Momentum and heat transfer from a semi-circular cylinder in Bingham plastic fluids

Abstract

In this study, momentum and heat transfer from a semi-circular cylinder immersed in Bingham plastic fluids have been investigated numerically in the laminar flow regime. The governing differential equations have been solved over wide ranges of conditions as: Reynolds number, 0.1⩽Re⩽30, Prandtl number, 1⩽Pr⩽100 and Bingham number, 0⩽Bn⩽103. New extensive results on the size and shape of the yielded/unyielded zones, drag coefficient and Nusselt number are presented and discussed. The detailed flow and temperature fields in the vicinity of the cylinder surface are examined in terms of the streamline and isotherm contours respectively. Next, the influence of the type of thermal boundary condition like constant wall temperature (CWT) and constant heat flux (CHF) imposed on the surface of the semi-cylinder has been also discussed. Irrespective of the type of the thermal boundary condition prescribed on the surface of the semi-circular cylinder, the functional dependence of the Nusselt number on the governing dimensionless parameters, namely, like Reynolds number, Prandtl number and Bingham number is qualitatively similar. The rate of heat transfer for the constant wall temperature (CWT) is somewhat higher than that for the constant heat flux condition. Finally, the individual and total drag coefficients have been correlated via simple equations in terms of the modified Reynolds number and the average Nusselt number (in terms of the Colburn j-factor) as a function of the modified Reynolds number and Prandtl number thereby enabling its prediction in a new application.