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Lateral effects in a thermal boundary layer Robbins, Robert Jaroslaw

Abstract

Analytical and numerical analyses along with experimental results are presented for laminar forced convection from a heated flat plate. The heating is of either the constant flux or constant temperature type with a discontinuity in the lateral as well as the free-stream direction. The principal objective was to examine the disturbance created by the lateral discontinuity in heating. Analytical solutions of the boundary layer type relating the wall temperature variation to a specific heat flux distribution were found. These involve Heaviside calculus, Fourier transform techniques and the Lévque velocity approximation, and although formally correct only as the Prandtl number approaches infinity, are found to be fairly accurate for Prandtl numbers as low as unity. Reduction of the energy equation to a two-dimensional elliptic equation by a double similarity transform enabled the calculation of numerical solutions valid in any free-stream cross-section removed from the leading edge. Results for technologically interesting cases of heated strips were found by superposition. The error in assuming such strips to be two-dimensional throughout their lateral extent is calculated. A velocity profile corresponding with the Blasius profile and a cross-sectional temperature field above a wind tunnel model of a heated flat plate were measured with a constant temperature anemometer and a rake of miniature thermocouples respectively. A temperature profile well into the heated portion is of two-dimensional form and the temperature field at the lateral step correlates with a numerical solution. In general, there is good agreement between all three approaches.

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