Natural Convection Around a Locally Heated Circular Cylinder Placed in a Rectangular Enclosure

Abstract

AbstractNatural convective flow and heat transfer around a locally heated circular cylinder kept in a rectangular enclosure are investigated. At first, a problem valid for a rectangular domain is formulated and then an analytical coordinate transformation is introduced to map the rectangular domain to the physical domain considered here. Based on the coordinate transformation, a set of governing equations is obtained which is further simulated by imposing appropriate conditions on the walls of the cavity and the inner solid bodies. Numerical solutions are validated through comparison of the present results with the available published data. It is found that streamlines and isotherms are greatly influenced by the width (w) and breadth (b) of the heat source and the Rayleigh number (\mathit{Ra}). The Nusselt number (\mathit{Nu}) is computed at the surface of the inner and outer cylinders, revealing that it grows considerably when controlling parameters w, b, and \mathit{Ra} are increased. The strength and number of the vortices generated within the velocity field heavily depend on the size and location of the outer cylinder. The span-wise local Nusselt number variation shows some sharp rises compared to the neighboring values in {\mathit{Nu}_{i}} and {\mathit{Nu}_{o}}, which is due to the large temperature gradient at those points.