Effects of Reynolds number, plastic number, and flow intensity on the flow and on the heat transfer of a viscoplastic fluid flowing through a planar expansion followed by a contraction

Non-Newtonian fluids are a constant presence in several industrial applications so it becomes interesting to understand their behavior and to optimize their use. One behavior of commercial interest is the viscoplastic behavior characterized by an abrupt change of the apparent viscosity when a certain amount of stress is achieved. The present work performs a study of the effect of Reynolds number, the plastic number, and the flow intensity over flow parameters of industrial interest, namely, mean Nusselt number, displacement efficiency, and head loss. The mechanical model is approximated by a finite volume method implemented by an OpenFOAM (R) routine developed by the authors. The SMD model was chosen to model the viscoplastic behavior. The adopted geometry is of a planar channel with an abrupt expansion followed by an abrupt contraction. The channel walls are kept insulated and heat transfer occurs only at the cavity formed between the expansion and contraction planes. For the studied range of parameters, mean Nusselt number has a positive dependence on Reynolds number and flow intensity but a negative dependence on plastic number; displacement efficiency has a positive dependence on Reynolds number and flow intensity but a negative dependence on plastic number. The head loss has a negative dependence on Reynolds number and plastic number and an overall positive dependence on flow intensity.