A quasi-analytical conjugate heat transfer model is developed for a two dimensional vertical flat plate with discrete heat sources of arbitrary size and power level under natural convection. The plate is located in an extensive, quiescent fluid which is maintained at uniform temperature. The model consists of an approximate analytical boundary layer solution and a one dimensional numerical conduction analysis in which an allowance is made to account for radiation heat transfer. These fluid and solid solutions are coupled through an iterative procedure. A conjugate problem is solved when a converged temperature distribution is obtained at the plate-fluid interface, concurrently satisfying the thermal fields on both sides of the interface. Comparisons of the surface temperature variations obtained by using the present model are made with existing numerical and experimental data which were obtained for cases with two strip heat sources mounted flush with the surface of a vertical plate in air. The model is shown to be in good agreement. In addition, the convection and radiation heat flux variations are presented. The results illustrate the importance of radiation heat transfer for estimating surface temperatures of the plate.
Conjugate Heat Transfer From a Vertical Plate With Discrete Heat Sources Under Natural Convection
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Lee, S., and Yovanovich, M. M. (December 1, 1989). "Conjugate Heat Transfer From a Vertical Plate With Discrete Heat Sources Under Natural Convection." ASME. J. Electron. Packag. December 1989; 111(4): 261–267. https://doi.org/10.1115/1.3226545
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