Abstract
Steady state free convective flow enclosed within a cavity and subjected to a temperature gradient is predicted using the finite element method. The matrix equations resulting from the finite element discretisation and formulation are solved using both an iterative and a modified Newton-Raphson scheme. An assessment of the variation in the characteristics of the flow regime is made in association with the dimensionless Prandtl and Rayleigh numbers. A further parameter of interest in such problems is the cavity aspect ratio. The upper limit for the Rayleigh number (based on cavity width) presented in the present paper is 10 7 . The flow patterns are obtained for Prandtl numbers in the range 10 −2 ⩽ Pr ⩽ 10 3 and for aspect ratios 1, 10, 20. Where possible the results are compared with existing solutions obtained using the finite difference method. A satisfactory correlation exists where such comparisons can be made. The results complement and extend those obtained during previous theoretical and numerical investigations.
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