A model for the convective cooling of electronic components with application to optimal placement

  • Authors:

  • B. Cahlon;I. Gertsbakh;I. E. Schochetman;M. Shillor

  • Affiliations:

  • Department of Mathematical Sciences, Oakland University Rochester, MI, 48309 USA;Department of Mathematics and Computer Science, Ben Gurion University, Beersheva, Israel;Department of Mathematical Sciences, Oakland University Rochester, MI, 48309 USA;Department of Mathematical Sciences, Oakland University Rochester, MI, 48309 USA

  • Venue:
  • Mathematical and Computer Modelling: An International Journal
  • Year:
  • 1991

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Abstract

A mathematical model for the description of the evolution of temperature in a board of electronic devices is considered. The board consists of a grid with thermally active devices. These generate heat which is conducted to their neighbors and the edges of the board, as well as exchanged with a forced convective flow of cool air. The model consists of a discrete system of equations for the temperatures of the devices. Two versions of the model are presented, the cooling term being linear in one, and nonlinear in the other. Existence and uniqueness of solutions is proved for both models as well as convergence to the respective steady states. The model is used, in conjunction with the annealing algorithm, to find the optimal placement of electronic devices on a board in such a way as to decrease the maximum temperature of the system.