Controlling Rayleigh–Bénard Magnetoconvection in Newtonian Nanoliquids by Rotational, Gravitational and Temperature Modulations: A Comparative Study

Arabian Journal for Science and Engineering - Tập 47 - Trang 7837-7857 - 2022
Meenakshi Nerolu1, Pradeep G. Siddheshwar2
1Department of Mathematics, College of Arts and Sciences, Howard University, Washington, USA
2Centre for Mathematical Needs, Department of Mathematics, CHRIST (Deemed to be University), Bengaluru, India

Tóm tắt

The effect of three different types of time periodic modulations on the Rayleigh–Bénard magnetic system involving Newtonian nanoliquids is studied. Multiple-scale analysis (homogenization method) is used to arrive at the Ginzburg–Landau equation. The curiosity in the work is to know the individual effects of (1) rotation, (2) gravity and (3) temperature modulations on Rayleigh–Bénard magnetoconvection in weakly electrically conducting Newtonian nanoliquids. A significant effort in this research is devoted toward linear and nonlinear stability analyses as well as the homogenization method which leads to the Ginzburg–Landau evolution equation. Although several studies have concluded similar results for nanoliquids compared with those of pure base fluids, many fundamental issues like the choice of phenomenological models for the thermo-physical properties and “the” best type of nanoparticles are not well understood. This research focuses on several important issues involving mathematical and computational problems arising in heat transfer analysis in the presence of nanoliquids. Effects of various nanoliquid parameters, frequency and amplitude of modulation on heat transport are analyzed. This investigation focuses on five nanoliquids, with water as a carrier liquid and five nanoparticles, viz. copper, copper oxide, silver, alumina and titania. Enhanced heat transport was observed for rotation, gravity and temperature modulations. In the case of rotation modulation, it is found that increase in the amplitude of modulation results in a decrease in the critical Rayleigh number and thereby to an increase in the mean Nusselt number. The increase in the amplitude of the gravity modulation is shown to enhance the heat transport, whereas increase in frequency is to inhibit the heat transport. Two types of temperature modulations are considered, viz. in-phase (synchronous) and out-of-phase (asynchronous) temperature modulations with the assumption that the boundary temperatures vary sinusoidally with time. The amplitudes of modulation are considered to be very small. In the case of in-phase modulation, there is no significant difference between the heat transports in the presence and in the absence of temperature modulation. On this reason, out-of-phase temperature modulation is used to either enhance or diminish heat transport by suitably adjusting the frequency and phase difference of the modulated temperature. The effect of magnetic field, in all three cases of modulations, is to inhibit the onset of convection and thereby diminish the heat transport.

Tài liệu tham khảo

