Combined effects of thermo-diffusion, diffusion-thermo and internal heat generation on the stabilization/destabilization of the flow in a cavity differentially heated and salted

References

• H. Stommel, A. B. Arons and D. Blanchard, “An oceanographical curiosity: the perpetual salt fountain,” Deep Sea Res., vol. 3, no. 2, pp. 152–153, Feb. 1956. DOI: 10.1016/0146-6313(56)90095-8.
   Google Scholar
• L. Cheng, et al., “Improved estimates of changes in upper ocean salinity and the hydrological cycle,” J. Clim., vol. 33, no. 23, pp. 10357–10381, Dec. 2020. DOI: 10.1175/JCLI-D-20-0366.1.
   Web of Science ®Google Scholar
• Y. Liu, et al., “How well do CMIP6 and CMIP5 models simulate the climatological seasonal variations in ocean salinity,” Adv. Atmos. Sci., vol. 39, no. 10, pp. 1650–1672, Oct. 2022. DOI: 10.1007/s00376-022-1381-2.
   Web of Science ®Google Scholar
• C. F. Chen and D. H. Johnson, “Double-diffusive convection: a report on an engineering foundation conference,” J. Fluid Mech., vol. 138, pp. 405–416, Apr. 1984. DOI: 10.1017/S0022112084000173.
   Web of Science ®Google Scholar
• A. E. Mansouri, M. Hasnaoui, R. Bennacer and A. Amahmid, “Transient thermal performances of a salt gradient solar pond under semi-arid Moroccan climate using a 2D double-diffusive convection model,” Energy Convers. Manag., vol. 151, pp. 199–208, Nov. 2017. DOI: 10.1016/j.enconman.2017.08.093.
   Web of Science ®Google Scholar
• O. V. Trevisan and A. Bejan, “Natural convection with combined heat and mass transfer buoyancy effects in a porous medium,” Int. J. Heat Mass Transf., vol. 28, no. 8, pp. 1597–1611, Aug. 1985. DOI: 10.1016/0017-9310(85)90261-3.
   Web of Science ®Google Scholar
• F. Alavyoon, Y. Masuda and S. Kimura, “On natural convection in vertical porous enclosures due to opposing fluxes of heat and mass prescribed at the vertical walls,” Int. J. Heat Mass Transf., vol. 37, no. 2, pp. 195–206, Jan. 1994. DOI: 10.1016/0017-9310(94)90092-2.
   Web of Science ®Google Scholar
• M. Mamou, P. Vasseur and E. Bilgen, “Multiple solutions for double-diffusive convection in a vertical porous enclosure,” Int. J. Heat Mass Transf., vol. 38, no. 10, pp. 1787–1798, Jul. 1995. DOI: 10.1016/0017-9310(94)00301-B.
   Web of Science ®Google Scholar
• M. Karimi-Fard, M. C. Charrier-Mojtabi and K. Vafai, “Non-Darcian e-ects on double-di-usive convection within a porous medium,” Numer. Heat Transf. Part A Appl., vol. 31, no. 8, pp. 837–852, Jun. 1997. DOI: 10.1080/10407789708914067.
   Web of Science ®Google Scholar
• T. Nishimura, M. Wakamatsu and A. M. Morega, “Oscillatory double-diffusive convection in a rectangular enclosure with combined horizontal temperature and concentration gradients,” Int. J. Heat Mass Transf., vol. 41, no. 11, pp. 1601–1611, Jun. 1998. DOI: 10.1016/S0017-9310(97)00271-8.
   Web of Science ®Google Scholar
• A. Amahmid, M. Hasnaoui, M. Mamou and P. Vasseur, “Boundary layer flows in a vertical porous enclosure induced by opposing buoyancy forces,” Int. J. Heat Mass Transf., vol. 42, no. 19, pp. 3599–3608, Oct. 1999. DOI: 10.1016/S0017-9310(99)00019-8.
   Web of Science ®Google Scholar
• D. A. Nield, “Onset of Thermohaline convection in a porous medium,” Water Resour. Res., vol. 4, no. 3, pp. 553–560, Jun. 1968. DOI: 10.1029/WR004i003p00553.
