Unsteady MHD free convective flow past a permeable stretching vertical surface in a nano-fluid.

In this paper we investigate the transient MHD laminar free convection flow of nano-fluid past a vertical surface. The vertical surface is considered porous and stretched under acceleration. Four different types of water based nano-fluid are considered in this investigation where copper (Cu), copper oxide (CuO), aluminum oxide (Al 2 O 3 ), and titanium dioxide (TiO 2 ) are the nano-particles. The boundary-layer forms of the governing partial differential equations (momentum and energy equations) are transformed into highly nonlinear coupled ordinary differential equations (ODEs) using similarity technique. The ordinary differential equations are solved numerically using a fourth order Runge-Kutta method based shooting technique. For some special cases, an excellent agreement is observed between the current results and the results available in the existing literature. The effects of different parameters: the nanoparticle volume fraction ( φ ), unsteadiness parameter ( A ), magnetic parameter ( M ), buoyancy parameter ( λ ), suction parameter ( f w ) and different types of nanoparticles on the fluid velocity component ( f ′ ( η ) ) , temperature distribution ( θ ( η )), the skin friction coefficient ( C f R e x 1 / 2 ) , and the local Nusselt number ( N u x R e x − 1 / 2 ) are presented graphically and discussed in details. The results illustrate that selecting Al 2 O 3 and Cu as the nanoparticle leads to the minimum and maximum amounts of skin friction coefficient absolute value, and also Cu and TiO 2 nanoparticles have the largest and lowest local Nusselt number. [ABSTRACT FROM AUTHOR]