Fluid Dynamics of Parallel Plates Viscometer: a Case Study of Methods Of Series Summation

Abstract

The fluid dynamics of parallel plates viscometer is investigated mathematically using both the Navier-Stokes and continuity equations for an incompressible viscous fluid. The problem admits similarity solutions, thereby reducing the unsteady Navier-Stokes equations to a parameter dependent fourth order nonlinear ordinary differential equation. Analytical solutions are constructed for the problem using perturbation technique together with a special type of Hermite-Pad´e approximants and important properties of the overall structure of the flow are discussed. The model is appropriate to simulate laboratory tests on rheological phenomenon in food processing engineering.