Bulk transfer coefficient for heat transfer

A bulk heat-transfer relation applicable to unstable conditions is proposed. The relation incorporates the assumptions that heat transfer near the surface is by molecular conduction, and the bulk transfer relation does not depend explicitly on the surface roughness characteristics, provided that roughness elements are not large in comparison with the thickness of the thermal boundary layer. The predicted heat flux compares favorably with heat-transfer rates determined in the Great Plains field program and with measurements made by J. E. Vehrenkamp over a desert dry lake under conditions of extreme upward heat flux. The limiting case of very small surface stress is discussed, and the proposed formulation in this limit is compared with the heat-transfer relation observed in laboratory experiments on parallel-plate convection.