Abstract
In this paper is presented the model of an incompressible micropolar fluid flow with slip using the initial and boundary conditions when the wall velocity is considered depending on the frequency of the vibration. Regarding the boundary conditions of the velocity at the wall, we remark that there is a discontinuity of the velocity at the fluid-wall interface. The solutions for velocity and microrotation with the given conditions are obtained using the method of numerical inversion of Laplace transform.
Highlights
The theory of micropolar fluids was introduced for the first time by Eringen, [1]
In our paper where we study the Stokes’ second problem with slip boundary conditions, the numerical analysis is made for values of time greater than 5
Regarding the study of the Stokes’ second problem, it was analysed by Ibrahem [5], but in his paper was considered only the simplified case without slip boundary conditions
Summary
The theory of micropolar fluids was introduced for the first time by Eringen, [1]. The polar fluids are those fluids that have a non-symmetric stress tensor. Devakar and Iyengar [3], studied Stokes’ first problem for a micropolar fluid, i.e. the fluid flow through a half-space delimited by a flat plate. Ibrahem et al [5] solved a Stokes’ second problem for a micropolar fluid, embedded into a thermal analysis With this idea in mind, we take into account a slip between the velocity of the fluid at the wall and the speed of the wall uw. In our paper where we study the Stokes’ second problem with slip boundary conditions, the numerical analysis is made for values of time greater than 5. Regarding the study of the Stokes’ second problem, it was analysed by Ibrahem [5], but in his paper was considered only the simplified case without slip boundary conditions. I 1⁄4 Z1 þ Z2 þ Z3 þ Z4 A 1⁄4 z1Z1 À z1Z2 þ z3Z3 À z3Z4 A2 1⁄4 z12Z1 þ z12Z2 þ z32Z3 þ z32Z4 A3 1⁄4 z13Z1 À z13Z2 þ z33Z3 À z33Z3
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