Natural convection due to lateral uniform heat flux in a slender porous cavity saturated with nanofluid: Departure from LTE state

References

• M. Musto, N. Bianco, G. Rotondo, F. Toscano, and G. Pezzella, “A simplified methodology to simulate a heat exchanger in an aircraft’s oil cooler by means of a porous media model,” Appl. Therm. Eng., vol. 94, pp. 836–845, 2016. DOI: 10.1016/j.applthermaleng.2015.10.147.
   Web of Science ®Google Scholar
• A. A. Hussien, W. A. Kouz, M. E. Hassan, A. A. Janvekar, and A. J. Chamkha, “A review of flow and heat transfer in cavities and their applications,” Eur. Phys. J. Plus, vol. 136, no. 4, pp. 353, 2021. DOI: 10.1140/epjp/s13360-021-01320-3.
   Web of Science ®Google Scholar
• A. Koponen et al., “Permeability of three dimensional random fiber webs,” Phys. Rev. Lett., vol. 80, no. 4, pp. 716–719, 1998. DOI: 10.1103/PhysRevLett.80.716.
   Web of Science ®Google Scholar
• J. Fu et al., “Four kinds of the two-equation turbulence model’s research on flow field simulation performance of DPF’s porous media and swirl-type regeneration burner,” Appl. Therm. Eng., vol. 93, pp. 397–404, 2016. DOI: 10.1016/j.applthermaleng.2015.09.116.
   Web of Science ®Google Scholar
• P. R. Dando, D. Stuben, and S. P. Varnavas, “Hydrothermalism in the mediterranean sea,” Prog. Oceanogr., vol. 44, no. 1–3, pp. 333–367, 1999. DOI: 10.1016/S0079-6611(99)00032-4.
   Web of Science ®Google Scholar
• R. Ghasemizadeh et al., “Equivalent porous media (EPM) simulation of groundwater hydraulics and contaminant transport in karst aquifers,” PLoS One, vol. 10, no. 9, pp. e0138954, 2015. DOI: 10.1371/journal.pone.0138954.
   PubMed Web of Science ®Google Scholar
• S. U. S. Choi and J. A. Eastman, “Enhancing thermal conductivity of fluids with nanoparticles,” ASME-Publ.-Fed, vol. 231, pp. 99–106, 1995.
   Google Scholar
• A. Bejan, “The boundary layer regime in a porous layer with uniform heat flux from the side,” Int. J. Heat Mass Transf., vol. 26, no. 9, pp. 1339–1346, 1983. DOI: 10.1016/S0017-9310(83)80065-9.
   Web of Science ®Google Scholar
• G. Degan, P. Vasseur, and E. Bilgen, “Convective heat transfer in a vertical anisotropic porous layer,” Int. J. Heat Mass Transf., vol. 38, no. 11, pp. 1975–1987, 1995. DOI: 10.1016/0017-9310(94)00330-X.
   Web of Science ®Google Scholar
• G. Degan and P. Vasseur, “Boundary-layer regime in a vertical porous layer with anisotropic permeability and boundary effects,” Int. J. Heat Mass Transf., vol. 18, no. 3, pp. 334–343, 1997. DOI: 10.1016/S0142-727X(97)00011-8.
   Google Scholar
• P. Bera, V. Eswaran, and P. Singh, “Double-diffusive convection in slender anisotropic porous enclosures,” J. Porous Media, vol. 3, no. 1, pp. 11–29, 2000. DOI: 10.1615/JPorMedia.v3.i1.20.
   Web of Science ®Google Scholar
• P. Bera and A. Khalili, “Double-diffusive natural convection in an anisotropic porous cavity with opposing buoyancy forces: Multi-solutions and oscillations,” Int. J. Heat Mass Transf., vol. 45, no. 15, pp. 3205–3222, 2002. DOI: 10.1016/S0017-9310(02)00024-8.