   Web of Science ®Google Scholar
• B. T. Murray and C. F. Chen, “Double-diffusive convection in a porous medium,” J. Fluid Mech., vol. 201, no. 1, pp. 147–166, Apr. 1989. DOI: 10.1017/S002211208900087X.
   Google Scholar
• O. V. Trevisan and A. Bejan, “Mass and heat transfer by high Rayleigh number convection in a porous medium heated from below,” Int. J. Heat Mass Transf., vol. 30, no. 11, pp. 2341–2356, Nov. 1987. DOI: 10.1016/0017-9310(87)90226-2.
   Web of Science ®Google Scholar
• F. Chen and C. F. Chen, “Double-diffusive fingering convection in a porous medium,” Int. J. Heat Mass Transf., vol. 36, no. 3, pp. 793–807, Feb. 1993. DOI: 10.1016/0017-9310(93)80055-Y.
   Web of Science ®Google Scholar
• A. Amahmid, M. Hasnaoui, M. Mamou and P. Vasseur, “Double-diffusive parallel flow induced in a horizontal Brinkman porous layer subjected to constant heat and mass fluxes: analytical and numerical studies,” Heat Mass Transf., vol. 35, no. 5, pp. 409–421, Oct. 1999. DOI: 10.1007/s002310050343.
   Web of Science ®Google Scholar
• S. Chapman and T. G. Cowling, The Mathematical Theory of Non-Uniform Gases. Cambridge, England: Cambridge University Press, 1952,
   Google Scholar
• V. Shevtsova, “IVIDIL experiment onboard the ISS,” Adv. Sp. Res., vol. 46, no. 5, pp. 672–679, Sep. 2010. DOI: 10.1016/j.asr.2010.04.001.
   Web of Science ®Google Scholar
• K. Clusius and G. Dickel, “New process for separation of gas mixtures and isotopes,” Naturwissenschaften, vol. 26, no. 33, pp. 546–546, Aug. 1938. DOI: 10.1007/BF01675498.
   Google Scholar
• J. K. Platten, M. M. Bou-Ali and J. F. Dutrieux, “Enhanced molecular separation in inclined thermogravitational columns,” J. Phys. Chem. B, vol. 107, no. 42, pp. 11763–11767, Oct. 2003. DOI: 10.1021/jp034780k.
   Web of Science ®Google Scholar
• B. Elhajjar, M. C. Charrier-Mojtabi and A. Mojtabi, “Separation of a binary fluid mixture in a porous horizontal cavity,” Phys. Rev. E, vol. 77, no. 2, pp. 026310, Feb. 2008. DOI: 10.1103/PhysRevE.77.026310.
   Web of Science ®Google Scholar
• A. Martin, M. M. Bou-Ali, H. Barrutia and D. Alonso de Mezquia, “Microfluidic separation process by the Soret effect in biological fluids,” C. R. Mecanique, vol. 339, no. 5, pp. 342–348, May 2011. DOI: 10.1016/j.crme.2011.03.012.
   Web of Science ®Google Scholar
• A. Abbasi, M. Z. Saghir and M. Kawaji, “Study of thermodiffusion of carbon dioxide in binary mixtures of n-butane & carbon dioxide and ndodecane & carbon dioxide in porous media,” Int. J. Therm. Sci., vol. 50, no. 2, pp. 124–132, Feb. 2011. DOI: 10.1016/j.ijthermalsci.2010.10.009.
   Web of Science ®Google Scholar
• E. Blums and S. Odenbach, “Thermophoretic separation of ultrafine particles in ferrofluids in thermal diffusion column under the effect of an MHD convection,” Int. J. Heat Mass Transf., vol. 43, no. 9, pp. 1637–1649, May 2000. DOI: 10.1016/S0017-9310(99)00224-0.
   Web of Science ®Google Scholar
• A. Rtibi, M. Hasnaoui and A. Amahmid, “Analytico-numerical study of optimal separation of species in an inclined Darcy–Brinkman porous cavity saturated with a binary mixture,” Acta Astronaut., vol. 98, pp. 71–85, May 2014. DOI: 10.1016/j.actaastro.2014.01.012.
   Web of Science ®Google Scholar
• B. Chandra Shekar and N. Kishan, “Soret and Dufour effects on free convective heat and solute transfer in fluid saturated inclined porous cavity,” Eng. Sci. Technol. Int. J., vol. 18, no. 4, pp. 543–554, Dec. 2015. DOI: 10.1016/j.jestch.2015.04.001.
