Analytical solution of the flow of a Newtonian fluid with pressure-dependent viscosity in a rectangular duct

We derive a fully analytical solution for the steady flow of an isothermal Newtonian fluid with pressure-dependent viscosity in a rectangular duct. The analytical solution for the governing equations is exact (based on the work by Akyildiz and Siginer, Int. J. Eng. Sc., 104, 2016), while the total mass balance constraint is satisfied with a high-order asymptotic expression in terms of the dimensionless pressure-dependent coefficient ε, and an excellent improved solution derived with Shanks' nonlinear transformation. Numerical calculations confirm the correctness, accuracy and consistency of the asymptotic expression, even for large values of ε. Results for the average pressure difference required to drive the flow are also presented and discussed, revealing the significance of the pressure-dependent viscosity even for steady, unidirectional, Newtonian flow.