Shivakumara, I.S.; Rudraiah, N.; Nanjundappa, C.E.: Effect of non-uniform basic temperature gradient on Rayleigh-Bénard-Marangoni convection in ferrofluids. J. Magn. Magn. Mater. 248(3), 379–395 (2002) Siddheshwar, P.G.; Pranesh, S.: Effect of a non-uniform basic temperature gradient on Rayleigh-Bénard convection in a micropolar fluid. Int. J. Eng. Sci. 36(11), 1183–1196 (1998) Siddheshwar, P.G.; Pranesh, S.: Effect of temperature/gravity modulation on the onset of magneto-convection in weak electrically conducting fluids with internal angular momentum. J. Magnetism Magnetic materials 192(1), 159–176 (1999) Siddheshwar, P.G.; Pranesh, S.: Magnetoconvection in fluids with suspended particles under \(1g\) and \(\mu \)g. Aerospace Science and Technology 6(2), 105–114 (2002) Bhattacharjee, J.K.; McKane, A.J.: Lorenz model for the rotating Rayleigh-Bénard problem. J. Phys. A: Math. Gener. 21, L555–L558 (1988) Busse, F.H.: Thermal instabilities in rapidly rotating systems. J. Fluid Mech. 44(03), 441–460 (1970) Chandrasekhar, S.: Hydrodynamic and hydromagnetic stability. Clarendon Press, Oxford, UK (1961) Ecke, R.E.: Scaling of heat transport near onset in rapidly rotating convection. Phys. Letts. A 379, 2221–2223 (2015) Ecke, R.E.; Zhong, F.; Knobloch, E.: Hopf bifurcation with broken reflection symmetry in rotating Rayleigh-Bénard convection. Europhys. Lett. 19, 177–182 (1992) Julien, K.; Legg, S.; McWilliams, J.; Werne, J.: Rapidly rotating turbulent Rayleigh-Bénard convection. J. Fluid Mech. 322, 243–273 (1996) King, E.M.; Stellmach, S.; Aurnou, J.M.: Heat transfer by rapidly rotating Rayleigh-Bénard convection. J. Fluid Mech. 691, 568–582 (2012) Kooij, G.L.; Botchev, M.A.; Geurts, B.J.: Direct numerical simulation of Nusselt number scaling in rotating Rayleigh-Bénard convection. Int. J. Heat Fluid Flow 55, 26–33 (2015) Kuo, E.Y.; Cross, M.C.: Traveling-wave wall states in rotating Rayleigh-Bénard convection. Phys. Rev. E 47, 2245–2248 (1993) Lucas, P.G.J.; Pfotenhauer, J.M.; Donnelly, R.J.: Stability and heat transfer of rotating cryogens Part 1 Influence of rotation on the onset of convection in liquid 4He. J. Fluid Mech. 129, 251–264 (1983) Ning, L.; Ecke, R.E.: Rotating Rayleigh-Bénard convection: aspect-ratio dependence of the initial bifurcations. Phys. Rev. E 47, 3326–3333 (1993) Veronis, G.: Cellular convection with finite amplitude in a rotating fluid. J. Fluid Mech. 5, 401–435 (1959) Zhong, F.; Ecke, R.: Pattern dynamics and heat transport in rotating Rayleigh-Bénard convection. Chaos: Interdiscip. J. Nonlin. Sci. 2, 163–171 (1992) Zhong, F.; Ecke, R.; Steinberg, V.: Rotating Rayleigh-Bénard convection: K\(\ddot{u}\)ppers-Lortz transition. Physica D: Nonlin. Phenomena 51, 596–607 (1991) Bhattacharjee, J.K.: Rotating Rayleigh-Bénard convection with modulation. J. Phys. A: Math. Gener. 22(24), L1135–L1139 (1989) Bhattacharjee, J.K.: Convective instability in a rotating fluid layer under modulation of the rotating rate. Physical Rev. A 41, 5491–5494 (1990) De Nigris, G.; Nicolis, G.; Frisch, H.: Stochastic perturbations of Rayleigh-bénard instability: effect of random rotation. Phys. Rev. A 34, 4211–4216 (1986) Kumar, K.; Bhattacharjee, J.K.; Banerjee, K.: Onset of the first instability in hydrodynamic flows: effect of parametric modulation. Physical Rev. A 34, 5000–5006 (1986) Niemela, J.J.; Smith, M.R.; Donnelly, R.J.: Convective instability with time-varying rotation. Physical Rev. A 44, 8406–8409 (1991) Thompson, K.L.; Bajaj, K.M.S.; Ahlers, G.: Traveling concentric-roll patterns in Rayleigh-Bénard convection with modulated rotation. Phys. Rev. E 65, 046218 (2002) Aanam, A.N.; Siddheshwar, P.G.; Nagouda, S.S.; Pranesh, S.: Thermoconvective instability in a vertically oscillating horizontal ferrofluid layer with variable viscosity. Heat Transfer 49(8), 4543–4564 (2020) Ahlers, G.; Hohenberg, P.C.; Lücke, M.: Externally modulated Rayleigh-Bénard convection: experiment and theory. Phys. Rev. Letts. 