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Influence of Internal Heat Source on Thermal Instability in a Horizontal Porous Layer with Mass Flow and Inclined Temperature Gradient

Authors: Anjanna Matta, P. A. L. Narayana

Abstract:

An investigation has been presented to analyze the effect of internal heat source on the onset of Hadley-Prats flow in a horizontal fluid saturated porous medium. We examine a better understanding of the combined influence of the heat source and mass flow effect by using linear stability analysis. The resultant eigenvalue problem is solved by using shooting and Runga-Kutta methods for evaluate critical thermal Rayleigh number with respect to various flow governing parameters. It is identified that the flow is switch from stabilizing to destabilizing as the horizontal thermal Rayleigh number is enhanced. The heat source and mass flow increases resulting a stronger destabilizing effect.

Keywords: porous medium, heat source, linear stability analysis, mass flow

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1108474

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References:


[1] G. Bendrichi and L. W. Shemilt, “Mass transfer in horizontal flow channels with thermal gradients”, The Canadian Journal of Chemical Engineering, vol. 75, pp. 1067-1074, 1997.
[2] X. Chen and A. Li, “An experimental study on particle deposition above near-wall heat source”, Building and Environment, vol. 81, pp. 139-149, 2014.
[3] W. Schwiderskei and J. A. Schwabh, “Convection experiments with electrolytically heated fluid layers”, J. Fluid Mech., vol. 48, pp. 703-719, 1971.
[4] J. Trittond and M. N. Zarraua, “Convection in horizontal layers with internal heat generation”, J. Fluid Mech., vol. 30, pp. 21-31, 1967.
[5] P. H. Roberts, “Convection in horizontal layers with internal heat generation: Theory”, J. Fluid Mech., vol. 30, pp. 33-49, 1967.
[6] R. Thirlby, “Convection in an internally heated layer”, J. Fluid Mech., vol. 44 pp. 673-693, 1970.
[7] C. Parthiban and P. R. Patil, “Effect of non-uniform boundary temperatures on thermal instability in a porous medium with internal heat source”, Int. Commun. Heat Mass Transfer, vol. 22, pp. 683-692, 1995.
[8] C. Parthiban and P. R. Patil, “Thermal instability in an anisotropic porous medium with internal heat source and inclined temperature gradient”, Int. Comm. Heat Mass Transfer, vol. 24, pp. 1049-1058, 1997.
[9] A. Barletta, M. Celli and D. A. Nield, “Unstable buoyant flow in an inclined porous layer with an internal heat source”, International Journal of Thermal Sciences, vol. 79 pp. 176-182, 2014.
[10] S. Rionero and B. Straughan, “Convection in a porous medium with internal heat source and variable gravity effects”, Int. J. Eng. Sci., vol. 28 pp. 497-503, 1990.
[11] S. M. Alex and P. R. Patil, “Effect of a variable gravity field on convection in an anisotropic porous medium with internal heat source and inclined temperature gradient”, Transactions of the ASME, pp. 144-150, 2002.
[12] A. A. Hill, “Double-diffusive convection in a porous medium with a concentration based internal heat source, Proc. R. Soc. A, vol. 461, pp. 561-574, 2005.
[13] A. J. Chamka, A. Raheem and A. Khaled, “Similarity solutions for hydromagnetic simultaneous heat and mass transfer by natural convection from an inclined plate with internal heat generation or absorption”, J. Heat Mass Transfer, vol. 37, pp. 117-123, 2001.
[14] B. S. Bhadauria, “Double diffusive convection in a saturated anisotropic porous layer with internal heat source”, Transp. Porous Media, vol. 92, pp. 299-320, 2012.
[15] A. Borujerdi, A. R. Noghrehabadi and D. A. S. Rees, “Onset of convection in a horizontal porous channel with uniform heat generation using a thermal nonequilibrium model”, Trans. Porous Med., vol. 69, pp. 343-357, 2007
[16] A. N Borujerdi, A. R. Noghrehabadi and D. A. S. Rees, “Influence of Darcy number on the onset of convection in a porous layerwith a uniform heat source”, Int. J. of Thermal Sciences, vol. 47, pp. 1020-1025, 2008.
[17] D. A. Nield and A. Bejan, Convection in Porous Media, 4th ed., Springer 2013.
[18] J. E. Weber, “Convection in a porous medium with horizontal and vertical temperature gradients”, Int J Heat Mass Transf, vol. 17, pp. 241-248, 1974.
[19] D. A. Nield, “Convection in a porous medium with inclined temperature gradient and horizontal mass flow”, Heat Transfer, vol. 5, pp. 153-185, 1990.
[20] D. A. Nield, “Convection in a porous medium with inclined temperature gradient”, Int. J. Heat Mass Transfer, vol. 34, pp. 87-92, 1991.
[21] D. A. Nield, “Convection in a porous medium with inclined temperature gradient: additional results”, Int J. Heat Mass Transfer, vol. 37, pp. 3021-3025, 1994.