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On unsteady motions of a second-order fluid over a plane wall. (English) Zbl 1348.76061
Summary: In this paper, three types of unsteady flows of second-order fluids are considered, namely, flow caused by impulsive motion of a flat plate, flow induced by a constantly accelerating plane and flow imposed by a flat plate that applies a constant tangential stress to the fluid. The previous attempts made regarding these problems, by using the Laplace transform, have failed. In this paper, the sine and the cosine transforms are used to solve these problems and exact solutions for the velocity distributions are found in terms of definite integrals. It is shown that these exact solutions satisfy the initial and the boundary conditions and the governing equation.

MSC:
76D10 Boundary-layer theory, separation and reattachment, higher-order effects
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
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