Title: Group analysis and numerical solution of slip flow of a nanofluid in porous media with heat transfer

Authors: Mohammed Jashim Uddin; Mohammad Ferdows; Mohammad Mehdi Rashidi; Amir Basiri Parsa

Addresses: American International University-Bangladesh, Banani, Dhaka 1213, Bangladesh; School of Mathematical Sciences, University Sains Malaysia, Penang, 11800, Malaysia ' Department of Mathematics, Dhaka University, Dhaka 1000, Bangladesh ' Mechanical Engineering Department, Engineering Faculty of Bu-Ali Sina University, Hamedan, Iran ' Mechanical Engineering Department, Engineering Faculty of Bu-Ali Sina University, Hamedan, Iran; Young Researchers Club, Hamadan Branch, Islamic Azad University, Hamadan, Iran

Abstract: The steady laminar viscous incompressible free convective boundary layer flow of a nanofluid past a chemically reacting horizontal plate situated in porous medium taking into account heat generation/absorption and the thermal slip boundary condition is studied numerically. Similarity transformations are generated by Lie group analysis. Using the similarity transformations, the transport equations are reduced to a branch of coupled similarity equations which are solved by Runge-Kutta-Fehlberg fourth-fifth order numerical method. Our analysis reveals that true similarity solution will exist provided thermal slip factor is inversely proportional to two third power of the axial distance. Effect of the governing parameters on the dimensionless velocity, temperature, nanoparticle volume fraction has been presented. Excellent agreement between our results and published is obtained. A sample of numerical results for the reduced Nusselt number and the Sherwood number is provided in a table for various values of the parameters. The reduced Nusselt number is increased with the Lewis number and reaction parameter whilst it is decreased with the order of chemical reaction, thermal slip and generation parameters. Further, the reduced Sherwood number is enhanced with the Lewis number, generation and reaction parameters whilst it is suppressed with thermal slip and order of chemical reaction parameters.

Keywords: chemical reaction; internal heat; heat generation; heat absorption; nanofluids; thermal slip boundary condition; porous media; nanotechnology; heat transfer; laminar flow; viscous flow; incompressible flow; free convective boundary layer; Lie group analysis.

DOI: 10.1504/PCFD.2016.076297

Progress in Computational Fluid Dynamics, An International Journal, 2016 Vol.16 No.3, pp.190 - 200

Published online: 13 Apr 2016 *

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