   Google Scholar
• B. Chandra Shekar, N. Kishan and A. J. Chamkha, “Soret and Dufour effects on MHD natural convective heat and solute transfer in a fluid-saturated porous cavity,” J. Por. Media, vol. 19, no. 8, pp. 669–686, Dec. 2016. DOI: 10.1615/JPorMedia.v19.i8.20.
   Web of Science ®Google Scholar
• S. Bettaibi, F. Kuznik, E. Sediki and S. Succi, “Numerical study of thermal diffusion and diffusion thermo effects in a differentially heated and salted driven cavity using MRT-lattice boltzmann finite difference model,” Int. J. Appl. Mech., vol. 13, no. 04, pp. 2150049, Jun. 2021. DOI: 10.1142/S1758825121500496.
   Google Scholar
• J. Large and A. Pesyridis, “Investigation of micro gas turbine systems for high speed long loiter tactical unmanned Air systems,” Aerospace, vol. 6, no. 5, pp. 55, May 2019. DOI: 10.3390/aerospace6050055.
   Web of Science ®Google Scholar
• M. El Hossaini, “Review of the new combustion technologies in modern gas turbines,” in Progress in Gas Turbine Performance, Norderstedt, Germany: BoD–Books on Demand, 2013. DOI: 10.5772/54403.
   Google Scholar
• Y. Ju and K. Maruta, “Microscale combustion: technology development and fundamental research,” Prog. Energy Combust. Sci., vol. 37, no. 6, pp. 669–715, Dec. 2011. DOI: 10.1016/j.pecs.2011.03.001.
   Web of Science ®Google Scholar
• Y. Nakamura, J. Gao and T. Matsuoka, “Progress in small-scale combustion,” J. Therm. Sci. Technol., vol. 12, no. 1, pp. JTST0001–JTST0001, Jan. 2017. DOI: 10.1299/jtst.2017jtst0001.
   Web of Science ®Google Scholar
• S. Hasnaoui, A. Amahmid, A. Raji, H. Beji, A. El Mansouri and M. Hasnaoui, “LBM simulation of stabilizing/destabilizing effects of thermodiffusion and heat generation in a rectangular cavity filled with a binary mixture,” Int. Commun. Heat Mass Transf., vol. 126, pp. 105417, Jul. 2021. DOI: 10.1016/j.icheatmasstransfer.2021.105417.
   Web of Science ®Google Scholar
• P. Deshmukh, S. K. Mitra and U. N. Gaitonde, “Investigation of natural circulation in cavities with uniform heat generation for different Prandtl number fluids,” Int. J. Heat Mass Transf., vol. 54, no. 7–8, pp. 1465–1474, Mar. 2011. DOI: 10.1016/j.ijheatmasstransfer.2010.11.046.
   Web of Science ®Google Scholar
• Y. M. Shim and J. M. Hyun, “Transient confined natural convection with internal heat generation,” Int. J. Heat Fluid Flow, vol. 18, no. 3, pp. 328–333, Jun. 1997. DOI: 10.1016/S0142-727X(97)00027-1.
   Web of Science ®Google Scholar
• M. A. Hossain, M. Z. Hafiz and D. A. S. Rees, “Buoyancy and thermocapillary driven convection flow of an electrically conducting fluid in an enclosure with heat generation,” Int. J. Therm. Sci., vol. 44, no. 7, pp. 676–684, Jul. 2005. DOI: 10.1016/j.ijthermalsci.2004.11.005.
   Web of Science ®Google Scholar
• Y. S. Jeong, S. Bin Seo and I. C. Bang, “Natural convection heat transfer characteristics of molten salt with internal heat generation,” Int. J. Therm. Sci., vol. 129, pp. 181–192, Jul. 2018. DOI: 10.1016/j.ijthermalsci.2018.01.036.
   Web of Science ®Google Scholar
• F. A. Kulacki and R. J. Goldstein, “Thermal convection in a horizontal fluid layer with uniform volumetric energy sources,” J. Fluid Mech., vol. 55, no. 02, pp. 271–287, Sep. 1972. DOI: 10.1017/S0022112072001855.
