This paper investigated the buoyancy and surface tension-driven ferro-thermal-convection (FTC) in a ferrofluid (FF) layer due to influence of general boundary conditions. The lower surface is rigid with insulating to temperature perturbations, while the upper surface is stress-free and subjected to general thermal boundary condition. The numerically Galerkin technique (GT) and analytically regular perturbation technique (RPT) are applied for solving the problem of eigenvalue. It is analyzed that increasing Biot number, decreases the magnetic and Marangoni number is to postponement the onset. Additionally, magnetization nonlinearity parameter has no effect on FTC in the non-existence of Biot number. The results under the limiting cases are found to be in good agreement with those available in the literature.
References
[1]
Rosensweig, R.E. (1985) Ferrohydrodynamics. Cambridge University Press, Cambridge.
[2]
Bashtovoy, V.G., Berkovsky, B.N. and Vislovich, A.N. (1988) Introduction to Thermo Mechanics of Magnetic Fluids. Springer, Berlin, Heidelberg.
[3]
Berkovsky, B.M., Medvedev, V.F. and Krakov, M.S. (1993) Magnetic Fluids, Engineering Applications. Oxford University Press, Oxford.
[4]
Odenbach, S. (2003) Magnetic Fluids-Suspensions of Magnetic Dipoles and Their Mantic Controls. Journal of Physics: Condensed Matter, 15, S1497-S1508. https://doi.org/10.1088/0953-8984/15/15/312
[5]
Finlayson, B.A. (1972) Method of Weighted Residuals and Variational Principles. Academic Press, Cambridge.
[6]
Qin, Y. and Kaloni, P.N. (1994) Nonlinear Stability Problem of a Ferromagnetic Fluid with Surface Tension Effect. European Journal of Mechanics B: Fluids, 13, 305-321.
[7]
Hennenberg, M., Weyssow, B., Slavtchev, S. and Legros, J.C. (2001) Coupling between Marangoni and Rosensweig Instabilities. Part I: The Transfer Wave. European Physics Journal of Applied Physics, 16, 217-229. https://doi.org/10.1051/epjap:2001212
[8]
Shivakumara, I.S., Rudraiah, N. and Nanjundappa, C.E. (2002) The Effect of Different forms of Basic Temperature Gradients on the Onset of Ferroconvection Driven by Combined Surface Tension and Buoyancy Forces. Indian Journal of Pure Applied Physics, 40, 95-106.
[9]
Shivakumara, I.S. and Nanjundappa, C.E. (2006) Marngoni Ferroconvection with Different Initial Temperature Gradients. Journal of Energy and Heat Mass Transfer, 28, 1-45.
[10]
Nanjundappa, C.E. and Shivakumara, I.S. (2008) Effect of Velocity and Temperature Boundary Conditions on Convective Instability in a Ferrofluid Layer. ASME Journal of Heat Transfer, 130, Article ID: 104502. https://doi.org/10.1115/1.2952742
[11]
Shivakumara, I.S., Nanjundappa, C.E. and Chavaraddi, K.B. (2009) Darcy-Benard-Marangoni Convection in Porous Media. International Journal of Heat and Mass Transfer, 52, 2815-2823. https://doi.org/10.1016/j.ijheatmasstransfer.2008.09.038
[12]
Nanjundappa, C.E., Shivakumara, I.S. and Arunkumar, R. (2010) Bénard-Marangoni Ferroconvection with Magnetic Field Dependent Viscosity. Journal of Magnetism and Magnetic Materials, 322, 2256-2263. https://doi.org/10.1016/j.jmmm.2010.02.021
[13]
Nanjundappa, C.E., Shivakumara, I.S. and Savitha, B. (2014) Onset of Bénard-Marangoni Rroconvection with a Convective Surface Boundary Condition: The Effects of Cubic Temperature Profile and MFD Viscosity. International Communications in Heat and Mass Transfer, 51, 39-44. https://doi.org/10.1016/j.icheatmasstransfer.2013.11.010
[14]
