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Free Convection Past a Vertical Flat Plate
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| Department: | Chemical Engineering |
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2005-01-05
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The notebook computes the velocity and temperature profiles for free convection past an isothermal vertical plate. Results are obtained after solving two coupled nonlinear differential equations. The shooting method is used to obtain the boundary conditions, required to solve the coupled ODEs, which match the conditions in the outer fluid. We plot velocity and temperature profiles versus a similarity variable for different Prandtl numbers (Pr=0.01, 1, 10 and 100). The figures obtained are in agreement with those given in Analysis of Transport Phenomena, William M. Deen, OUP, 1998 (figures 12-5 and 12-6 pages 500-501). This problem was solved originally by Ostrach, “An analysis of laminar free-convection flow and heat transfer about a flat plate parallel to the direction of the generating body force”, NACA Tech. Rept. No 1111, 1953. Derivation of the governing equations can be found in Deen’s book.
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Free convection, shooting method, temperature profile, velocity profile, Prandtl number, coupled nonlinear ODEs, transport phenomena, flow past vertical flat plate
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| FreeConvectionFlatPlate2.nb (275.5 KB) - Mathematica Notebook |
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