Natural Convection from a Heated Sphere in Bingham Plastic Fluids
2014
Nirmalkar, N. | Gupta, A K | Chhabra, R. P.
Laminar natural convection from an isothermal sphere immersed in cold Bingham plastic media has been investigated numerically over wide ranges of the pertinent dimensionless parameters (Rayleigh number, 10² ≤ Ra ≤ 10⁶; Prandtl number, 10 ≤ Pr ≤ 100; and Bingham number, 0 ≤ Bn ≤ 10⁴). Extensive results on the flow and heat-transfer aspects are presented in terms of the streamlines and isotherm contours in the close proximity of the sphere; morphology of the yielded and unyielded regions; and the local and average Nusselt number as functions of the Rayleigh number, Prandtl number, and Bingham number. For a given value of the Rayleigh number, there exists a limiting Bingham number beyond which no convection occurs and heat is transferred from the sphere to the fluid only by conduction. Broadly, fluidlike regions are seen to gradually diminish with the increasing Bingham number, and eventually the flow field is completely frozen, corresponding to the fully plastic limit. Finally, the present numerical results of the average Nusselt number are correlated via a simple expression, thereby enabling the interpolation of the present results for the intermediate values of the parameters.
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