Some Unsteady Flows of a Jeffrey Fluid between Two Side Walls over a Plane Wall

Abstract

In this paper, some time-dependent flows of a non-Newtonian fluid between two side walls over a plane wall are investigated. The following three problems have been studied: (i) flow due to an oscillating plate, (ii) flow due to an accelerating plate, and (iii) flow due to applied constant stress. The explicit expressions for the velocity field are determined by using the integral transforms. The solutions that have been obtained, depending on the initial and boundary conditions, are written as sum of the steady state and transient solutions. The similar solutions for second-grade and Newtonian fluids can be deduced as limiting cases of our solutions. Furthermore, in absence of the side walls they reduce to the similar solutions over an infinite plate. The effects of some important parameters due to side walls on the flow field are investigated.