Darcy-Benard surface tension driven convection in a composite layer with temperature dependent heat source

R. Sumithra; M. A. Archana; R. K. Vanishree

doi:10.26637/MJM0804/0127

Abstract

The effect of temperature dependent heat source on single component Benard Surface tension driven convection in a composite layer system comprising of an incompressible fluid saturated porous layer underlying a layer of same fluid, is studied. The lower surface of the porous layer is rigid and the upper surface is free with surface tension depending on temperature. The governing partial differential equations are non-dimensionalized using suitable transformation variables. The eigen value problem obtained after normal mode analysis is solved analytically using Exact Method. An expression for the eigenvalue, the Thermal Marangoni number is obtained for two sets of thermal boundary conditions on the boundaries of the composite layer, set (i) Adiabatic-Adiabatic and set (ii) Isothermal-Adiabatic. The effects of different physical parameters on the same are discussed in detail.

Keywords:

Composite layer, Surface tension driven convection, Temperature dependent heat source

Mathematics Subject Classification:

Mathematics

Authors Imprint References Funding Related Articles Downloads

R. Sumithra Department of UG, PG Studies and Research in Mathematics, Government Science College Autonomous, Bengaluru, Karnataka, India.
M. A. Archana Department of UG, PG Studies and Research in Mathematics, Government Science College Autonomous, Bengaluru, Karnataka, India.
R. K. Vanishree Department of Mathematics, Maharani Science College for Women, Maharani Cluster University, Bengaluru, Karnataka, India. https://orcid.org/0000-0003-2844-5127

Pages: 2074-2081
Date Published: 01-10-2020
Vol. 8 No. 04 (2020): Malaya Journal of Matematik (MJM)

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