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Momentum and heat transfer characteristics of a thin circular disk in Bingham plastic fluids

ABSTRACT The laminar forced convection momentum and heat transfer aspects of a circular disk oriented normal to the flow and maintained at a constant flux or a constant temperature condition in a stream of a Bingham plastic fluid are studied over wide ranges of parameters as follows: Reynolds number, Re ≤ 150; Prandtl number, 1 ≤Pr ≤ 100; Bingham number, Bn ≤ 100, and thickness-to-diameter ratio, 0.01 ≤ (t/d) ≤ 0.075. The new results on hydrodynamics are analyzed in terms of streamline plots, recirculation length, morphology of yielded/unyielded regions, and drag coefficient, and on heat transfer aspects in terms of isotherm contours, local and average Nusselt number. The flow domain is spanned by the simultaneous existence of the yielded and unyielded sub-regions, depending upon the relative strengths of the fluid inertia (Re) and yield stress (Bn). All else being equal, the rate of heat transfer is higher for an isothermal disk than that for the isoflux condition. Both the drag and average Nusselt number bear a positive dependence on the Bingham number. The drag is influenced only slightly (∼5%) by thickness (t/d); however, the heat transfer can increase on this count by up to 15% under appropriate conditions. Finally, the present numerical results on drag and Nusselt number (in terms of jH-factor) have been correlated via simple empirical equations using the modified definitions of the Reynolds (Re*) and Prandtl number (Pr*), thereby enabling a priori estimation of drag and heat transfer in a new application.