Throughflow and Gravity Modulation Effects on Thermal Convection in a Couple Stress Fluids Saturating a Porous Medium with an Internal Heat Source
DOI:
https://doi.org/10.37934/cfdl.15.3.6680Keywords:
Gravity modulation, throughflow, couple stress fluid, weakly non-linear theory, internal heating, Ginzburg-Landau modelAbstract
In this paper, the effect of throughflow and gravity modulation on thermal convection in a couple stress fluids saturating a porous medium with an internal heating source is investigated. A weakly nonlinear stability analysis is proposed to study the stationary mode of convection. The amplitude of gravity modulation is assumed to be very small and the disturbances are extended in terms of the power series of the amplitude of convection. Using a non-autonomous Ginzburg- Landau amplitude equation, heat transport is evaluated in terms of the Nusselt number. The finite-amplitude of convection has been derived in the third order. The amplitude and frequency of modulation have the effects of increasing or diminishing heat transport. The presence of a couple-stress parameter with internal heat source throughflow and modulation effects has been discussed. The effect of the internal heat source increases or decreases heat transfer in the system. For suitable ranges of Ω the throughflow and internal heating have both destabilizing and stabilizing effects. Finally flow patterns are presented in terms of streamlines and isotherms.
References
Nelson, Emily S. An examination of anticipation of g-jitter on space station and its effects on materials processes. NASA Technical Memorandum 103775, 1994.
Wadih, M., and B. Roux. "Natural convection in a long vertical cylinder under gravity modulation." Journal of Fluid Mechanics 193 (1988): 391-415. https://doi.org/10.1017/S0022112088002198
Wadih, M., N. Zahibo, and B. Roux. "Effect of gravity jitter on natural convection in a vertical cylinder." Low Gravity Fluid Dynamics and Transport Phenomena, edited by J. N. Koster and R. L. Sani (AIAA, New York, 1990) (1990): 309-354. https://doi.org/10.2514/5.9781600866036.0309.0352
Gershuni, G. Z., E. M. Zhukhovitskii, and Iu S. Iurkov. "On convective stability in the presence of periodically varying parameter: PMM vol. 34, n≗ 3, 1970, pp. 470-480." Journal of Applied Mathematics and Mechanics 34, no. 3 (1970): 442-452. https://doi.org/10.1016/0021-8928(70)90090-0
Gresho, P. M., and R. L. Sani. "The effects of gravity modulation on the stability of a heated fluid layer." Journal of Fluid Mechanics 40, no. 4 (1970): 783-806. https://doi.org/10.1017/S0022112070000447
Yang, Wen-Mei. "Stability of viscoelastic fluids in a modulated gravitational field." International Journal of Heat and Mass Transfer 40, no. 6 (1997): 1401-1410. https://doi.org/10.1016/S0017-9310(96)00194-9
Malashetty, M. S., and V. Padmavathi. "Effect of gravity modulation on the onset of convection in a fluid and porous layer." International Journal of Engineering Science 35, no. 9 (1997): 829-840. https://doi.org/10.1016/S0020-7225(97)80002-X
Rees, D. Andrew S., and I. Pop. "The effect of g-jitter on vertical free convection boundary-layer flow in porous media." International Communications in Heat and Mass Transfer 27, no. 3 (2000): 415-424. https://doi.org/10.1016/S0735-1933(00)00122-6
Govender, S. "Stability of convection in a gravity modulated porous layer heated from below." Transport in Porous Media 57, no. 1 (2004): 113-123. https://doi.org/10.1023/B:TIPM.0000032739.39927.af
Kuznetsov, A. V. "Linear stability analysis of the effect of vertical vibration on bioconvection in a horizontal porous layer of finite depth." Journal of Porous Media 9, no. 6 (2006): 597-608. https://doi.org/10.1615/JPorMedia.v9.i6.80
Bhadauria, B. S., and P. Kiran. "Weak nonlinear double diffusive magneto-convection in a Newtonian liquid under gravity modulation." Journal of Applied Fluid Mechanics 8, no. 4 (2015): 735-746. https://doi.org/10.18869/acadpub.jafm.67.223.22740
