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

• Autores: B. Cahlon, I.E. Schochetman, M. Shillor
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Nº 3, 1993, pág. 351
• Idioma: inglés
• DOI: 10.1016/0377-0427(93)90062-g
• Texto completo no disponible (Saber más ...)
• Resumen

  • A mathematical model for the evolution of the component and air temperatures in a board of electronic devices is considered. The board consists of a grid with thermally active devices which generate heat that is conducted to their neighbors and to the edges of the board, as well as exchanged with a forced convective flow of cool air. The model consists of two coupled, discrete systems of equations: one for the temperatures of the devices and the other for the associated air temperatures. In our version of the model, the cooling term, i.e., the heat exchange between the board and the air, is linear. Existence and uniqueness of solutions is proved for our model, as well as convergence to the steady-state solution. 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 an objective function of the temperature of the system, with applications to the reliability of such boards.