Abstract
The paper presents new exact solutions of equations derived earlier. Three of them describe unsteady motions of a polymer solution near the stagnation point. A class of partially invariant solutions with a wide functional arbitrariness is found. An invariant solution of the stationary problem in which the solid boundary is a logarithmic curve is constructed.
Highlights
Exact Solutions of Boundary LayerThe theory of motion of a viscous fluid based on the Navier–Stokes equations is unable to describe the flow of a weak aqueous polymer solution, as the Navier–Stokes theory does not take into account the properties that the equilibrium state in the liquid, corresponding to the rheological Newton’s law, establishes, not instantly, after a change in external conditions, as required by this law, but after some time, characterized by the value of the relaxation time [1]
If we introduce the Misers variables into the initial equations of motion of the polymer solution in the Pavlovskii model, and perform their asymptotic simplification in the sense of the boundary layer theory, at the limit for a stationary flow we obtain exactly Equation (43)
The present paper deals with the plane unsteady boundary layer equations describing the behaviour of an aqueous polymer solution
Summary
The theory of motion of a viscous fluid based on the Navier–Stokes equations is unable to describe the flow of a weak aqueous polymer solution, as the Navier–Stokes theory does not take into account the properties that the equilibrium state in the liquid, corresponding to the rheological Newton’s law, establishes, not instantly, after a change in external conditions, as required by this law, but after some time, characterized by the value of the relaxation time [1]. If P( x, t) = ekt F ( xe−kt ), where k is constant and g00 6= 0, the extension of the kernel of admitted Lie algebras is defined by the generator:. The knowledge of an admitted Lie group allows for constructing invariant and partially invariant solutions.
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