Abstract
A study is made of an invariant solution of the equations of a viscous heat-conducting fluid, which is treated as unidirectional motion of two such fluids in a plane layer with a common boundary under the action of an unsteady pressure gradient. A priori estimates of the velocity and temperature are obtained. The steady state is determined, and it is shown (under some conditions on the pressure gradient) that, at larger times, this state is the limiting one. For semiinfinite layers, a solution in closed form is obtained using the Laplace transform.
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References
V. K. Andreev, O. V. Kaptsov, V. V. Pukhnachev, and A. A. Rodionov, Use of Group-Theoretical Methods in Hydrodynamics [in Russian], Nauka, Novosibirsk (1994).
L. G. Loitsyanskii, Mechanics of Liquids and Gases, Pergamon, Oxford (1966).
G. K. Batchelor, An introduction to Fluid Dynamics, Cambridge University Press, Cambridge (1967).
M. A. Lavrent’ev and M. A. Shabat, Methods of the Theory of Functions of a Complex Variable [in Russian], Nauka, Moscow (1973).
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 4, pp. 94–107, July–August, 2008.
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Andreev, V.K. Evolution of the joint motion of two viscous heat-conducting fluids in a plane layer under the action of an unsteady pressure gradient. J Appl Mech Tech Phy 49, 598–609 (2008). https://doi.org/10.1007/s10808-008-0077-4
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DOI: https://doi.org/10.1007/s10808-008-0077-4