Laminar Free Convection in Bingham Plastic Fluids from an Isothermal Semicircular Cylinder

Abstract

Laminar free convection heat transfer in Bingham plastic fluids from an isothermal semicircular cylinder has been studied numerically over the following ranges of conditions: Rayleigh number ; Prandtl number and Bingham number . New extensive results on the streamline and isotherm contours adjacent to the semicircular cylinder, yield surfaces separating the fluidlike and solidlike regions, drag coefficient, and local and surface average Nusselt number are discussed in detail, especially with reference to the corresponding behavior observed in ordinary Newtonian fluids. The extent of the unyielded regions progressively increases with Bingham number and/or with the decreasing value of the Rayleigh number. Naturally, conduction dominates heat transfer in the unyielded regions, and convection is relevant only to the yielded regions. In summary, for a given Bingham number, the Nusselt number bears a positive dependence on the Rayleigh number. On the other hand, as the value of the Bingham number is gradually increased, the average Nusselt number decreases from its maximum value in Newtonian media () to its conduction limit () when practically most of the fluid is frozen. Finally, the present numerical values of the average Nusselt number have been consolidated in terms of the modified Rayleigh number and Prandtl number , thereby enabling its prediction in a new application and/or for the intermediate values of the governing parameters.