Natural convection in a square cavity filled with an anisotropic porous medium due to sinusoidal heat flux on horizontal walls

References

• C. J. Hsu, “Heat transfer in a round tube with sinusoidal wall heat flux distribution,” AIChE. J., vol. 11, no. 4, pp. 690–695, 1965. DOI: 10.1002/aic.690110423.
   Web of Science ®Google Scholar
• M. Musto, N. Bianco, G. Rotondo, F. Toscano, and G. Pezzella, “A simplified methodology to simulate a heat exchanger in an aircrafts 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
• Z. G. Xu and C. Y. Zhao, “Enhanced boiling heat transfer by gradient porous metals in saturated pure water and surfactant solutions,” Appl. Therm. Eng, vol. 100, pp. 68–77, 2016. DOI: 10.1016/j.applthermaleng.2016.02.016.
   Web of Science ®Google Scholar
• R. Ghasemizadeh, X. Yu, C. Butscher, F. Hellweger, I. Padilla, and A. Alshawabkeh, “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
• J. Fu, Y. Tang, J. Li, Y. Ma, W. Chen, and H. Li, “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.
   Google Scholar
• M. Cascetta, G. Cau, P. Puddu, and F. Serra, “A comparison between CFD simulation and experimental investigation of a packed-bed thermal energy storage system,” Appl. Therm. Eng, vol. 98, pp. 1263–1272, 2016. DOI: 10.1016/j.applthermaleng.2016.01.019.
   Web of Science ®Google Scholar
• J. H. Stang, and J. E. Bush, “The periodic method for testing compact heat exchanger surfaces,” J. Engrs. Power, vol. 96, no. 2, pp. 87–94, 1974. DOI: 10.1115/1.3445767.
   Google Scholar
• M. Mishra, P. K. Das, and S. Sarangi, “Transient behavior of crossflow heat exchangers due to sinusoidal excitation,” J. Heat Transf., vol. 132, no. 9, pp. 091801–091801, 2010.
   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, no. 2, pp. 287–309, 2017. DOI: 10.1108/HFF-07-2015-0272.
   Web of Science ®Google Scholar
• A. Barletta, and E. Zanchini, “Laminar forced convection with sinusoidal wall heat flux distribution: Axially periodic regime,” Heat Mass Transf., vol. 31, no. 1/2, pp. 41–48, 1995. DOI: 10.1007/BF02537420.
   Web of Science ®Google Scholar
• A. Barletta, and E. Rossi di Schio, “Effects of viscous dissipation on laminar forced convection with axially periodic wall heat flux,” Heat Mass Transf., vol. 35, no. 1, pp. 9–16, 1999. DOI: 10.1007/s002310050292.
   Web of Science ®Google Scholar
• K. Zniber, A. Oubarra, and J. Lahjomri, “Analytical solution to the problem of heat transfer in an MHD flow inside a channel with prescribed sinusoidal wall heat flux,” Energy Conversion manage., vol. 46, no. 7/8, pp. 1147–1163, 2005. DOI: 10.1016/j.enconman.2004.06.023.
   Web of Science ®Google Scholar
• I. E. Sarris, I. Lekakis, and N. S. Vlachos, “Natural convection in a 2D enclosure with sinusoidal upper wall temperature,” Numer. Heat Transf A, vol. 42, no. 5, pp. 513–530, 2002. DOI: 10.1080/10407780290059675.
   Web of Science ®Google Scholar
• E. Bilgen, and R. B. Yedder, “Natural convection in enclosure with heating and cooling by sinusoidal temperature profiles on one side,” Int. J. Heat Mass Transf., vol. 50, no. 1-2, pp. 139–150, 2007. DOI: 10.1016/j.ijheatmasstransfer.2006.06.027.
   Web of Science ®Google Scholar
• A. Dalal, and M. K. Das, “Numerical study of laminar natural convection in a complicated cavity heated from top with sinusoidal temperature and cooled from other sides,” Comput. Fluids, vol. 36, no. 4, pp. 680–700, 2007. DOI: 10.1016/j.compfluid.2006.05.005.
   Web of Science ®Google Scholar
• Q. H. Deng, and J. J. Chang, “Natural convection in a rectangular enclosure with sinusoidal temperature distributions on both side walls,” Numer. Heat Transf. A, vol. 54, no. 5, pp. 507–524, 2008. DOI: 10.1080/01457630802186080.
