PREDICTION OF NATURAL CONVECTION IN NONRECTANGULAR ENCLOSURES USING ORTHOGONAL CURVILINEAR COORDINATES

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Abstract
In order to predict natural convection in nonrectangular enclosures the equations of motion are written for orthogonal curvilinear coordinates, using stream function and vorticity as dependent variables. Special integration techniques are described that permit an accurate grid to be found. The solution of the finite-difference equations is obtained by using a novel iterative technique that solves simultaneously for vorticity and stream function along lines. This was found to be economical and stable despite the use of a high-order boundary condition on vorticity. These techniques were applied to the problem of laminar two-dimensional natural convection in an air layer bounded above by an isothermal flat plate and below by a higher-temperature vee-corrugated isothermal surface. The dependence of heat transfer on Rayleigh number, aspect ratio and inclination angle is presented. Where possible, comparisons are made with previous predictions and measurements.