Convection of Viscoplastic Fluid in U-Tube Bends

Viscoplastic fluids are found among both man-made and natural materials frequently. They are characterized by the presence of yield stress, which results in complex fluid rheology. During heat treatment, such materials undergo convection. The convection patterns are expected to be complex due to the presence of yield stress and delayed fluid movement. In this work, heat transfer and flow characteristics of viscoplastic fluid in a square duct with 180° sharp bend have been studied numerically. The duct is filled with viscoplastic fluid obeying Herschel–Bulkley model. The flow is assumed to be two dimensional, laminar and steady. Finite volume-based scheme is used to obtain the flow domain behavior. The effects of Reynolds number, input height to output height ratio (IOR), Yield number and power law index on the flow and heat transfer characteristics of the viscoplastic fluid have been investigated. Results are presented in terms of streamlines, isotherms and velocities under different heating conditions. Yielded and unyielded regions in the flow domain have been identified. It has been found that vortices are emanating near the sharp corner. A strong correlation of the size of vortices, reattachment length and heat flow with variable parameters has been obtained.