On unsteady motion of a rotating fluid bounded by flat porous plates

Abstract

In this paper, an investigation is made of the unsteady flow generated in a viscous, incompressible and homogeneous fluid bounded by (i) an infinite horizontal porous plate atz=0, or (ii) two infinite horizontal porous plates atz=0 andz=D. The fluid together with the plate(s) is in a state of solid body rotation with a constant angular velocity Ω about the z-axis normal to the plate(s), and additionally, the plate(s) performs non-torsional elliptic harmonic oscillations in its (their) own plane(s). A uniform suction or injection is introduced in the configurations through the porous plate(s) and its influence on the unsteady flow and the associated boundary layers is examined. The unsteady flow field as well as the associated boundary layers is obtained explicitly. In contrast to the unsteady rotating flow without suction, solutions of the present problem with suction exhibit no resonant phenomena. It is shown that the suction is responsible for making the boundary layers thinner and for the elimination of the resonant phenomena. It is confirmed that the velocity field and the associated multiple boundary layers are significantly modified by suction. Physical significances of the mathematical results are discussed. Several limiting cases of interest are recovered from this analysis. The initial value problem for both the configurations is exactly solved by the Heaviside operational calculus combined with the theory of residues.