynamic effect. The results are illustrated by an application to lubrication.