Effects of Throughflow and Gravity Modulation on Thermal Convection in a Couple Stress Fluid Saturated Porous Layer
DOI:
https://doi.org/10.37934/cfdl.14.7.117Keywords:
Throughflow, gravity modulation, weak non-linear theory, couple stress fluid, Ginzburg-Landau modelAbstract
In this paper, we have investigated the effects of throughflow and gravity modulation on a couple stress fluid saturated porous layer using non-autonomous Ginzburg-Landau model. A small variation of disturbances has been considered to examine the nonlinear thermal instability in a couple stress fluid saturated porous media. At third order, the finite amplitude of convection has been calculated which determines heat transfer. The effect of throughflow i.e., inflow and outflow have dual nature of heat transfer. The couple-stress parameter has stabilizing nature on thermal instability. The couple-stress parameter has stabilizing nature on thermal instability. Further it is found that upward directed flow enhances and downward directed flow diminishes heat transfer.
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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., Palle Kiran, and M. Belhaq. "Nonlinear thermal convection in a layer of nanofluid under g-jitter and internal heating effects." In MATEC Web of Conferences, vol. 16, p. 09003. EDP Sciences, 2014. https://doi.org/10.1051/matecconf/20141609003
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
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
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., and Palle Kiran. "Weak non-linear oscillatory convection in a viscoelastic fluid layer under gravity modulation." International Journal of Non-Linear Mechanics 65 (2014): 133-140. https://doi.org/10.1016/j.ijnonlinmec.2014.05.002
Bhadauria, B. S., and Palle Kiran. "Weak nonlinear oscillatory convection in a viscoelastic fluid-saturated porous medium under gravity modulation." Transport in Porous Media 104, no. 3 (2014): 451-467. https://doi.org/10.1007/s11242-014-0343-2
Bhadauria, B. S., and Palle Kiran. "Chaotic and oscillatory magneto-convection in a binary viscoelastic fluid under G-jitter." International Journal of Heat and Mass Transfer 84 (2015): 610-624. https://doi.org/10.1016/j.ijheatmasstransfer.2014.12.032
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
Govender, S. "Linear stability and convection in a gravity modulated porous layer heated from below: transition from synchronous to subharmonic solutions." Transport in Porous Media 59, no. 2 (2005): 227-238. https://doi.org/10.1007/s11242-004-1369-7
Chand, Ramesh, G. C. Rana, and Dhananjay Yadav. "Thermal instability in a layer of couple stress nanofluid saturated porous medium." Journal of Theoretical and Applied Mechanics 47, no. 1 (2017): 69-84. https://doi.org/10.1515/jtam-2017-0005
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
Ingham, Derek B., and Ioan Pop. Transport phenomena in porous media. Elsevier, 1998.
Nield, Donald A., and Adrian Bejan. Convection in porous media. New York: Springer, 2013. https://doi.org/10.1007/978-1-4614-5541-7
Vafai, Kambiz, ed. Handbook of porous media. CRC Press, 2005. https://doi.org/10.1201/9780415876384
Jamai, H., S. O. Fakhreddine, and H. Sammouda. "Numerical study of sinusoidal temperature in magneto-convection." Journal of Applied Fluid Mechanics 7, no. 3 (2014): 493-502. https://doi.org/10.36884/jafm.7.03.19566
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.
Kiran, Palle, and B. S. Bhadauria. "Chaotic convection in a porous medium under temperature modulation." Transport in Porous Media 107, no. 3 (2015): 745-763. https://doi.org/10.1007/s11242-015-0465-1
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
Kuqali, M., S. Babuin, and J. J. Niemela. "Effect of periodic bottom plate heating on large scale flow in turbulent Rayleigh-Bénard convection." Journal of Applied Fluid Mechanics 8, no. 3 (2015): 483-489. https://doi.org/10.18869/acadpub.jafm.67.222.21362
Shivakumara, I. S., S. Sureshkumar, and N. Devaraju. "Effect of non-uniform temperature gradients on the onset of convection in a couple-stress fluid-saturated porous medium." Journal of Applied Fluid Mechanics 5, no. 1 (2012): 49-55. https://doi.org/10.36884/jafm.5.01.11957
Malashetty, M. S., and M. S. Swamy. "Effect of gravity modulation on the onset of thermal convection in rotating fluid and porous layer." Physics of Fluids 23, no. 6 (2011): 064108. https://doi.org/10.1063/1.3593468
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
Siddheshwar, P. G., B. S. Bhadauria, and Alok Srivastava. "An analytical study of nonlinear double-diffusive convection in a porous medium under temperature/gravity modulation." Transport in Porous Media 91, no. 2 (2012): 585-604. https://doi.org/10.1007/s11242-011-9861-3
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
Nelson, Emily S. An examination of anticipated g-jitter on space station and its effects on materials processes. No. NAS 1.15: 103775. 1994.