   Web of Science ®Google Scholar
• H. T. Cheong, Z. Siri, and S. Sivasankaran, “Effect of aspect ratio on natural convection in an inclined rectangular enclosure with sinusoidal boundary condition,” Int. Comm. Heat Mass Transf., vol. 45, pp. 75–85, 2013. DOI: 10.1016/j.icheatmasstransfer.2013.04.017.
   Web of Science ®Google Scholar
• S. Sivasankaran, and K. L. Pan, “Natural convection of nanofluids in a cavity with nonuniform temperature distributions on side walls,” Numer. Heat Transf., A, vol. 6, no. 3, pp. 247–268, 2014. DOI: 10.1080/10407782.2013.825510.
   Google Scholar
• I. Mejri, A. Mahmoudi, M. A. Abbassi, and A. Omri, “Magnetic field effect on entropy generation in a nano fluid-filled enclosure with sinusoidal heating on both side walls,” Powder Technol., vol. 266, pp. 340–353, 2014. DOI: 10.1016/j.powtec.2014.06.054.
   Web of Science ®Google Scholar
• M. Sheikholeslami, and A. J. Chamkha, “Electrohydrodynamic free convection heat transfer of a nanofluid in a semi-annulus enclosure with a sinusoidal wall,” Numer. Heat Transfer, Part A, vol. 69, no. 7, pp. 781–793, 2016. DOI: 10.1080/10407782.2015.1090819.
   Web of Science ®Google Scholar
• A. I. Alsabery, A. J. Chamkha, H. Saleh, and I. Hashim, “Heat line visualization of conjugate natural convection in a square cavity filled with nanofluid with sinusoidal temperature variations on both horizontal walls,” Int. J. Heat Mass Transf., vol. 100, pp. 835–850, 2016. DOI: 10.1016/j.ijheatmasstransfer.2016.05.031.
   Web of Science ®Google Scholar
• W. He, G. Qin, Y. Wang, and Z. Bao, “A segregated spectral element method for thermo-magnetic convection of paramagnetic fluid in rectangular enclosures with sinusoidal temperature distribution on one side wall,” Numer. Heat Transfer Part A, vol. 76, no. 2, pp. 51–72, 2019. DOI: 10.1080/10407782.2019.1615787.
   Web of Science ®Google Scholar
• N. H. Saeid, “Natural convection in porous cavity with sinusoidal bottom wall temperature variation,” Int. Comm. Heat Mass Transf., vol. 32, no. 3-4, pp. 454–463, 2005. DOI: 10.1016/j.icheatmasstransfer.2004.02.018.
   Web of Science ®Google Scholar
• T. Basak, S. Roy, T. Paul, and I. Pop, “Natural convection in a square cavity filled with a porous medium: Effects of various thermal boundary conditions,” Int. J. Heat Mass Transf., vol. 49, no. 7-8, pp. 1430–1441, 2006. DOI: 10.1016/j.ijheatmasstransfer.2005.09.018.
   Web of Science ®Google Scholar
• Y. Varol, H. F. Oztop, and I. Pop, “Numerical analysis of natural convection for a porous rectangular enclosure with sinusoidally varying temperature profile on the bottom wall,” Int. Comm. Heat Mass Transf., vol. 35, no. 1, pp. 56–64, 2008. DOI: 10.1016/j.icheatmasstransfer.2007.05.015.
   Web of Science ®Google Scholar
• M. Bhuvaneswari, S. Sivasankaran, and Y. J. Kim, “Magnetoconvection in a square enclosure with sinusoidal temperature distributions on both side walls,” Numer. Heat Transf. A, vol. 59, no. 3, pp. 167–184, 2011. DOI: 10.1080/10407782.2011.541219.
   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, vol. 63, no. 1, pp. 14–30, 2013. DOI: 10.1080/10407782.2012.715985.
   Web of Science ®Google Scholar
• F. Wu, G. Wang, and W. Zhou, “Buoyancy induced convection in a porous cavity with sinusoidally and partially thermally active sidewalls under local thermal non-equilibrium condition,” Int. Comm. Heat Mass Transf., vol. 75, pp. 100–114, 2016. DOI: 10.1016/j.icheatmasstransfer.2016.03.026.
   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 non-equilibrium model,” