Rotational viscoelastic laminar boundary layer flow around a rotating disc

TLDR: In this article, the equations of motion for the laminar boundary layer flow over a rotating disc have been derived for a fluid which obeys a Rivlin-Ericksen type of constitutive equation and whose material parameters are assumed to be arbitrary functions of the second invariant of the rate of deformation tensor.

Abstract: The equations of motion for the laminar boundary layer flow over a rotating disc have been derived for a fluid which obeys aRivlin-Ericksen type of constitutive equation and whose material parameters are assumed to be arbitrary functions of the second invariant of the rate of deformation tensor. The analysis establishes the conditions under which a true similarity solution is possible. An inspectional analysis yields a relationship between the moment coefficient, a generalizedReynolds number and a modifiedWeissenberg number which incorporates a variable relaxation time with a process time characteristic of the boundary layer flow on the disc. Experimental data obtained are analysed in terms of the derived relationship and the agreement between the two, after the determination of the unknown constants, is found to be quite sound. A brief discussion follows which emphasizes the role of geometry, regime of flow and viscoelastic material parameters in giving a wide variety of flow phenomena.