Article

# On the free convection from a horizontal plate

The University Department of Mathematics Durham England

Zeitschrift für angewandte Mathematik und Physik ZAMP (Impact Factor: 1.21). 01/1958; 9(3):276-282. DOI: 10.1007/BF02033031 - [Show abstract] [Hide abstract]

**ABSTRACT:**An analysis is performed to study aerosol particle transport and deposition onto an isothermal horizontal or vertical plate due to the combined effects of laminar natural convection, Brownian diffusion and thermophoresis. Four configurations are considered: flow above a heated horizontal plate, flow beneath a cold horizontal plate, flow due to a heated vertical plate and that due to a cold vertical plate. Nano to micro sized particles (particle diameter in the range 1 nm–5 μm) in air are considered. It is found that the deposition velocity decreases with an increase in particle diameter dpdp (i.e. an increase in particle Schmidt number ScSc), and increases with a decrease in the value of non-dimensional temperature difference ΔTˆ (from positive to negative values). For a downward facing cold horizontal plate or cooled vertical plate, the thermal drift of particles assists Brownian diffusion which enhances deposition velocity. For an upward facing heated horizontal plate or heated vertical plate, the thermal drift away from the surface decreases the overall deposition velocity which decreases drastically above a certain particle size. It is shown that the thermal drift may enhance the deposition rate by several orders of magnitude under certain circumstances. The profound role of using different expressions for the thermophoretic force coefficient (κκ) is assessed. It is found that the deposition velocity calculated by using the expression for κκ suggested by Talbot et al. (1980) is always higher than the values predicted by employing the expression proposed by Beresnev and Chernyak (1995). The difference in the calculated deposition velocity for the two thermophoretic models is significant when the particle diameter dpdp is large and the fluid to particle thermal conductivity ratio λrλr is small. For example, at dpdp ∼1 μm, the Talbot et al. model may overpredict the deposition velocity by a factor 3, and at dpdp ∼5 μm, the Talbot et al. model may overpredict the deposition velocity by a factor 10. There is negligible difference between the two models when dpdp <100 nm.Journal of Aerosol Science 11/2014; · 2.71 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**In the present study a new similarity theory is developed to study the fluid flow and heat transfer characteristics for the steady laminar natural convection boundary layer flow of an incompressible and electrically conducting fluid past a semi-infinite horizontal plate subjected to a constant wall temperature under the action of transverse magnetic field. The governing parabolic boundary layer PDEs are transformed to ordinary differential equations using similarity transformation. This results in a set of three coupled, non-linear ordinary differential equations with variable coefficients (representing the interaction of the temperature and velocity fields) which are then solved by the shooting method. Asymptotic analyses and series solutions are also constructed to explore the mathematical behaviour of the solutions. The numerical results are obtained for various values of Prandtl number and magnetic field parameter ζ. The effects of various values of Prandtl number and magnetic field parameter ζ on the velocity profiles, temperature profiles, wall shear stress and heat transfer coefficients are presented. The results indicate that the wall shear stress τw decreases whereas the local Nusselt number Nux increases with increase in Prandtl number if the magnetic field parameter ζ is held constant at a particular value. On the other hand, both the wall shear stress and Nusselt number decrease with increase in the magnetic field parameter ζ for a fluid with constant Prandtl number. Generic correlations for Nux and τw have been developed in terms of the fluid Prandtl number Pr and magnetic field parameter ζ. A generic relation for free convection flow with magnetohydrodynamic effects, that is equivalent to the well-known Reynolds analogy for forced convection flow, has also been formulated in the present work.Communications in Nonlinear Science and Numerical Simulation 12/2013; 18(12):3407-3422. · 2.57 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**The steady mixed convection boundary-layer flow on an upward facing horizontal surface heated convectively is considered. The problem is reduced to similarity form, a necessary requirement for which is that the outer flow and surface heat transfer coefficient are spatially dependent. The resulting similarity equations involve, apart from the Prandtl number, two dimensionless parameters, a measure of the relative strength of the outer flow M and a heat transfer coefficient γ. The free convection, M=0, case is considered with the asymptotic limits of large and small γ being derived. Results for the general, M>0, case are presented and the asymptotic limit of large M being treated.Meccanica 11/2013; · 1.82 Impact Factor

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