Heat Transport in Rayleigh-Benard Convection under Rotation Speed Modulation

S.H. Manjula¹

Section:Research Paper, Product Type: Journal-Paper
Vol.6 , Issue.6 , pp.28-35, Dec-2019

CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i6.2835

Online published on Dec 31, 2019

Copyright © S.H. Manjula . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

View this paper at   Google Scholar | DPI Digital Library

XML View     PDF Download

How to Cite this Paper

561 Views    329 Downloads    130 Downloads

Abstract :
The purpose of this article is to analyse, theoretically, the effect of modulated rotation speed on rotating Rayleigh-Benard convection in a fluid layer. Rayleigh-B`enard momentum equation with Coriolis term has been used to describe the flow. The system is considered rotating about it own axis with non-uniform rotation speed. In particular, we assume that the rotation speed is varying sinusoidally with time. A non-linear stability analysis has been performed to find the effect of modulation on heat transport. Nusselt number is obtained in terms of amplitude of convection, and depicted graphically with respect to time, showing the effect of various parameters of the system on heat transport. It is found that the effect of rotation speed modulation is to stabilize or destabilize the system depending on the frequency of modulation.

Key-Words / Index Term :
Rotation speed modulation, Rayleigh-B`enard convection, Coriolis force, Taylor number, Nonlinear stability