53(1), 48–51 (1984) Bhadauria, B.S.; Bhatia, P.K.; Debnath, L.: Convection in Hele-Shaw cell with parametric excitation. Int. J. Nonlin. Mech. 40, 475–484 (2005) Bhadauria, B.S.; Bhatia, P.K.; Debnath, L.: Weakly non-linear analysis of Rayleigh-Bénard convection with time periodic heating. Int. J. Nonlin. Mech. 44(1), 58–65 (2009) Bhadauria, B.S.; Hashim, I.; Siddheshwar, P.G.: Effect of internal-heating on weakly non-linear stability analysis of Rayleigh-Bénard convection under g-jitter. Int. J. Nonlin. Mech. 54, 35–42 (2013) Biringen, S.; Peltier, L.J.: Computational study of 3-D Bénard convection with gravitational modulation. Phys. Fluids A 2, 279–283 (1990) Boulal, T.; Aniss, S.; Belhaq, M.; Rand, R.: Effect of quasiperiodic gravitational modulation on the stability of a heated fluid layer. Physical Rev. E 76(5), 056320 (2007) Cisse, I.; Bardan, G.; Mojtabi, A.: Rayleigh-Bénard convective instability of a fluid under high-frequency vibration. Int. J. Heat Mass Transfer 47(19), 4101–4112 (2004) Finucane, R.G.; Kelly, R.E.: Onset of instability in a fluid layer heated sinusoidally from below. Int. J. Heat Mass Transfer 19(1), 71–85 (1976) Freund, G.; Pesch, W.; Zimmermann, W.: Rayleigh-Bénard convection in the presence of spatial temperature modulations. J. Fluid Mech. 673, 318–348 (2011) Gershuni, G.Z.; Zhukhovitskii, E.M.: On parametric excitation of convective instability. J. App. Math. Mech. 27, 1197–1204 (1963) Gresho, P.M.; Sani, R.L.: The effects of gravity modulation on the stability of a heated fluid layer. J. Fluid Mech. 40, 783–806 (1970) Hohenberg, P.C.; Swift, J.B.: Hexagons and rolls in periodically modulated Rayleigh-Bénard convection. Phys. Rev. A 35(9), 3855 (1987) Kaur, P.; Singh, J.; Bajaj, R.: Rayleigh-Bénard convection with two-frequency temperature modulation. Phys. Rev. E 93(4), 043111 (2016) Pesch, W.; Palaniappan, D.; Tao, J.; Busse, F.H.: Convection in heated fluid layers subjected to time-periodic horizontal accelerations. J. Fluid Mech. 596, 313–332 (2008) Ramaswamy, B.: Finite element analysis of two dimensional Rayleigh-Bénard convection with gravity modulation effects. Int. J. Numer. Methods Heat Fluid Flow 3(5), 429–444 (1993) Roppo, M.N.; Davis, S.H.; Rosenblat, S.: Bénard convection with time-periodic heating. Phys. Fluids 27(4), 796–803 (1984) Rosenblat, S.; Herbert, D.M.: Low-frequency modulation of thermal instability. J. Fluid Mech. 43(02), 385–398 (1970) Rosenblat, S.; Tanaka, G.A.: Modulation of thermal convection instability. Phys. Fluids 14(7), 1319–1322 (1971) Schmitt, S.; Lücke, M.: Amplitude equation for modulated Rayleigh-Bénard convection. Phys. Rev. A 44(8), 4986–5002 (1991) Siddheshwar, P.G.: A series solution for the Ginzburg-Landau equation with a time-periodic coefficient. Appl. Math. 1, 542–554 (2010) Singh, J.; Bajaj, R.: Temperature modulation in Rayleigh-Bénard convection. ANZIAM J. 50(02), 231–245 (2008) Venezian, G.: Effect of modulation on the onset of thermal convection. J. Fluid Mech. 35, 243–254 (1969) Volmar, U.E.; Müller, H.W.: Quasiperiodic patterns in Rayleigh-Bénard convection under gravity modulation. Phys. Rev. E 56(5), 5423–5430 (1997) Wheeler, A.A.; Mc Fadden, G.B.; Murray, B.T.; Coriell, S.R.: Convective stability in the Rayleigh-Bénard and directional solidification problems: high-frequency gravity modulation. hPhys. Fluids A: Fluid Dyn. (1989-1993) 3(12), 2847–2858 (1991) Yih, C.S.; Li, C.H.: Instability of unsteady flows or configurations Part 2 Convective instability. J. Fluid Mech. 54(01), 143–152 (1972) Abu-Nada, E.: Application of nanofluids for heat transfer enhancement of separated flows encountered in a backward facing step. Int. J. Heat Fluid Flow 29(1), 242–249 (2008) Agarwal, S.; Bhadauria, B.S.: Unsteady heat and mass transfer in a rotating nanofluid layer. Continuum Mech. Thermodyn. 