Decoupling Convective and Conductive Heat Transfer Using the Adiabatic Heat Transfer Coefficient

Abstract

In many heat transfer situations, such as those found in the electronics cooling field, more than a single mode of heat transfer occurs. For example, modules on a printed circuit board dissipate heat through convection to the air, through conduction to the board and through radiation to the surroundings. The adiabatic heat transfer coefficient, had, works well in such situations because it describes the change in wall temperature due to each incremental change in the convective heat transfer rate (due to conduction, radiation, or generation in the wall). The value of had is independent of the surface heat transfer distribution and can be used with the superposition method to interface between a convection solver and a conduction solver and “decouple” a conjugate heat transfer problem. If one uses the heat transfer coefficient based on the mean fluid temperature, hm, the problem is complicated because the value of hm is a function of the surface heat transfer distribution. This decoupling strategy is demonstrated through a series of numerical computations which solve the fully conjugate problem for laminar flow in a duct. These results are then compared to the decoupled solution. Excellent agreement between the fully conjugate and the decoupled solution is found for all cases when had and Tad are used to decouple the problem. Using hm and Tm can result in temperature prediction errors as large as 50 percent (for the cases studied here). The results show that when the Biot number (formulated as the resistance to axial wall conduction over the resistance to convection) is greater than 1.0 the adiabatic heat transfer coefficient should be used to decouple the problem. If the Biot number is below this value, h based on the mean temperature (for uniform surface temperature) can be used as the decoupler.