Effects of Uniform and Non-Uniform Temperature Gradients on Marangoni Convection in a Composite Layer with Variable Heat Sources
Authors
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Department of UG, PG Studies and Research in Mathematics, Government Science College Autonomous, Bengaluru, Karnataka ,IN
R. Sumithra -
Department of UG, PG Studies and Research in Mathematics, Government Science College Autonomous, Bengaluru, Karnataka ,INM. A. Archana
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Department of UG, PG Studies and Research in Mathematics, Government Science College Autonomous, Bengaluru, Karnataka ,INDeepa R. Acharya
DOI:
https://doi.org/10.18311/jmmf/2022/31855Keywords:
Marangoni Convection, Eigen Value, Variable Heat Source, Non-Uniform Temperature Profiles.Abstract
An investigation is carried out to determine the effect of uniform and non-uniform temperature profiles on single component Darcy-Benard Marangoni (DBM) convection in a composite layer system consisting of an incompressible fluid saturated porous layer on top of which is a layer of the same fluid with variable heat sources in both layers. The upper surface of the fluid layer is free with surface tension effects depending on temperature and the lower surface of the porous layer is rigid. The eigen value, thermal Marangoni number (TMN) is solved exactly for linear, parabolic and inverted parabolic temperature profiles for the adiabatic thermal boundary conditions at the horizontal boundaries of the composite layer. The influence of various dimensionless parameters on the eigen value against depth ratio is discussed in detail.
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References
Kuznetsov, A.V., Nield, D.A. (2016). The effect of spatially nonuniform internal heating on the onset of convection in a horizontal fluid layer. ASME. J.Heat Transfer, 138(6), 062503: 1- 9.
Mokhtar, N.F.M et al. (2011). Effect of heat generation on the onset of Marangoni convection in superposed layers of fluid and saturated porous medium. International Journal of Pure and Applied Mathematics, 67(4), 387-405.
Nanjundappa Rudraiah, Pradeep G. Siddheshwar. (2000). Effect of non-uniform basic temperature gradients on the onset of Marangoni convection in a fluid with suspended particles. Aerospace Science and Technology, 4(8), 517-523.
Nield, D. A., Kuznetsov, A.V. (2016). The onset of convection in a horizontal porous layer with spatially non-uniform internal heating. Trans.Porous.Med, 111, 541-553.
Pearson, J.R. (1958). On convection cells induced by surface tension. Journal of Fluid Mechanics. 4, 489-500.
Ramachandramurthy, V., and aruna, A.S. (2018). Rayleigh-Benard-Taylor convection in temperature-sensitive Newtonian liquid with heat source. International Journal of Engineering Research and Technology. 7(7), 166-170.
Riahi. N. (1984). Nonlinear convection in a horizontal layer with an internal heat source. Journal of Physical Society of Japan. 53(12), 4169-78.
Shah, Y.T., Andras Szeri. (1974). Marangoni instability in case of a non-uniform heat source. International Journal of heat and Mass Transfer. 17(11), 1419-21.
Shivakumara, I.S., Rudraiah, N., Nanjundappa, C.E. (2002). Effect of non-uniform basic temperature gradient on Rayleigh-Benard-Marangoni convection in ferrofluids. Journal of Magnetism and Magnetic Materials, 248(3), 379-395.
Shivakumara, I.S., Suma, S.P., Gangadharaiah, Y.H. (2011). Effect of non-uniform basic temperature gradients on Marangoni convection with a boundary slab of finite conductivity. International Journal of Engineering Science and Technology. 3(5), 4151-60.
Siti Suzilliana Putri Mohamed Isa et al. (2009). Effects of non-uniform temperature gradients on Marangoni convection with free slip condition. American Journal of Scientific Research(1). 37-44.
Sumithra, R., Archana, M.A., Vanishree, R.K. (2020). Darcy-Benard surface tension driven convection in a composite layer with temperature dependent heat source. Malaya Journal of Mathematik. 8(4), 2074-81.
Sumithra, R., Shyamala Venkatraman. (2020). Effects of uniform and non-uniform heat profiles on Darcy-Benard-Marangoni convection in a composite layer comprising of couple stress fluid. Malaya Journal of Mathematik, 8(4), 2215-27.
Sumithra, R., Vanishree, R.K., Deepa R Acharya.(2020) Non-Darcian Benard Marangoni Convection in a superposed fluid-porous layer with temperature dependent heat source. Malaya Journal of Mathematik, 8(4), 2233-42.
Sumithra, R., Vanishree, R.K., and Manjunatha, N. (2020). Effect of constant heat source/sink on single component Marangoni convection in a composite layer bounded by adiabatic boundaries in the presence of uniform & non uniform temperature gradients. Malaya Journal of Matematik. 8(2), 306-313.
Vanishree, R.K., Sumithra, R., and Manjunatha, N. (2020). Effect of uniform and non uniform temperature gradients on Benard-Marangoni convection in a superposed fluid and porous layer in the presence of heat source. Gedag & Organisite Review. 33(2), 746-758.
