A matrix to evaluate the conjugate cooling of a heaters' array

Circuit boards are usually cooled by forced airflow and the heat transfer from the discrete electronic components may be enhanced by conductive boards. The conjugate forced convection-conduction cooling of an array of N heaters mounted on a conductive substrate was described by means of dimensionless conjugate coefficients g+kj grouped in a N-square matrix G+. Experiments were performed with one or two rows of protruding heaters mounted on the conductive lower wall of a rectangular duct, made of either Aluminum or Plexiglas. One end of the duct was closed and the heaters were cooled by two impinging airflows exiting from square holes at the duct upper wall. For each substrate plate, the conjugate coefficients were obtained from tests with a single active heater at a time and expressed as functions of a Reynolds number in the range from 2000 to 7000. Additional tests with two or three active heaters at a time were then performed and the measured temperature increase of each heater above the flow inlet temperature was predicted quite well using the previously obtained coefficients matrix G+. These results showed that the conjugate coefficients are invariant with the conjugate cooling rates from the heaters. The conjugate coefficients were also used to predict the allowable conjugate cooling rates for an array of heaters, in order to keep their temperature within reliable limits. Numerical simulations were performed for a duct configuration similar to that of the experiments, but with flush mounted heaters. The numerical results were thus distinct from those of the experiments with protruding heaters, but they showed similar trends of change with the Reynolds number and they indicated a perspective of the effects of the heaters height.