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Fluid dynamics of parallel plates viscometer: a case study of methods of series summation. (English) Zbl 1152.76358
Summary: 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-Padé 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.

MSC:
76D05Navier-Stokes equations (fluid dynamics)
76A99Foundations, constitutive equations, rheology
76M45Asymptotic methods, singular perturbations (fluid mechanics)
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