# Motion of a Thin Film of a Fourth Grade Nanofluid with Heat Transfer Down a Vertical Cylinder: Homotopy Perturbation Method Application

## Authors

• Nabil Tawfik El-dabe Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt
• Mohamed Yahya Abou-zeid Department of Mathematics, Faculty of Education, Ain Shams University, Roxy, Cairo, Egypt
• Ola S. Ahmed Department of Mathematics and Computer Science, Faculty of Science, Beni-Suef University, Egypt

## Keywords:

MHD flow, heat transfer, non-Newtonian nanofluid, homotopy perturbation method

## Abstract

The effects of uniform magnetic field, heat generation and chemical reaction on the flow of non-Newtonian nanofluid down a vertical cylinder is investigated. The fluid is incompressible and electrically conducting and obeys fourth grade model. The viscous and Ohmic dissipation are considered. The problem is modulated mathematically by a system of non-linear partial differential equations which describe the continuity, momentum, and nanoparticles concentration as well as Lorentz equation. This system is transformed into a non-dimensional system of ordinary differential equations and then is solved analytically by using homotopy perturbation method. The obtained solutions are functions of the physical parameters of the problem. The effects of these parameters on the obtained solutions are discussed numerically and illustrated graphically through some figures. It is obvious that these physical parameters play an important rule to control and modify the velocity, temperature and nanoparticles concentration of non-Newtonian nanofluid.

2020-12-25

## How to Cite

El-dabe, N. T. ., Abou-zeid, M. Y. ., & S. Ahmed, O. . (2020). Motion of a Thin Film of a Fourth Grade Nanofluid with Heat Transfer Down a Vertical Cylinder: Homotopy Perturbation Method Application. Journal of Advanced Research in Fluid Mechanics and Thermal Sciences, 66(2), 101–113. Retrieved from https://www.akademiabaru.com/submit/index.php/arfmts/article/view/2827
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