Abstract
Two one-parameter series of real solutions describing the process of deceleration and acceleration of a viscoplastic medium under the action of a time-varying pressure gradient are obtained. The problem of axisymmetric unsteady viscoplastic flow is reduced to the solution of the Stefan boundary-value problem for the heat conduction equation with a nonlinear condition on the boundary of the quasi-rigid core. By a self-similar change of variables the problem can be reduced to a second-order ordinary differential equation. The solutions of this equation are represented in terms of Bessel and elementary functions. As a result, two one-parameter series of solutions, the first of which describes the acceleration and the second the deceleration of a viscoplastic medium in a pipe under the action of a time-varying pressure gradient are obtained.
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Petrov, A.G., Cherepanov, L.V. Exact Solutions of the Problem of Unsteady Flow of a Viscoplastic Medium in a Circular Pipe. Fluid Dynamics 38, 175–185 (2003). https://doi.org/10.1023/A:1024208732537
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DOI: https://doi.org/10.1023/A:1024208732537