References :
[1]S. Chandrasekhar, “Hydrodynamic and hydromagnetic stability”, Oxford University Press, Oxford (U.K.) (1961).
[2]P.G. Drazin, D.H. Reid, “Hydrodynamic stability”, Cambridge University Press Cambridge, (2004).
[3] G. Venezian, “Effect of modulation on the onset of thermal convection”, J Fluid Mech 35, 243-254, 1969.
[4]S. Rosenblat, G.A. Tanaka, “Modulation of thermal convection instability”, Phys. Fluids, 14,1319-1322. 1971.
[5]R.G. Finucane, R.E. Kelly, “Onset of instability in a fluid layer heated sinusoidally from below”, Int. J. Heat Mass Transfer, 19, 71-85, 1976.
[6] S.H. Davis, “The stability of time periodic flows”, Annu Rev Fluid Mech, 8, 57-74, 1976.
[7]M.H. Roppo, S.H. Davis, S. Senblat, “Benard convection with time periodic heating”, Phys. Fluids, 27, 796-803, 1984.
[8]G. Ahlers, P.C. Hohenberg, M. Lucke, “Thermal convection under external modulation of the driving force”, I. The Lorenz model, Phys. Rev. A 32 (6), 3493-3518, 1985.
[9] J.J. Niemela, R.J. Donnelly, “Externally modulation of Rayleigh-Benard convection”, Phys Rev Lett, 59 (21) 2431-2434, 1987.
[10] S. Schmitt, M. Lucke, “Amplitude equation for modulated Rayleigh-Benard convection”, Phys Rev A 44 (8), 4986-5002, 1991.
[11] A.C. Or, R.E. Kelly, “Time modulated convection with zero mean temperature gradient”, Phys. Rev. E 60 (2), 1741-1747, 1999.
[12] A.C. Or, “Onset condition of modulated Rayleigh-Benard at low frequency”. Phys Rev E 64 (2001) 0502011-0502013.
[13] B.S. Bhadauria, P.K. Bhatia, “Time-periodic heating of Rayleigh-Benard convection”, Physica Scripta, 66, 59-65, 2002.
[14] B.S. Bhadauria, “Time-periodic heating of Rayleigh-Benard convection in a vertical magnetic field”, Physica Scripta, 73, 296-302, 2006.
[15] B.S. Bhadauria, P.K. Bhatia, L. Debnath, “Weakly non-linear analysis of Rayleigh-Benard convection with time periodic heating”, Int. J. Nonlinear Mech 44, 58-65, 2009.
[16] P.G. Siddheshwar, “A Series Solution for the Ginzburg-Landau Equation With a Time Periodic Coefficient”, Appl Math, 1(6) , 542-554., 2010.
[17] V.R.K. Raju, S.N. Bhattacharya, “Onset of thermal instability in a horizontal layer of fluid with modulated boundary temperatures”, J Engg Math, 66, 343-351, 2010.
[18] B.S. Bhadauria, P. Kiran, “Heat Transport in an Anisotropic Porous Medium Saturated with Variable Viscosity Liquid Under Temperature Modulation”, Transp Porous 100., 279-295, 2013.
[19] J.W. Rauscher, R.E. Kelly, “Effect of modulation on the onset of thermal convection in a rotating fluid”, Int. J. Heat Mass Transfer, 18, 1216-1217, 1975.
[20] Y. Liu, R.E. Ecke, “Heat Transport Scaling in Turbulent Rayleigh-Benard Convection: Effects of Rotation and Prandtl Number”, Phys Rev Lett 79 2257-2260, 1997.
[21] M.S. Malashetty, M. Swamy, “Effect of thermal modulation on the onset of convection in rotating fluid layer”, Int. J. heat and mass transp, 51, 2814-2823, 2008.
[22] R.C. Kloosterziel, G.F. Carnevale, “Closed-form linear stability conditions for rotating Rayleigh Benard convection with rigid stress-free upper and lower boundaries”, J. Fluid Mech. 480 25-42, 2003.
[23] M.S. Malashetty, M. Swamy, “Combined effect of thermal modulation and rotation on the onset of stationary convection in porous layer”, Transp Porous Med, 69, 313-330., 2007.
[25] B.S. Bhadauria, P.G. Siddheshwar, Om.P. Suthar, “Non-linear thermal instability in a rotating viscous fluid layer under temperature/gravity modulation”, J. Heat Transf. 34, 102-502, 2012.
[26] A. Srivastava, B.S. Bhadauria, P.G. Siddheshwar, “Heat transport in an anisotropic porous medium saturated with variable viscosity liquid under g-jitter and internal heating effects”, Transp in Porous Med, 99, 359-376, 2013.
[27]B.S. Bhadauria, P. Kiran, “Nonlinear thermal Darcy convection in a nanofluid saturated porous medium under gravity modulation” Advanced Science Letters 20, 903-910, 2014.
[28] B.S. Bhadauria, P. Kiran, “Weak nonlinear double diffusive magneto- convection in a Newtonian liquid under gravity modulation”, J of Applied Fluid Mech. 8,(4) 735-746, 2014.
[29]P. Kiran, “Throughow and g-jitter effects on binary fluid saturated porous medium” Applied Math and Mech 36,(10), 1285—1304, 2015, 2015..
[30]B.S. Bhadauria, P. Kiran, “Weak Nonlinear Double Diffusive Magneto-Convection in a Newtonian Liquid under Gravity Modulation”, J of Applied Fluid Mech 8 (4), 735-746, 2015.
[31]P. Kiran, “Nonlinear thermal convection in a viscoelactic nanofluid saturated porous medium under gravity modulation” Ain Shams Eng J. 7, 639-651 (2015)
