Use of superposition in calculating cooling requirements for circuit cards containing arrays of electronic components

The work reported here describes heat-transfer and fluid-friction behavior on surfaces populated with arrays of heat-dissipating components and relates to cooling problems now being faced by the electronics industry. A superposition approach has been developed for calculating the temperature distribution in a regular array of arbitrarily heated cubical elements on an adiabatic wall in a channel. Heat-transfer coefficient and temperature-superposition kernel functions have been determined as a function of position downstream of a single heated element in an array over a range of velocities and channel heights for two different array densities. The measured superposition kernel functions allow prediction of temperature distribution. Furthermore, with the introduction of concepts of array-velocity and array-density parameters, the heat-transfer behavior of the family of in-line cubical elements can be predicted from a relatively small set of input information. These concepts, when applied to other regular arrays, will allow heat-transfer behavior to be predicted over a wide range of flows and passage heights with minimal testing specific to the array in question.