   Web of Science ®Google Scholar
• H. Chandra, P. Bera, and A. K. Sharma, “Natural convection in a square cavity filled with an anisotropic porous medium due to sinusoidal heat flux on horizontal walls,” Numer. Heat Transf. A Appl., vol. 77, no. 3, pp. 317–341, 2020. DOI: 10.1080/10407782.2019.1690348.
   Web of Science ®Google Scholar
• H. Chandra and P. Bera, “Magneto-convection in an anisotropic porous cavity due to nonuniform heat flux at bottom wall,” Numer. Heat Transf. A Appl. DOI: 10.1080/10407782.2022.2104590.
   Web of Science ®Google Scholar
• H. Chandra and P. Bera, “Buoyancy-induced convective flow and heat transfer over obstacles embedded inside a Cu-water nanofluid-saturated porous cavity,” Numer. Heat Transf. A Appl., vol. 83, no. 7, pp. 726–744, 2023. DOI: 10.1080/10407782.2022.2160851.
   Web of Science ®Google Scholar
• M. Sankar, M. Bhuvaneswari, S. Sivasankaran, and Y. Do, “Buoyancy induced convection in a porous cavity with partially thermally active sidewalls,” Int. J. Heat Mass Transf., vol. 54, no. 25–26, pp. 5173–5182, 2011. DOI: 10.1016/j.ijheatmasstransfer.2011.08.029.
   Web of Science ®Google Scholar
• M. Bhuvaneswari, S. Sivasankaran, and Y. J. Kim, “Effect of aspect ratio on convection in a porous enclosure with partially active thermal walls,” Comput. Math. Appl., vol. 62, no. 10, pp. 3844–3856, 2011. DOI: 10.1016/j.camwa.2011.09.033.
   Web of Science ®Google Scholar
• S. Sivasankaran and K. L. Pan, “Numerical simulation on mixed convection in a porous lid-driven cavity with nonuniform heating on both side walls,” Numer. Heat Transf. A, vol. 61, no. 2, pp. 101–121, 2012. DOI: 10.1080/10407782.2011.643741.
   Web of Science ®Google Scholar
• S. Sivasankaran and M. Bhuvaneswari, “Natural convection in a porous cavity with sinusoidal heating on both sidewalls,” Numer. Heat Transf. A Appl., vol. 63, no. 1, pp. 14–30, 2013. DOI: 10.1080/10407782.2012.715985.
   Web of Science ®Google Scholar
• H. T. Cheong, S. Sivasankaran, and M. Bhuvaneswari, “Natural convection in a wavy porous cavity with sinusoidal heating and internal heat generation,” Int. J. Numer. Methods Heat Fluid Flow, vol. 27, pp. 1–29, 2017.
   Web of Science ®Google Scholar
• S. Sivasankaran, M. A. Mansour, A. M. Rashad, and M. Bhuvaneswari, “MHD mixed convection of Cu-water nanofluid in a two-sided lid-driven porous cavity with a partial slip,” Numer. Heat Transf. A, vol. 70, no. 12, pp. 1356–1370, 2016. DOI: 10.1080/10407782.2016.1243957.
   Web of Science ®Google Scholar
• W. A. Kouz et al., “Heat transfer and entropy generation analysis of water-Fe3O4/CNT hybrid magnetic nanofluid flow in a trapezoidal wavy enclosure containing porous media with the Galerkin finite element method,” Eur. Phys. J. Plus, vol. 136, no. 11, pp. 1184, 2021. DOI: 10.1140/epjp/s13360-021-02192-3.
   Web of Science ®Google Scholar
• K. A. Farhany, K. K. A. Chlaihawi, M. F. A. Dawody, N. Biswas, and A. J. Chamkha, “Effects of fins on magnetohydrodynamic conjugate natural convection in a nanofluid-saturated porous inclined enclosure,” Int. Commun. Heat Mass Transf., vol. 126, pp. 105413, 2021. DOI: 10.1016/j.icheatmasstransfer.2021.105413.