Nanjundappa, C.E., Shivakumara, I.S. and Arunkumar, R. (2013) Onset of Marangoni-Bénard Ferroconvection with Temperature Dependent Viscosity. Microgravity Science and Technology, 25, 103-112. https://doi.org/10.1007/s12217-012-9330-9
[15]
Nanjundappa, C.E., Prakash, H.N., Shivakumara, I.S. and Lee, J. (2014) Effect of Temperature Dependent Viscosity on the Onset of Bénard-Marangoni Ferroconvection. International Communications in Heat and Mass Transfer, 51, 25-30. https://doi.org/10.1016/j.icheatmasstransfer.2014.01.010
[16]
Nanjundappa, C.E., Shivakumara, I.S. and Arunkumar, R. (2011) Onset of Bénard-Marangoni Ferroconvection with Internal Heat Generation. Microgravity Science and Technology, 23, 29-39. https://doi.org/10.1007/s12217-010-9218-5
[17]
Nanjundappa, C.E., Shivakumara, I.S. and Srikumar, K. (2013) On the Penetrative Bénard-Marangoni Convection in a Ferromagnetic Fluid Layer. Aerospace Science and Technology, 27, 57-66. https://doi.org/10.1016/j.ast.2012.06.007
[18]
Shivakumara, I.S. and Nanjundappa, C.E. (2006) Effects of Coriolis Force And Different Basic Temperature Gradients On Marangoni Ferroconvection. Acta Mechanica, 182, 113-124. https://doi.org/10.1007/s00707-005-0296-1
[19]
Nanjundappa, C.E., Shivakumara, I.S. and Lee, J. (2015) Effect of Coriolis Force on Bénard-Marangoni Convection in a Rotating Ferrofluid Layer with MFD Viscosity, Microgravity Science and Technology, 27, 27-37. https://doi.org/10.1007/s12217-014-9410-0
[20]
Shivakumara, I.S., Lee, J. and Nanjundappa, C.E. (2012) Onset of Thermogravitational Convection in a Ferrofluid Layer with Temperature Dependent Viscosity. Journal of Heat Transfer, 134, Article ID: 012501. https://doi.org/10.1115/1.4004758
[21]
Nanjundappa, C.E., Ravisha, M., Lee, J. and Shivakumara, I.S. (2011) Penetrative Ferroconvection in a Porous Layer. Acta Mechanica, 216, 243-257. https://doi.org/10.1007/s00707-010-0367-9
[22]
Nanjundappa, C.E., Shivakumara, I.S., Lee, J. and Ravisha, M. (2011) Effect Of Internal Heat Generation on the Onset of Brinkman-Bénard Convection in a Ferrofluid Saturated Porous Layer. International Journal of Thermal Sciences, 50, 160-168. https://doi.org/10.1016/j.ijthermalsci.2010.10.003
[23]
Nanjundappa, C.E., Shivakumara, I.S. and Prakash, H.N. (2012) Penetrative Ferroconvection via Internal Heating in a Saturated Porous Layer with Constant Heat Flux at the Lower Boundary. Journal of Magnetism and Magnetic Materials, 324, 1670-1678. https://doi.org/10.1016/j.jmmm.2011.11.057
[24]
Nanjundappa, C.E., Pavithra, A. and Shivakuamara, I.S. (2021) Effect of Dusty Particles on Darcy-Brinkman Gravity-Driven Ferro-Thermal-Convection in a Ferrofluid Saturated Porous Layer with Internal Heat Source: Influence of Boundaries, International Journal of Applied Computational Mathematics, 7, Article No. 21. https://doi.org/10.1007/s40819-020-00948-6
[25]
Savitha, Y.L., Nanjundappa, C.E. and Shivakumara, I.S. (2021) Penetrative Brinkman Ferroconvection via Internal Heating in High Porosity Anisotropic Porous Layer: Influence of Boundaries. Heliyon, 7, Article ID: e06153. https://doi.org/10.1016/j.heliyon.2021.e06153
[26]
Gotoh, K. and Yamada, M. (1982) Thermal Convection in a Horizontal Layer of Magnetic Fluids. Journal of Physical Society of Japan, 51, 3042-3048. https://doi.org/10.1143/JPSJ.51.3042
[27]
Sparrow, E.M., Goldstein, R.J. and Jonsson, U.K. (1964) Thermal Instability in a Horizontal Fluid Layer: Effect of Boundary Conditions and Non-Linear Temperature Profiles. Journal of Fluid Mechanics, 18, 513-528. https://doi.org/10.1017/S0022112064000386
