Darcy-Benard double diffusive Marangoni convection in a composite layer system with constant heat source along with non uniform temperature gradients
DOI:
https://doi.org/10.11113/mjfas.v17n1.1984Keywords:
Darcy model, Adiabatic boundaries, Depth ratio, Composite layer, Heat source, Three profiles,Abstract
The problem of Benard double diffusive Marangoni convection is investigated in a horizontally infinite composite layer system enclosed by adiabatic boundaries for Darcy model. This composite layer is subjected to three temperature gradients with constant heat sources in both the layers. The lower boundary of the porous region is rigid and upper boundary of the fluid region is free with Marangoni effects. The Eigenvalue problem of a system of ordinary differential equations is solved in closed form for the Thermal Marangoni number, which happens to be the Eigen value. The three different temperature profiles considered are linear, parabolic and inverted parabolic profiles with the corresponding thermal Marangoni numbers are obtained. The impact of the porous parameter, modified internal Rayleigh number, solute Marangoni number, solute diffusivity ratio and the diffusivity ratio on Darcy-Benard double diffusive Marangoni convection are investigated in detail.
References
Akil J. Harfash., Fahad K. Nashmi., 2017. Triply resonant double diffusive convection in a fluid layer. Mathematical Modelling and Analysis, 22(6), 809-826.
Bennacer, R., Beji, H., Mohamad, A. A., 2003. Double diffusive convection in a vertical enclosure inserted with two saturated porous layers confining a fluid layer. International Journal of Thermal Sciences, 42(2), 141-151.
Chen C. F., Cho Lik Chan., 2010. Stability of buoyancy and surface tension driven convection in a horizontal double-diffusive fluid layer, International Journal of Heat and Mass Transfer, 53(7–8), 1563-1569.
Gangadharaiah, Y. H., Suma, S. P., 2013. Bernard-Marangoni convection in a fluid layer overlying a layer of an anisotropic porous layer with deformable free surface, Advanced Porous Materials, 1(2), 229-238.
Kanchana, C., YiZhao., P.G.Siddheshwar., 2020. Küppers–Lortz instability in rotating Rayleigh–Bénard convection bounded by rigid/free isothermal boundaries”. Applied Mathematics and Computation, 385, 125406.
Massimo Corcione, Stefano Grignaffini, Alessandro Quintino., 2015. Correlations for the double-diffusive natural convection in square enclosures induced by opposite temperature and concentration gradients. International Journal of Heat and Mass Transfer, 81, 811-819.
Norazam Arbin, Nur Suhailayani Suhaimi, Ishak Hashim., 2016. Simulation on double-diffusive Marangoni convection with the presence of entropy generation. Indian Journal of Science and Technology, 9(31), DOI: 10.17485/ijst/2016/v9i31/97817.
Saleem, M., Hossain, M. A., Suvash C. Saha., 2014. Double diffusive Marangoni convection flow of electrically conducting fluid in a square cavity with chemical reaction. J. Heat Transfer, 136(6), 1-9.
Sheng Chen, Jonas Tlke, Manfred Krafczyk., 2014. Numerical investigation of double-diffusive (natural) convection in vertical annuluses with opposing temperature and concentration gradients. International Journal of Heat and Fluid Flow, 31(2), 217-226.
Sumithra, R., 2014. Double diffusive magneto Marangoni convection in a composite layer. International Journal of Application or Innovation in Engineering & Management. 3(2), 12-25.
Sumithra, R., Vanishree, R. K., Manjunatha, N., 2020. Effect of constant heat source / sink on single component Marangoni convection in a composite layer bounded by adiabatic boundaries in presence of uniform & non uniform temperature gradients. Malaya Journal of Matematik, 8(2), 306-313.
Tatyana Lyubimova., Ekaterina Kolchanova., 2018. The onset of double-diffusive convection in a superposed fluid and porous layer under high-frequency and small-amplitude vibrations. Transport in Porous Media, 122(11), 97-124.
Vanishree, R. K., Sumithra, R., Manjunatha, N., 2020. Effect on uniform and non uniform temperature gradients on Benard-Marangoni convection in a superposed fluid and porous layer in the presence of heat source”. Gedrag en Organisatie. 33(2), 746-758.