   Web of Science ®Google Scholar
• C. C. Cho, “Natural convection of Cu-water nanofluid in enclosed cavity with porous effect and wavy surface based on energy-flux-vector visualization method,” Phys. Fluids, vol. 32, no. 10, pp. 103607, 2020. DOI: 10.1063/5.0024773.
   Web of Science ®Google Scholar
• A. Amiri, K. Vafai, and T. M. Kuzay, “Effects of boundary conditions on non-Darcian heat transfer through porous media and experimental comparisons,” Numer. Heat Transf. A Appl., vol. 27, no. 6, pp. 651–664, 1995. DOI: 10.1080/10407789508913724.
   Web of Science ®Google Scholar
• B. Alazmi and K. Vafai, “Constant wall heat flux boundary conditions in porous media under local thermal non-equilibrium conditions,” Int. J. Heat Mass Transf., vol. 45, no. 15, pp. 3071–3087, 2002. DOI: 10.1016/S0017-9310(02)00044-3.
   Web of Science ®Google Scholar
• S. Sivasankaran, T. Aasaithambi, and S. Rajan, “Natural convection of nanofluids in a cavity with linearly varying wall temperature,” Maejo Int. J. Sci. Technol., vol. 4, pp. 468–482, 2010.
   Web of Science ®Google Scholar
• S. Pippal and P. Bera, “A thermal non-equilibrium approach for 2D natural convection due to lateral heat flux: Square as well as slender enclosure,” Int. J. Heat Mass Transf., vol. 56, no. 1–2, pp. 501–515, 2013. DOI: 10.1016/j.ijheatmasstransfer.2012.09.003.
   Web of Science ®Google Scholar
• F. Wu, W. Zhou, and X. Ma, “Natural convection in a porous rectangular enclosure with sinusoidal temperature distributions on both side walls using a thermal non-equilibrium model,” Int. J. Heat Mass Transf., vol. 85, pp. 756–771, 2015. DOI: 10.1016/j.ijheatmasstransfer.2015.02.039.
   Web of Science ®Google Scholar
• M. Dehghan, M. S. Valipour, A. Keshmiri, S. Saedodin, and N. Shokri, “On the thermally developing forced convection through a porous material under the local thermal non-equilibrium condition: An analytical study,” Int. J. Heat Mass Transf., vol. 92, pp. 815–823, 2016. DOI: 10.1016/j.ijheatmasstransfer.2015.08.091.
   Web of Science ®Google Scholar
• P. Bera, S. Pippal, and A. Khan, “A thermal non-equilibrium approach on thermo-solutal natural convection due to the lateral flux of heat and solute on enclosure walls: Multi-solutions and oscillations,” Int. J. Heat Mass Transf., vol. 128, pp. 1322–1343, 2019. DOI: 10.1016/j.ijheatmasstransfer.2018.08.076.
   Web of Science ®Google Scholar
• A. C. Baytas, “Thermal non-equilibrium natural convection in a square enclosure filled with a heat-generating solid phase, non-Darcy porous medium,” Int. J. Energy Res., vol. 27, pp. 975–988, 2003.
   Web of Science ®Google Scholar
• F. Wu, G. Wang, and W. Zhou, “A thermal non-equilibrium approach to natural convection in a square enclosure due to the partial cooled sidewalls of the enclosure,” Numer. Heat Transf. A Appl., vol. 67, no. 7, pp. 771–790, 2015. DOI: 10.1080/10407782.2014.949189.
   Web of Science ®Google Scholar
• F. Wu, D. Lu, and G. Wang, “Numerical analysis of natural convection in a porous cavity with the sinusoidal thermal boundary condition using a thermal nonequilibrium model,” Numer. Heat Transf. A Appl., vol. 69, no. 11, pp. 1280–1296, 2016. DOI: 10.1080/10407782.2015.1127025.
   Web of Science ®Google Scholar
• F. Wu, G. Wang, and W. Zhou, “Aspect ratio effect on natural convection in a square enclosure with a sinusoidal active thermal wall using a thermal non-equilibrium model,” Numer. Heat Transf. A Appl., vol. 70, no. 3, pp. 310–329, 2016. DOI: 10.1080/10407782.2016.1173474.
