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MHD free convection in trapezoidal cavities has attracted the interest of many researchers due to its importance applications in several thermal engineering problems such as in the design of electronic devices, solar thermal receivers, and uncovered flat plate solar collectors having rows of vertical strips geothermal reservoirs, and so on. This analysis is largely concerned with the effects of circular cylindrical block on heat flow for MHD free convection in a non-uniformly heated trapezoidal enclosure. Free convection within a trapezoidal enclosure is considered as non-uniformly heated bottom wall and insulated top wall while side walls are isothermal with inclination angles ( ). Heat flows in the presence of free convection within trapezoidal enclosures have been analyzed with heatlines concept. A set of Similarity transformations are used to transform the momentum and energy equations under consideration into coupled non-dimensional governing equations. The non-dimensional governing equations are discretized by using Galerkin weighted residual method of finite element formulation. The numerical results are presented in terms of streamlines, isotherms, local Nusselt number along the bottom wall for non-uniform heating for different combinations of the governing parameters namely Prandtl number Pr, Hartmann number Ha and Rayleigh number Ra. The validity of the numerical results is checked graphically by comparing the results obtained for some specific cases with those available in the literature, and a comparatively excellent agreement is reached.

Effects of Circular Cylindrical Block On Heat Flow For MHD Free Convection In A Non-Uniformly Heated Trapezoidal Enclosure