Series solution of slip ow of Al2O3 and Fe3O4 nanoparticles in a horizontal channel with a porous medium by using least square and Galerkin methods

Document Type : Article

Authors

1 Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur 63100, Pakistan.

2 Department of Computer Sciences, Bahria University Islamabad Campus, Islamabad 44000, Pakistan.

3 Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur 63100, Pakistan

4 Department of Mathematics, Allama Iqbal Open University, Islamabad 44000, Pakistan.

5 Department of Mathematics, University of Education, Attock Campus, 43600, Pakistan.

Abstract

In this problem, we present a theoretical study for the slip effects on the two-dimensional flow of a nano liquid in a semi-porous channel designed by two long rectangular plates having porous media. One of the channel walls is porous and other is rigid as well as slippery. A magnetic field of homogenous strength is also applied transversely to direction of flow. Magnetic nanoparticles and non-magnetic nanoparticles are considered with ethylene glycol and water as base fluids. Least Square method and Galerkin method are adopted to solve the equations transformed from partial differential equations to ordinary ones by Berman’s similarity transformations. The obtained results from the two analytical methods are compared with the results obtained by fourth order Runge-Kutta numerical method(NM). By comparing the results of GM and LSM it is observed that variation in velocity profiles is minimal however the accuracy of GM is higher than LSM. The contributions of various flow parameters on flow field are presented through graphs. Results show a decrease in the fluid velocity with an increase in the slip parameter and porosity parameter. Flow field is less for the case of magnetic nanoparticles as compared to nonmagnetic particles for different base fluids.

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