26, 437–445 (2014) Bondarenko, D.S.; Sheremet, M.A.; Oztop, H.F.; Ali, M.E.: Impacts of moving wall and heat-generating element on heat transfer and entropy generation of \({A}l_2 {O}_3/{H}_2 {O}\) nanofluid. J. Thermal Analysis Calorimetry 136(2), 673–686 (2019) Kanchana, C.; Siddheshwar, P.G.; Zhao, Y.: Regulation of heat transfer in Rayleigh-Bénard convection in Newtonian liquids and Newtonian nanoliquids using gravity, boundary temperature and rotational modulations. J. Therm. Anal. Calorim. 142(4), 1579–1600 (2020) Meenakshi, N.; Siddheshwar, P.G.: A theoretical study of enhanced heat transfer in nanoliquids with volumetric heat source. J. Appl. Math. and Computing 57(1–2), 703–728 (2018) Wakif, A.; Boulahia, Z.; Sehaqui, R.: An accurate method to study the Rayleigh-Bénard problem in a rotating layer saturated by a Newtonian nanofluid. Int. J. Innov. Sci. Res. 20, 25–37 (2016) Wen, D.; Ding, Y.: Formulation of nanofluids for natural convective heat transfer applications. Int. J. Heat Fluid Flow 26(6), 855–864 (2005) Xuan, Y.; Li, Q.: Heat transfer enhancement of nanofluids. Int. J. Heat Fluid Flow 21(1), 58–64 (2000) Yadav, D.; Agrawal, G.S.; Bhargava, R.: Thermal instability of rotating nanofluid layer. Int. J. Engg. Sci. 49(11), 1171–1184 (2011) Yadav, D.; Bhargava, R.; Agrawal, G.S.: Numerical solution of a thermal instability problem in a rotating nanofluid layer. Int. J. Heat Mass Transfer 63, 313–322 (2013) Vekas, L.: Magnetic nanofluids properties and some applications. Romanian Journal of Physics 49(9–10), 707–721 (2004) Caizer, C.: Nanoparticle Size Effect on Some Magnetic Properties. Handbook of Nanoparticles. Springer, New York (2015) Yadav, D.; Wang, J.; Bhargava, R.; Lee, J.; Cho, H.H.: Numerical investigation of the effect of magnetic field on the onset of nanofluid convection. Appl. Therm. Engg. 103, 1441–1449 (2016) Yadav, D.; Wang, J.; Lee, J.: Onset of Darcy-Brinkman convection in a rotating porous layer induced by purely internal heating. J. Porous Media 20, 8 (2017) Yadav, D.; Wang, J.: Convective heat transport in a heat generating porous layer saturated by a non-Newtonian nanofluid. Heat Transf. Eng. 8, 20 (2018) Niazi, M.D.K.; Xu, H.: Fully developed flow of a nanofluid through a circular micropipe in the presence of electroosmotic effects. Math. Problems Eng. 20, 6 (2020) Ahmed, S.E.; Mansour, M.A.; Rashad, A.M.; Salah, T.: MHD natural convection from two heating modes in fined triangular enclosures filled with porous media using nanofluids. J. Therm. Anal. Calorim. 139(5), 3133–3149 (2020) Armaghani, T.; Chamkha, A.; Rashad, A.M.; Mansour, M.A.: Inclined magneto convection, internal heat, and entropy generation of nanofluid in an I-shaped cavity saturated with porous media. J. Therm. Anal. Calorim. 142(6), 2273–2285 (2020) Belhaj, S.; Ben-Beya, B.: Magnetoconvection and entropy generation of nanofluid in an enclosure with an isothermal block: Performance evaluation criteria analysis. J. Therm. Sci. Technol. 