Convective cooling and optimal placement of electronic components with variable ambient temperature. I: The linear model (Q1313188)

For a board of thermally active electronic devices a mathematical model is presented which simulates the evolution of its thermal state. Heat exchange among the components themselves as well as between the components, the edges and a convective flow of cool air is considered, thus giving rise to two discrete systems of equations. The heat exchange between air and board is assumed to satisfy a linear equation. Existence and uniqueness of a steady state solution are proven. Numerical results are obtained by using a non-deterministic scheme, the annealing algorithm.