Abstract

Numerical solutions of third grade nanofluid in the presence of viscous dissipation, heat absorption, magnetic effect, thermal radiation, and convective boundary conditions is investigated. Influence of thermophoresis and Brownian motion are also considered in the problem. The similarity solution is used to transform the system of partial differential equations, describing the problem under consideration, into a boundary value problem of coupled ordinary differential equations, and an efficient numerical technique is implemented to solve the reduced system. The results are presented graphically and in tabular form and the conclusion is drawn that the flow field and other quantities of physical interest are significantly influenced by these parameters. 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, 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 bigger values of material parameters 𝛽1 and 𝛽2 are used. The results further revealed that the temperature and thermal boundary layer thickness are increasing functions of Newtonian heating parameter 𝛾. An increase in thermophoresis and Brownian motion parameters lead to an enhancement in the temperature. The results are compared with existing results in literature and there is excellent agreement.