ANALYTICAL MODEL OF TEMPERATURE DISTRIBUTION OVER AN ELECTRONIC CIRCUIT BOARD

Abstract

The thermal model of an electronic circuit board with installed heat dissipating components is presented as a two-dimension steady-state heat conduction problem with multiple sources distributed over a rectangular region. The corresponding energy equation includes a source term and a temperature-dependent term to account for linear heat transfer in z-direction. Boundary conditions are of first type with unique temperature along the perimeter. The integral-transform technique is applied to obtain closed-form integral solution. Assuming that all dissipated components have a rectangular contact area with the plate, multiple integrals for each dissipated sub-region are easily found. A temperature map over the board is calculated from the closed expression with a triple sum of series with respect to each coordinate and source. The error is evaluated by the estimation of the truncated terms. The solution was applied to obtain the temperature distribution over the electronic Driver Plate of the CEP block of the CIMEX Brazilian experiment for flight qualifying of the Optical Block Detector Assembling.