Application of variation of the parameters method for micropolar flow in a porous channel

Abstract

This work devoted to study the injective micropolar flow in a porous channel. The flow is driven by suction or injection on the channel walls, and the micropolar model is used to characterize the working fluid. The governing nonlinear partial differential equations are reduced to the nonlinear ordinary coupled differential equations by using Berman's similarity transformation. These equations are solved for large mass transfer via variation of parameters method (VPM) which has been used effectively in the solution of nonlinear equations recently. This method has not previously been applied to a problem of micropolar flow. The results of the variation of parameters method are found to be in excellent agreement with the results of the Matlab bvp4c solver (NUM). With this validity, the effects of the some important parameters on the velocity and rotation profile of micropolar flow are discussed in detail. It can be seen that increases in the values and have different results in comparison with increasing.

Application of differential transformation and Hermite wavelet methods for micropolar flow through a permeable channel

“…The results presented in a table and several graphs illustrate the influence of the important dimensionless parameters such as $${N}_{1},{N}_{2},{N}_{3}$$, and $$\text{Re}$$ on the velocity profile and microrotation profile. To validate our findings, the results are compared with those reported by Güngör and Arslantürk 50 as presented in Tables 2 and 3 for different values of $$\eta $$. In this case, an extremely motivating concurrence connecting the solutions is observed too, which confirms the outstanding strength of the HWM and DTM.…”

“…$$u$$ and $$v$$ are the velocity component in the $$x$$ and $$y$$ directions, and $$N$$ is microrotation, respectively. The relevant equations governing the flow are 50 $$${\partial }_{x}u+{\partial }_{y}v=0$$$ $$$\rho {L}_{1}u=-{\partial }_{x}P+(\mu +\kappa ){L}_{2}u+\kappa \,{\partial }_{y}N$$$ $$$\rho {L}_{1}v=-{\partial }_{y}P+(\mu +\kappa ){L}_{2}v-\kappa \,{\partial }_{x}N$$$ $$$\rho {L}_{1}N=-\frac{\kappa }{j}(2N+{\partial }_{y}u-{\partial }_{x}v)+\frac{{\mu }_{s}}{j}{L}_{2}N$$$where $$\rho $$ is the fluid density, $$\mu $$ is the dynamic viscosity, …”