Conduction-radiation effect on transient natural convection with thermophoresis

• Published in: Applied mathematics and mechanics 2012-03, Vol.33 (3), p.271-288
• Main Authors: Mahfooz, S. M., Hossain, M. A.
• Format: Article
• Language: English
• Subjects: Applications of Mathematics; Classical Mechanics; Fluid- and Aerodynamics; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Partial Differential Equations; 传导; 偏微分方程组; 宾夕法尼亚州; 数值求解; 暂态; 热泳; 自然对流; 辐射效应
• ISSN: 0253-4827; 1573-2754
• DOI: 10.1007/s10483-012-1549-6

This paper discusses the effect of thermophoretic particle deposition on the transient natural convection laminar flow along a vertical fiat 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 pa- rameters, 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℃ and 1.013 × 10^5 Pa.