Conduction-radiation effect on transient natural convection with thermophoresis

This paper discusses the effect of thermophoretic particle deposition on the transient natural convection laminar flow along a vertical flat surface, which is immersed in an optically dense gray fluid in the presence of thermal radiation. In the analysis, the radiative heat flux term is expressed by adopting the Rosseland diffusion approximation. The governing equations are reduced to a set of parabolic partial differential equations. Then, these equations are solved numerically with a finite-difference scheme in the entire time regime. The asymptotic solutions are also obtained for sufficiently small and large time. The obtained asymptotic solutions are then compared with the numerical solutions, and they are found in excellent agreement. Moreover, the effects of different physical parameters, i.e., the thermal radiation parameter, the surface temperature parameter, and the thermophoretic parameter, on the transient surface shear stress, the rate of surface heat transfer, and the rate of species concentration, as well as the transient velocity, temperature, and concentration profiles are shown graphically for a fluid (i.e., air) with the Prandtl number of 0.7 at 20°C and 1.013 × 105 Pa.