Analytical solutions of the boundary-value problem of nonstationary flow of viscoplastic medium between two plates |
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Authors: | D M Klimov A G Petrov |
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Institution: | (1) Institute for Problems in Mechanics of the Russian Academy of Sciences, Prospect Vernadskogo, 101, Moscow, 117526, Russia, RU |
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Abstract: | Summary Nonstationary flow of a viscoplastic medium between two parallel plates is considered for the case of a varying pressure
gradient. The problem is reduced to the Stephan problem, with the condition on the boundary separating the flow domain from
the quasi-rigid domain. Four multiparameter families of exact solutions are found. The first family describes the flow decelerations
up to a full stop. The second family determines the development of the flow from the state of rest as the pressure gradient
increases. The third family describes the development of the flow for the case where (1) the pressure gradient is constant
and exceeds the threshold value related to the yield stress, (2) the upper plate does not move, and (3) the lower plate moves
with a constant acceleration. Finally, the fourth family determines the flow retardation, when the pressure gradient is constant
and is less than the threshold value. The decrease in the flow of the viscoplastic medium can be achieved for certain values
of parameters by increasing the quasi-rigid domain, whereas the viscoplastic flow remains unchanged.
Received 7 October 1998; accepted for publication 8 April 1999 |
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Keywords: | viscoplastic flow boundary-value problem analytical solution self-similar solution |
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