   Web of Science ®Google Scholar
• M. Dehghan, M. S. Valipour, S. Saedodin, and Y. Mahmoudi, “Thermally developing flow inside a porous-filled channel in the presence of internal heat generation under local thermal non-equilibrium condition: A perturbation analysis,” Appl. Therm. Eng., vol. 98, pp. 827–834, 2016. DOI: 10.1016/j.applthermaleng.2015.12.133.
   Web of Science ®Google Scholar
• A. M. Rashad, S. Sivasankaran, M. A. Mansour, and M. Bhuvaneswari, “Magneto-convection of nanofluids in a lid-driven trapezoidal cavity with internal heat generation and discrete heating,” Numer. Heat Transf. A: Appl., vol. 71, no. 12, pp. 1223–1234, 2017. DOI: 10.1080/10407782.2017.1347000.
   Web of Science ®Google Scholar
• A. F. Baytas and A. C. Baytas, “Thermal non-equilibrium natural convection in a square enclosure with heat-generating porous layer on inner walls,” Transp. Porous Media, vol. 120, pp. 167–182, 2017.
   Web of Science ®Google Scholar
• S. A. Mikhailenko and M. A. Sheremet, “Impacts of rotation and local element of variable heat generation on convective heat transfer in a partially porous cavity using local thermal non-equilibrium model,” Int. J. Therm. Sci., vol. 155, pp. 106427–1, 2020. DOI: 10.1016/j.ijthermalsci.2020.106427.
   Web of Science ®Google Scholar
• A. C. Baytas and I. Pop, “Free convection in a square porous cavity using a thermal nonequilibrium model,” Int. J. Therm. Sci., vol. 41, no. 9, pp. 861–870, 2002. DOI: 10.1016/S1290-0729(02)01379-0.
   Web of Science ®Google Scholar
• P. Bera, S. Pippal, and A. K. Sharma, “A thermal non-equilibrium approach on double-diffusive natural convection in a square porous-medium cavity,” Int. J. Heat Mass Transf., vol. 78, pp. 1080–1094, 2014. DOI: 10.1016/j.ijheatmasstransfer.2014.07.041.
   Web of Science ®Google Scholar
• M. A. Sheremet, I. Pop, and R. Nazar, “Natural convection in a square cavity filled with a porous medium saturated with a nanofluid using the thermal non-equilibrium model with a Tiwari and Das nano-fluid model,” Int. J. Mech. Sci., vol. 100, pp. 312–321, 2015. DOI: 10.1016/j.ijmecsci.2015.07.007.
   Web of Science ®Google Scholar
• S. Sivasankaran, A. I. Alsabery, and I. Hashim, “Internal heat generation effect on transient natural convection in a nanofluid-saturated local thermal non-equilibrium porous inclined cavity,” Phys. A, vol. 509, pp. 275–293, 2018. DOI: 10.1016/j.physa.2018.06.036.
   Web of Science ®Google Scholar
• S. A. M. Mehryan, M. Ghalambaz, A. J. Chamkha, and M. Izadi, “Numerical study on natural convection of Ag-MgO hybrid/water nanofluid inside a porous enclosure: A local thermal non-equilibrium model,” Powder Technol., vol. 367, pp. 443–455, 2020. DOI: 10.1016/j.powtec.2020.04.005.
   Web of Science ®Google Scholar
• H. C. Brinkman, “The viscosity of concentrated suspensions and solutions,” J. Chem. Phys., vol. 20, no. 4, pp. 571–571, 1952. DOI: 10.1063/1.1700493.
   Web of Science ®Google Scholar
• T. Basak and A. J. Chamkha, “Heatline analysis on natural convection for nanofluids confined within square cavities with various thermal boundary conditions,” Int. J. Heat Mass Transf., vol. 55, no. 21–22, pp. 5526–5543, 2012. DOI: 10.1016/j.ijheatmasstransfer.2012.05.025.
   Web of Science ®Google Scholar