Laminar forced convection heat transfer from a two-dimensional transverse plate in Bingham plastic fluids

Abstract

In this work, the steady flow of a Bingham plastic fluid past a two-dimensional heated flat plate has been investigated to delineate its momentum and heat transfer characteristics. The governing partial differential equations (continuity, momentum and thermal energy) have been solved numerically over the range of conditions as follows: Reynolds number, 0.1⩽Re⩽25, Prandtl number, 1⩽Pr⩽100 and Bingham number, 0⩽Bn⩽1000. Furthermore, the results for the two commonly employed boundary conditions, namely, constant temperature (CWT) and constant heat flux (CHF), prescribed on the plane surface have been contrasted. Detailed structures of the flow and temperature fields near the plane surface have been studied in terms of the streamline and isotherm contours which also help delineate the yield surfaces demarcating the yielded and unyielded regions formed in the vicinity of the heated flat plate depending upon the magnitude of the local stress tensor vis-à-vis the fluid yield stress. Extensive results are reported on the distribution of the local Nusselt number along the surface of the heated plate. The overall behaviour is described in terms of the drag coefficients and the mean Nusselt number which have been correlated in terms of the modified Reynolds number and Prandtl number. The drag coefficients show a positive dependence on the Bingham number. Similarly, the average Nusselt number also shows a positive dependence on the Bingham number for the CWT condition where as for the CHF condition, this trend is modulated by the value of the Reynolds number. In overall terms, it is possible to augment the average heat transfer by up to 35–40% in such fluids under appropriate conditions.