Natural convection from a circular cylinder in confined Bingham plastic fluids

Heat transfer by laminar natural convection to Bingham plastic fluids from a heated horizontal circular cylinder in a square cavity has been investigated numerically. The governing partial differential equations describing the fluid flow and heat transfer have been solved (using the finite-element based COMSOL solver) over wide ranges of the pertinent dimensionless parameters, namely, Rayleigh number (103⩽Ra⩽105), Prandtl number (1⩽Pr⩽500) and Bingham number (0⩽Bn⩽Bnmax) for a range of values of the ratio of the cylinder diameter to the size of the square cavity, 0.125⩽B⩽0.5. The detailed flow and temperature fields in the proximity of the heated cylinder are visualized in terms of the streamline and isotherm profiles, respectively. These also facilitate the delineation of the yielded and unyielded regions formed in different parts of the cavity. Further insights are provided in terms of the distribution of the local Nusselt number along the cylinder surface together with its average value. It is found that the average Nusselt number decreases with the increasing Bingham number up to a limiting value of the Bingham number (Bnmax) beyond which the average Nusselt number attains its asymptotic value, close to the pure conduction limit due to the virtually unyielding nature of the fluid. Furthermore, the influence of the aspect ratio, B, on the maximum Bingham number (Bnmax) and the resulting average Nusselt number has been explored extensively. It is found that as the size of the cavity increases with respect to the cylinder diameter, i.e., decreasing value of B, the both maximum Bingham number and average Nusselt number increase. On the other hand, Nusselt number shows a very weak dependence on the Prandtl number beyond that included in the definition of the Rayleigh number.