Unsteady natural convection flow of multi-phase nanofluid past a vertical plate with constant heat flux

The objective of the present study is to investigate the two-dimensional transient natural convective boundary-layer flow of multi-phase nanofluid past a vertical plate with constant heat flux. The effects of Brownian motion and thermophoresis are incorporated in this nanofluid model. It is further considered that the nanoparticle volume fraction on the boundary is passively rather than actively controlled. An effective implicit finite difference technique of Crank-Nicolson method has been used to solve the governing non-linear coupled partial differential equations. The effects of time, Brownian motion parameter, thermophoresis parameter, buoyancy ratio parameter, Prandtl number and Lewis number on the dimensionless velocity, temperature and nanoparticle volume fraction have been illustrated graphically and analyzed in detail. The results for local as well as average skin-friction and Nusselt number are also presented graphically and discussed thoroughly. It is found that the velocity, temperature and nanoparticle volume fraction evolves with time and reached steady state as time progressed. The local Nusselt number is found to be slightly increased with increasing Brownian motion parameter and it decreased with increasing thermophoresis parameter, but the influence of buoyancy ratio parameter does not show any impact on the local Nusselt number. To validate the present numerical results, a comparison study has been carried out between the present steady state local Nusselt number results for a limiting case of regular fluid with the well-established experimental correlation results and an excellent agreement is found between the results. © 2017 Elsevier Ltd