Sharma, R. C., and Shivani Sharama. "On couple-stress fluid heated from below in porous medium." In Indian Journal of Physics and Proceedings of The Indian Association for The Cultivation of Science B, vol. 75, no. 2, pp. 137-139. Indian Association for the Cultivation of Science; 1999, 2001.
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
Sunil, R. C. Sharmab, and R. S. Chandel. "On Superposed Couple-stress Fluids in Porous Medium in Hydromagnetics The Use of Quantum-Chemical Semiempirical Methods to Calculate the Lattice Energies of Organic Molecular Crystals. Part II: The Lattice Energies of-and-Oxalic Acid (COOH) 2." Zeitschrift für Naturforschung A 57, no. 12 (2002): 955-960. https://doi.org/10.1515/zna-2002-1208
Stokes, Vijay Kumar. "Couple Stresses in Fluids." The Physics of Fluids 9, no. 9 (1966): 1709-1715. https://doi.org/10.1063/1.1761925
Umavathi, J. C., and M. S. Malashetty. "Oberbeck convection flow of a couple stress fluid through a vertical porous stratum." International Journal of Non-Linear Mechanics 34, no. 6 (1999): 1037-1045. https://doi.org/10.1016/S0020-7462(98)00074-2
Taylor, Kevin C., and Hisham A. Nasr-El-Din. "Water-soluble hydrophobically associating polymers for improved oil recovery: A literature review." Journal of Petroleum Science and Engineering 19, no. 3-4 (1998): 265-280. https://doi.org/10.1016/S0920-4105(97)00048-X
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
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
Mahajan, Amit, and Vinit Kumar Tripathi. "Effects of spatially varying gravity, temperature and concentration fields on the stability of a chemically reacting fluid layer." Journal of Engineering Mathematics 125, no. 1 (2020): 23-45. https://doi.org/10.1007/s10665-020-10068-1
Tripathi, Vinit Kumar, and Amit Mahajan. "The destabilizing effect of boundary slip on double-diffusive convection in a fluid layer with chemical reaction under variable gravity field." Heat Transfer Research 53, no. 3 (2022): 47-66. https://doi.org/10.1615/HeatTransRes.2021038508
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
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.
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
Kiran, Palle. "Nonlinear throughflow and internal heating effects on vibrating porous medium." Alexandria Engineering Journal 55, no. 2 (2016): 757-767. https://doi.org/10.1016/j.aej.2016.01.012
Kiran, Palle, and B. S. Bhadauria. "Weakly nonlinear oscillatory convection in a rotating fluid layer under temperature modulation." Journal of Heat Transfer 138, no. 5 (2016). https://doi.org/10.1115/1.4032329
Kiran, Palle, and Y. Narasimhulu. "Weakly nonlinear oscillatory convection in an electrically conduction fluid layer under gravity modulation." International Journal of Applied and Computational Mathematics 3, no. 3 (2017): 1969-1983. https://doi.org/10.1007/s40819-016-0218-z
Rebhi, Redha, Younes Menni, Giulio Lorenzini, and Hijaz Ahmad. "Forced-Convection Heat Transfer in Solar Collectors and Heat Exchangers: A Review." Journal of Advanced Research in Applied Sciences and Engineering Technology 26, no. 3 (2022): 1-15. https://doi.org/10.37934/araset.26.3.115
Khan, Ansab Azam, Khairy Zaimi, Suliadi Firdaus Sufahani, and Mohammad Ferdows. "MHD flow and heat transfer of double stratified micropolar fluid over a vertical permeable shrinking/stretching sheet with chemical reaction and heat source." Journal of Advanced Research in Applied Sciences and Engineering Technology 21, no. 1 (2020): 1-14. https://doi.org/10.37934/araset.21.1.114
Najib, Najwa, and Norfifah Bachok. "Boundary layer flow, heat and mass transfer of cu-water nanofluid over a moving plate with soret and dufour effects: Stability analysis." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 82, no. 1 (2021): 96-104. https://doi.org/10.37934/arfmts.82.1.96104
Mahadi, Shafaruniza, Yeak Su Hoe, Norazam Arbin, and Faisal Salah. "Numerical Solution for Unsteady Acceleration MHD Third-Grade Fluid Flow in a Rotating Frame Through Porous Medium Over Semi-Infinite Boundary Condition with a Presence of Heat Transfer." Journal of Advanced Research in Fluid Mechanics and Thermal Sciences 87, no. 2 (2021): 90-105. https://doi.org/10.37934/arfmts.87.2.90105
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