Bhadauria, B. S., P. G. Siddheshwar, Jogendra Kumar, and Om P. Suthar. "Weakly nonlinear stability analysis of temperature/gravity-modulated stationary rayleigh-bénard convection in a rotating porous medium." Transport in Porous Media 92, no. 3 (2012): 633-647. https://doi.org/10.1007/s11242-011-9925-4
Bhadauria, B. S., Ishak Hashim, and P. G. Siddheshwar. "Study of heat transport in a porous medium under G-jitter and internal heating effects." Transport in Porous Media 96, no. 1 (2013): 21-37. https://doi.org/10.1007/s11242-012-0071-4
Bhadauria, B. S., and Palle Kiran. "Nonlinear thermal Darcy convection in a nanofluid saturated porous medium under gravity modulation." Advanced Science Letters 20, no. 5-6 (2014): 903-910. https://doi.org/10.1166/asl.2014.5466
Kiran, Palle. "Nonlinear thermal convection in a viscoelastic nanofluid saturated porous medium under gravity modulation." Ain Shams Engineering Journal 7, no. 2 (2016): 639-651. https://doi.org/10.1016/j.asej.2015.06.005
Homsy, George M., and Albert E. Sherwood. "Convective instabilities in porous media with through flow." AIChE Journal 22, no. 1 (1976): 168-174. https://doi.org/10.1002/aic.690220121
Jones, M. C., and J. M. Persichetti. "Convective instability in packed beds with throughflow." AIChE Journal 32, no. 9 (1986): 1555-1557. https://doi.org/10.1002/aic.690320916
Shivakumara, I. S., and S. Sureshkumar. "Convective instabilities in a viscoelastic-fluid-saturated porous medium with throughflow." Journal of Geophysics and Engineering 4, no. 1 (2007): 104. https://doi.org/10.1088/1742-2132/4/1/012
Khalili, Arzhang, and I. S. Shivakumara. "Onset of convection in a porous layer with net through-flow and internal heat generation." Physics of Fluids 10, no. 1 (1998): 315-317. https://doi.org/10.1063/1.869540
Nield, D. A. "Convective instability in porous media with throughflow." AIChE Journal 33, no. 7 (1987): 1222-1224. https://doi.org/10.1002/aic.690330719
Suma, S. P., Y. H. Gangadharaiah, and R. Indira. "Effect of throughflow and variable gravity field on thermal convection in a porous layer." International Journal of Engineering Science and Technology 3, no. 10 (2011): 7657-7668.
Kiran, P. "Throughflow and g-jitter effects on binary fluid saturated porous medium." Applied Mathematics and Mechanics 36, no. 10 (2015): 1285-1304. https://doi.org/10.1007/s10483-015-1984-9
Kiran, P. "Throughflow and gravity modulation effects on heat transport in a porous medium." Journal of Applied Fluid Mechanics 9, no. 3 (2016): 1105-1113. https://doi.org/10.18869/acadpub.jafm.68.228.24682
Kiran, Palle, and B. S. Bhadauria. "Nonlinear throughflow effects on thermally modulated porous medium." Ain Shams Engineering Journal 7, no. 1 (2016): 473-482. https://doi.org/10.1016/j.asej.2015.03.010
Vanishree, R. K. "Effects of through-flow and internal heat generation on a thermo convective instability in an anisotropic porous medium." Journal of Applied Fluid Mechanics 7, no. 4 (2014): 581-590. https://doi.org/10.36884/jafm.7.04.19410
Hetsroni, G., M. Gurevich, and R. Rozenblit. "Natural convection in metal foam strips with internal heat generation." Experimental Thermal and Fluid Science 32, no. 8 (2008): 1740-1747. https://doi.org/10.1016/j.expthermflusci.2008.06.011
Bhadauria, B. S., Ishak Hashim, and P. G. Siddheshwar. "Study of heat transport in a porous medium under G-jitter and internal heating effects." Transport in Porous Media 96, no. 1 (2013): 21-37. https://doi.org/10.1007/s11242-012-0071-4
Bhadauria, B. S., Anoj Kumar, Jogendra Kumar, Nirmal C. Sacheti, and Pallath Chandran. "Natural convection in a rotating anisotropic porous layer with internal heat generation." Transport in Porous Media 90, no. 2 (2011): 687-705. https://doi.org/10.1007/s11242-011-9811-0
Saravanan, S. "Thermal non-equilibrium porous convection with heat generation and density maximum." Transport in Porous Media 76, no. 1 (2009): 35-43. https://doi.org/10.1007/s11242-008-9232-x
Bakar, Norhaliza Abu, and Rozaini Roslan. "Mixed Convection in a Lid-Driven Horizontal Cavity in the Presence of Internal Heat Generation or Absorption." Journal of Advanced Research in Numerical Heat Transfer 3, no. 1 (2020): 1-11.
