Integral equation formulation for buoyancy-driven convection problems |
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| Authors: | JS Vrentas CM Vrentas R Narayanan and SS Agrawal |
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| Institution: | (1) Department of Chemical Engineering, The Pennsylvania State University, 16802 University Park, PA, USA;(2) Department of Chemical Engineering, University of Florida, 32611 Gainesville, FL, USA;(3) Department of Chemical Engineering, Illinois Institute of Technology, 60616 Chicago, IL, USA |
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| Abstract: | An integral equation formulation for buoyancy-driven convection problems is developed and illustrated. Buoyancy-driven convection in a bounded cylindrical geometry with a free surface is studied for a range of aspect ratios and Nusselt numbers. The critical Rayleigh number, the nature of the cellular motion, and the heat transfer enhancement are computed using linear theory. Green's functions are used to convert the linear problem into linear Fredholm integral equations. Theorems are proved which establish the properties of the eigenvalues and eigenfunctions of the linear integral operator which appears in these equations. |
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