13(1), 1–23 (2018) Dogonchi, A.S.; Chamkha, A.J.; Ganji, D.D.: A numerical investigation of magneto-hydrodynamic natural convection of Cu-water nanofluid in a wavy cavity using CVFEM. J. Thermal Analysis Calorimetry 135(4), 2599–2611 (2019) Dogonchi, A.S.; Selimefendigil, F.; Ganji, D.D.: Magneto-hydrodynamic natural convection of CuO-water nanofluid in complex shaped enclosure considering various nanoparticle shapes. Int. J. Numer. Methods Heat Fluid Flow (2019) Dogonchi, A.S.; Tayebi, T.; Chamkha, A.J.; Ganji, D.D.: Natural convection analysis in a square enclosure with a wavy circular heater under magnetic field and nanoparticles. J. Thermal Analysis and Calorimetry 139(1), 661–671 (2020) Ghasemi, B.; Aminossadati, S.M.; Raisi, A.: Magnetic field effect on natural convection in a nanofluid-filled square enclosure. Int. J. Thermal Sci. 50(9), 1748–1756 (2011) Gupta, U.; Ahuja, J.; Wanchoo, R.K.: Magneto convection in a nanofluid layer. Int. J. Heat Mass Transfer 64, 1163–1171 (2013) Kadri, S.; Mehdaoui, R.; Elmir, M.: A vertical magneto-convection in square cavity containing a \({A}l_2{O}_3+\) water nanofluid: cooling of electronic compounds. Energy Procedia 18, 724–732 (2012) Mahmoudi, A.H.; Pop, I.; Shahi, M.: Effect of magnetic field on natural convection in a triangular enclosure filled with nanofluid. Int. J. Therm. Sci. 59, 126–140 (2012) Sadeghi, M.S.; Anadalibkhah, N.; Ghasemiasl, R.; Armaghani, T.; Dogonchi, A.S.; Chamkha, A.J.; Ali, H.; Asadi, A.: On the natural convection of nanofluids in diverse shapes of enclosures: an exhaustive review. J. Therm. Anal. Calorim 8, 1–22 (2020) Sheikholeslami, M.; Gorji-Bandpy, M.; Ganji, D.D.; Soleimani, S.: Effect of a magnetic field on natural convection in an inclined half-annulus enclosure filled with Cu-water nanofluid using CVFEM. Advanced Powder Technology 24(6), 980–991 (2013) Poongavanam, G.K.; Duraisamy, S.; Vigneswaran, V.S.; Ramalingam, V.: Review on the electrical conductivity of nanofluids: Recent developments. Mater. Today: Proc. 39, 1532–1537 (2020) Siddheshwar, P.G.; Meenakshi, N.: Amplitude equation and heat transport of Rayleigh-Bénard convection in Newtonian liquids with nanoparticles. Int. J. Appl. Comput. Math. (Springer) 2, 1–22 (2015) Siddheshwar, P.G.; Meenakshi, N.: Comparison of the effects of three types of time-periodic body force on linear and non-linear stability of convection in nanoliquids. European J. Mech. - B/Fluids 77, 221–229 (2019) Brinkman, H.C.: The viscosity of concentrated suspensions and solutions. The J. Chem. Phys. 20(4), 571–571 (1952) Hamilton, R.L.; Crosser, O.K.: Thermal conductivity of heterogeneous two-component systems. Industrial Engg. Chem. Fund. 1(3), 187–191 (1962) Garnett, J.C.M.: Xii. Colours in metal glasses and in metallic films. Philos. Trans. Royal Soc. London. Ser., A Contain. Pap. Math. Phys. Character 203(359–371), 385–420 (1904) Sihvola, A.H.: Lindell iv. Helsinki University of Technology, Effective permeability of mixtures. Espoo 8, 9 (1989) Lide, D.R.: CRC handbook of Chemistry and Physics, vol. 85. CRC Press, Boca Raton (2004) Hayat, T.; Nawaz, S.; Alsaedi, A.; Rafiq, M.: Mixed convective peristaltic flow of water based nanofluids with joule heating and convective boundary conditions. PLoS One 11(4), 1–28 (2016) Wakif, A.; Boulahia, Z.; Mishra, S.R.; Rashidi, M.M.; Sehaqui, R.: Influence of a uniform transverse magnetic field on the thermo-hydrodynamic stability in water-based nanofluids with metallic nanoparticles using the generalized Buongiorno’s mathematical model. Eur. Phys. J. Plus 133(5), 181 (2018) Wakif, A.; Chamkha, A.; Thumma, T.; Animasaun, I.; Sehaqui, R.: Thermal radiation and surface roughness effects on the thermo-magneto-hydrodynamic stability of alumina-copper oxide hybrid nanofluids utilizing the generalized buongiorno’s nanofluid model. J. Therm. Anal. Calorim. 8, 1–20 (2020) Geurts, B.J.; Kunnen, R.P.J.: Intensified heat transfer in modulated rotating Rayleigh-Bénard convection. Int. J. Heat Fluid Flow 49, 62–68 (2014)