[32]P. Kiran, “Throughflow and gravity modulation effects on heat transport in a porous medium”, J of Applied Fluid Mech. 9(3) 1105-1113, (2016)
[33]P. Kirna, B.S. Bhadauria., V. Kumar, “Thermal convection in a nanofluid saturated porous medium with internal heating and gravity modulation” J of nanofluid. 5, 01-12, 2016.
[34]P. Kirna, “Nonlinear throughflow and internal heating effects on vibrating porous medium” Alexandria Eng. J 55 (2), 757-767, 2016.
[35]P. Kiran, Y. Narasimhulu, “Centrifugally driven convection in a nanofluid saturated rotating porous medium with modulation”, J of Nanofluid, 6(1), 01- 11, 2017. DOI: 10.1166/jon.2017.1333
[36]P. Kiran, S.H. Manjula, Y. Narasimhulu, “Oscillatory convection in a rotating fluid layer under gravity modulation”, J of Emerging Tech and Innovative Research, 5(8), 227-242, 2018.
[37]P. Kiran, B.S. Bhadauria. “Chaotic convection in a porous medium under temperature modulation”, Transp Porous Media, 107, 745–763, 2015
[38]P. Kiran, B.S. Bhadauria. Nonlinear throughflow effects on thermally modulated porous medium. Ain Shams Eng J. 7(1), 473-482 (2015)
[39]P. Kiran, “Throughflow and non-uniform heating effects on double diffusive oscillatory convection in a porous medium”, Ain Shams Eng J7, 453– 462, 2016.
[40]P. Kiran, B.S. Bhadauria., Y. Narasimhulu, “Weakly nonlinear and nonlinear magneto-convection under thermal modulation”, J of Applied Nonlinear Dynamics, 6(4), 487-508, 2017.
[41]P Kiran, Y. Narasimhulu, “Internal Heating and Thermal Modulation Effects on Chaotic Convection in a Porous Medium”, Journal of Nanofluids 7 (3), 544- 555, 2018.
[42]Kiran, P., Bhadauria, B.S. “Weakly nonlinear oscillatory convection in a rotating fluid layer under temperature modulation” ASME J of Heat Transf. 138, 051702, 2016.
[43]P Kiran, S.H Manjula,Y Narasimhulu, “Weakly nonlinear oscillatory convection in a viscoelastic fluid saturated porous medium with through flow and temperature modulation”, Int J of Applied Mechanics and Engineering 23, 01-28, 2018,
[44]S.H Manjula, Palle Kiran, Y. Narasimhulu., “Heat transport in a porous medium saturated with variable viscosity under the effects of thermal modulation and internal heating”, J of Emerging Technologies and Innovative Research 5(8), 59-75, 2018.
[45]B.S. Bhadauria, P. Kiran, “Time periodic thermal boundary and rotation effects on heat transport in a temperature dependant viscosity liquid”, Int J of Applied Math and Mech 10(9), 61-75, 2014.
[46]R.J. Donnelly, “Experiments on the stability of viscous flow between rotating cylinders III: enhancement of hydrodynamic stability by modulation”, Proc. R. Soc. Lond. Ser A281, 130-139, 1964.
[47]J.K. Bhattacharjee, “Rotating Rayleigh-B`enard convection with modulation”, J Phys AMath Gen, 22, L1135-L1139, 1989.
[48]Om.P. Suthar, B.S. Bhadauria, A. Khan, “Modulated centrifugal convection in a rotating vertical porous layer distant from the axis of rotation”, Transp Porous Med, 79(2), 255-264, 2009.
[49] B.S. Bhadauria, P. Kiran, “Effect of rotational speed modulation on heat transport in a fluid layer with temperature dependent viscosity and internal heat source. Ain Shams Eng J. 5, 1287–1297 (2014)
[49]B.S. Bhadauria, P. Kiran, “Weak nonlinear analysis of magneto–convection under magnetic field modulation”, Physica Scripta, 89, 095209, 2014.
[50]P. Kiran, B.S. Bhadauria, Y. Narasimhulu., “Oscillatory magneto- convection under magnetic field modulation”, Alexandria Engg J, 57, 445-453, 2017.
[51]P. Kiran, B.S. Bhadauria, “Throughflow and rotational effects on oscillatory convection with modulated”, Nonlinear Studies, 23(3), 439-455, 2016.
[52]P. Kiran, B.S. Bhadauria, Y Narasimhulu, “Nonlinear throughflow effects on thermally modulated rotating porous medium”, J of Applied Nonlinear Dynamics 6, 27-44. 2017.
[53]S.H. Manjula, P. Kiran and P.R. Reddy and B.S. Bhadauria, “The complex Ginzburg Landau model for an oscillatory, convection in a rotating fluid layer”, Int J of Applied Mechanics and Engineering, 24, 01-17, 2019.
[54]BS. Bhadauria, MK. Singh, A. Singh, BK. Singh, P Kiran, “Stability analysis and internal heating effect on oscillatory convection in a viscoelastic fluid saturated porous medium under gravity modulation” Int. J of Applied Mechanics and Engg, 21 (4), 785-803, 2016.
[55]B.S. Bhadauria, P. Kiran, “Nonlinear thermal convection in a layer of nanofluid under g-jitter and internal heating effects” MATEC Web of Conference. 16, 09003, 2014.
[56]B.S. Bhadauria, P. Kiran, “Weak nonlinear double diffusive magneto-convection in a Newtonian liquid under temperature modulation”, Int J of Engg Mathematics, 2014, 01-14, 2014.