Boundary layer flow of third grade nanofluid with Newtonian heating and viscous dissipation

S. A. Shehzad¹, Tariq Hussain², T. Hayat^{3, 4}, M. Ramzan², A. Alsaedi³

(1. Department of Mathematics, Comsats Institute of Information Technology, Sahiwal 57000, Pakistan;
2. Department of Mathematics, Faculty of Computing, Mohammad Ali Jinnah University, Islamabad Campus, Pakistan;
3. Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 21589, Saudi Arabia;
4. Department of Mathematics, Quaid-i-Azam University 45320, Islamabad 44000, Pakistan)

Abstract:Two-dimensional boundary layer flow of an incompressible third grade nanofluid over a stretching surface is investigated. Influence of thermophoresis and Brownian motion is considered in the presence of Newtonian heating and viscous dissipation. Governing nonlinear problems of velocity, temperature and nanoparticle concentration are solved via homotopic procedure. Convergence is examined graphically and numerically. Results of temperature and nanoparticle concentration are plotted and discussed for various values of material parameters, Prandtl number, Lewis number, Newtonian heating parameter, Eckert number and thermophoresis and Brownian motion parameters. Numerical computations are performed. The results show that the change in temperature and nanoparticle concentration distribution functions is similar when we use higher values of material parameters β₁ and β₂. It is seen that the temperature and thermal boundary layer thickness are increasing functions of Newtonian heating parameter γ. An increase in thermophoresis and Brownian motion parameters tends to an enhancement in the temperature.

Key words:third grade nanofluid; Newtonian heating; viscous dissipation