   Google Scholar
• F. A. Kulacki and M. E. Nagle, “Natural convection in a horizontal fluid layer with volumetric energy sources,” J. Heat Transf., vol. 97, no. 2, pp. 204–211, May 1975. DOI: 10.1115/1.3450342.
   Web of Science ®Google Scholar
• M. A. Teamah, A. F. Elsafty and E. Z. Massoud, “Numerical simulation of double-diffusive natural convective flow in an inclined rectangular enclosure in the presence of magnetic field and heat source,” Int. J. Therm. Sci., vol. 52, no. 1, pp. 161–175, Feb. 2012. DOI: 10.1016/j.ijthermalsci.2011.09.006.
   Google Scholar
• S. N. Gaikwad and S. Kouser, “Double diffusive convection in a couple stress fluid saturated porous layer with internal heat source,” Int. J. Heat Mass Transf., vol. 78, pp. 1254–1264, Nov. 2014. DOI: 10.1016/j.ijheatmasstransfer.2014.07.021.
   Web of Science ®Google Scholar
• B. C. Sekhar, N. Chandr. Kishan and C. Haritha, “Convection in Nanofluid-Filled Porous Cavity with Heat Absorption/Generation and Radiation,” J. Thermophys. Heat Transf., vol. 31, no. 3, pp. 549–562, Jul. 2017. DOI: 10.2514/1.T5010.
   Web of Science ®Google Scholar
• S. Hasnaoui, et al., “Double-diffusive natural convection in an inclined enclosure with heat generation and Soret effect,” Eng. Comput., vol. 35, no. 8, pp. 2753–2774, Nov. 2018. DOI: 10.1108/EC-06-2017-0225.
   Google Scholar
• S. Hasnaoui, et al., “Hybrid lattice Boltzmann finite difference simulation of Soret convection flows in a square cavity with internal heat generation,” Numer. Heat Transf. Part A Appl, vol. 74, no. 1, pp. 948–973, Jul. 2018. DOI: 10.1080/10407782.2018.1487690.
   Web of Science ®Google Scholar
• N. F. M. Mokhtar, I. K. Khalid, Z. Siri, Z. B. Ibrahim and S. S. A. Gani, “Control strategy on the double-diffusive convection in a nanofluid layer with internal heat generation,” Phys. Fluids, vol. 29, no. 10, pp. 107105, Oct. 2017. DOI: 10.1063/1.4989584.
   Web of Science ®Google Scholar
• A. Lagra, M. Bourich, M. Hasnaoui, A. Amahmid and M. Er-Raki, “Analytical and numerical study of soret and dufour effects on double diffusive convection in a shallow horizontal binary fluid layer submitted to uniform fluxes of heat and mass,” Math. Probl. Eng., vol. 2018, pp. 1–12, Mar. 2018. DOI: 10.1155/2018/7946078.
   Web of Science ®Google Scholar
• H. Xu, Z. Luo, Q. Lou, S. Zhang and J. Wang, “Lattice Boltzmann simulations of the double-diffusive natural convection and oscillation characteristics in an enclosure with Soret and Dufour effects,” Int. J. Therm. Sci, vol. 136, pp. 159–171, Feb. 2019. DOI: 10.1016/j.ijthermalsci.2018.10.015.
   Web of Science ®Google Scholar
• Z. Guo and C. Shu, Lattice Boltzmann Method and Its Applications in Engineering, vol. 3. Singapore: World Scientific, 2013. DOI: 10.1142/8806.
   Google Scholar
• Y. Dahani, M. Hasnaoui, A. Amahmid and S. Hasnaoui, “A multiple-relaxation-time lattice-boltzmann analysis for double-diffusive natural convection in a cavity with heating and diffusing plate inside filled with a porous medium,” Transp. Porous Med., vol. 143, no. 1, pp. 195–223, May 2022. DOI: 10.1007/s11242-022-01792-6.
   Web of Science ®Google Scholar
• A. Mezrhab, M. Amine Moussaoui, M. Jami, H. Naji and M. Bouzidi, “Double MRT thermal lattice Boltzmann method for simulating convective flows,” Phys. Lett. A, vol. 374, no. 34, pp. 3499–3507, Jul. 2010. DOI: 10.1016/j.physleta.2010.06.059.
   Web of Science ®Google Scholar