Mahat, Rahimah, Muhammad Saqib, Imran Ulah, Sharidan Shafie, and Sharena Mohamad Isa. "MHD Mixed Convection of Viscoelastic Nanofluid Flow due to Constant Heat Flux." Journal of Advanced Research in Numerical Heat Transfer 9, no. 1 (2022): 19-25.
Loni, Reyhaneh, Gholamhassan Najafi, Rizalman Mamat, Mohd Fairusham Ghazali, and Nor Azwadi Che Sidik. "Nusselt Number Prediction for Oil and Water in Solar Tubular Cavity Receivers." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 97, no. 2 (2022): 157-174. https://doi.org/10.37934/arfmts.97.2.157174
Abidin, Nurul Hafizah Zainal, Nor Fadzillah Mohd Mokhtar, Izzati Khalidah Khalid, and Siti Nur Aisyah Azeman. "Oscillatory Mode of Darcy-Rayleigh Convection in a Viscoelastic Double Diffusive Binary Fluid Layer Saturated Anisotropic Porous Layer." Journal of Advanced Research in Numerical Heat Transfer 10, no. 1 (2022): 8-19.
Bhadauria, B. S., and Palle Kiran. "Heat transport in an anisotropic porous medium saturated with variable viscosity liquid under temperature modulation." Transport in Porous Media 100, no. 2 (2013): 279-295. https://doi.org/10.1007/s11242-013-0216-0
Kiran, Palle. "Throughflow and non-uniform heating effects on double diffusive oscillatory convection in a porous medium." Ain Shams Engineering Journal 7, no. 1 (2016): 453-462. https://doi.org/10.1016/j.asej.2015.04.003
Kiran, Palle. "Weak nonlinear oscillatory convection in a nonuniform heating porous medium with throughflow." International Journal of Engineering and Mathematical Modelling 2, no. 3 (2015): 63-78.
Venezian, Giulio. "Effect of modulation on the onset of thermal convection." Journal of Fluid Mechanics 35, no. 2 (1969): 243-254. https://doi.org/10.1017/S0022112069001091
Davis, Stephen H. "The stability of time-periodic flows." Annual Review of Fluid Mechanics 8, no. 1 (1976): 57-74. https://doi.org/10.1146/annurev.fl.08.010176.000421
Srivastava, Alok, B. S. Bhadauria, and I. Hashim. "Effect of internal heating on double diffusive convection in a couple stress fluid saturated anisotropic porous medium." Advances in Materials Science and Applications 3, no. 1 (2014): 24-45. https://doi.org/10.5963/AMSA0301004
Kippenhahn, Rudolf, and Alfred Weigert. Stellar structure and evolution. Berlin: Springer-Verlag, 1994.
Lapwood, E. R. "Convection of a fluid in a porous medium." In Mathematical Proceedings of the Cambridge Philosophical Society, vol. 44, no. 4, pp. 508-521. Cambridge University Press, 1948. https://doi.org/10.1017/S030500410002452X
