Expansion Ratio and the Heat Transfer Characteristics of Suddenly Expanding Viscoplastic Flows

The impact of the expansion ratio on heat transfer from Bingham viscoplastic non-Newtonian flows through axisymmetric sudden expansions has been studied numerically by solving the mass, momentum, and energy conservation equations. Two expansion ratios 1:5 and 1:2 have been investigated. The expansion ratio has a dramatic impact on the reattachment length, in the case of Newtonian flows, and the recirculation intensity, in the case of Newtonian and viscoplastic non-Newtonian flows. In general, a more intense recirculation is associated with higher expansion ratios. The non-dimensional yield stress, i.e., yield number, is found to have a significant impact on the flow and heat transfer behavior. The relative recirculation intensity substantially diminishes with the yield number for both expansion ratios. For a given Reynolds number, increasing the yield number, results in transitioning from a recirculating to a non-recirculating viscoplastic flow regime downstream of the expansion plane. Substantial heat transfer enhancement exists downstream the expansion. A single wall heat transfer peak is observed for Newtonian and non-separating viscoplastic flows, immediately downstream of the reattachment point and corner unyielded region, respectively. However, two local peaks are observed in the case of recirculating viscoplastic flow fields. The first is close to the center of the weak corner vortex and the second is downstream of the stagnant impingement region. Peak heat transfer rates were found to substantially increase with the yield number, Prandtl number, and, to a lesser extent, with the expansion ratio.