Darcy-Benard double diffusive Marangoni convection with Soret effect in a composite layer system

R. Sumithra; B. Komala; N. Manjunatha

doi:10.26637/MJM0804/0023

Abstract

The effect of Soret parameter on double diffusive Marangoni convection in a two-layer system, comprising an incompressible two component fluid saturated porous layer over which lies a layer of the same fluid under micro gravity condition is investigated analytically. The upper boundary of the fluid layer is free, the lower boundary of the porous layer is rigid and both the boundaries are insulating to heat and mass. At the interface, the velocity, shear stress, normal stress, heat, heat flux, mass and mass flux are assumed to be continuous. Thermal Marangoni number is obtained by solving ordinary differential equations using method of exact solution. The effect of different physical parameters on double diffusive Marangoni convection are also investigated in detail.

Keywords:

Double Diffusive Marangoni Convection, Soret Effect, Thermal Marangoni Number

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.
B. Komala School of Engineering, Dayananda Sagar University, Bengaluru, Karnataka, India.
N. Manjunatha School of Engineering, Dayananda Sagar University, Bengaluru, Karnataka, India.

Pages: 1473-1479
Date Published: 01-10-2020
Vol. 8 No. 04 (2020): Malaya Journal of Matematik (MJM)

A. Khadiri, A. Amahmid, M. Hasnaoui and A. Rtibi, Soret Effect on Double-Diffusive Convection in a Square Porous Cavity Heated and Salted from Below, An International Journal of Computation and Methodology, 57(11)(2010), 848-868.

B. Komala and R. Sumithra, Effects of Uniform and Non Uniform Salinity Gradients on the Onset of Double Diffusive Convection in a Composite Layer: An Analytical Study, ARPN Journal of Engineering and Applied Sciences, 14(4)(2019), 856-868.

Bennacer, R., Mahidjiba, A., Vasseur, P., Beji, H. and Duval, R., The Soret effect on convection in a horizontal porous domain under cross temperature and concentration gradients, International Journal of Numerical Methods for Heat and Fluid Flow, 13(2)(2003), 199-215.

${ }^{[4]}$ C. G. Mohan, A. Satheesh, Computational Investigation of Double-Diffusive Mixed Convective Flow in an Enclosed Square Cavity with Soret Effect, Frontiers in Heat and Mass Transfer, 8(36)(2017), 1-10.

Chigozie Israel-Cookey, Emeka Amos and Liberty Ebiwareme, Soret and Magnetic Field Effects on Thermosolutal Convection in a Porous Medium with Concentration Based Internal Heat Source, American Journal of Fluid Dynamics, 8(2)(2018), 41-46.

${ }^{text {[6] }}$ F. Chen, C.F. Chen and A.J. Pearlstein, Convective instability in superposed fluid and anisotropic porous layers, Physics of Fluids, 3(4)(1991), 556-565.

Hussam K. Jawad, Natural Convection And Soret Effect In A Multi-Layered Liquid And Porous System, 2012.

J. P. Pascal and S. J. D. D'Alessio, Thermosolutal Marangoni effects on the inclined flow of a binary liquid with variable density I, Linear Stability Analysis, 1(8)(2016), 083603(20).

M. Bhuvaneswari, S. Sivasankaran and Y. J. Kim, Numerical Study on Double Diffusive Mixed Convection with a Soret Effect in a Two-Sided Lid-Driven Cavity, $mathrm{Nu}$ merical Heat Transfer, Part A: Applications, 59(7)(2011), $543-560$.

M.S.Malashetty, S.N.Gaikwad and MahanteshSwamy, An analytical study of linear and non-linear double diffusive convection with Soret effect in couple stress liquids, International Journal of Thermal Sciences, 45(9)(2006), 897-907.

Nield D.A, Onset of Convection in a Fluid Layer overlying a layer of porous layer, J. Fluid Mech., 1977, 513-522.

P.V.S.N. Murthy and M.F. El-Amin, Thermo-Diffusion Effect on Free Convection Heat and Mass Transfer in a Thermally Linearly Stratified Non-Darcy Porous Media, The Open Transport Phenomena Journal, 3(2011), 49-55.

R. Sumithra and B. Komala, Effects of Parabolic and Inverted Parabolic Salinity Gradients on Double Diffusive Marangoni Convection in a Composite Layer: An Exact Study, International Journal of Application or Innovation in Engineering and Management, 3(10)(2014), 258-273.

Rishi Raj Kairi, Ch. Ram Reddy and Santanu Raut, Influence of viscous dissipation and thermo-diffusion on double diffusive convection over a vertical cone in a nonDarcy porous medium saturated by a non-Newtonian fluid with variable heat and mass fluxes, Nonlinear Engineering, 7(1)(2018), 65-72.

S. Saravanan, T. Sivakumar, Exact solution of Marangoni convection in a binary fluid with throughflow and Soret effect, Applied Mathematical Modelling, 33(2009), 3674-3681.

Venkatachalappa M, Prasad Shivakumara I S. and Sumithra R, Hydrothermal growth due to double diffusive convection in composite materials, Proceedings of 14th National Heat and Mass Transfer Conference and $3 mathrm{rd}$ ISHMT ASME Joint Heat and Mass Transfer Conference, December 1997, 29-31