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Heat and Mass Transfer

Double Diffusion From a Heated Sphere in an Infinite Porous Medium

[+] Author and Article Information
R. Ganapathy

 Department of Computer Applications, Saranathan College of Engineering, Anna University of Technology, Tiruchirapalli 620 012, Indiasowgar05@yahoo.com

J. Heat Transfer 134(9), 092001 (Jun 29, 2012) (9 pages) doi:10.1115/1.4006241 History: Received August 26, 2010; Revised February 15, 2012; Published June 27, 2012; Online June 29, 2012

Free convective heat and mass transfer from a sphere of constant temperature and concentration buried in an unbounded porous medium is studied analytically assuming the validity of the Darcy flow model. Using a regular perturbation analysis, transient and steady-state solutions have been obtained in the form of series expansions in terms of a thermal Rayleigh number, which is based on the temperature of the heated sphere and the medium permeability. The results are exemplified by drawing the streamlines at various times. Of special significance is the emergence of a downward flow in the transient state when the two buoyancy mechanisms are opposed. These results apply as well to the case of buoyancy-induced flows from a sphere generating simultaneously two different chemical components.

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Copyright © 2012 by American Society of Mechanical Engineers
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References

Figures

Grahic Jump Location
Figure 1

Configuration of interest. Spherical-polar coordinate system (r,ϕ,θ) with the origin at the centre of the sphere.

Grahic Jump Location
Figure 2

Transient flow pattern. Curves represent Ψ1  = const. (a) τ = 0.1, (b) τ = 0.2, (c) τ = 0.5, (d) τ = 1.0.

Grahic Jump Location
Figure 3

Map of the function W(η,η0 )

Grahic Jump Location
Figure 4

Graph of q(R,ϕ)

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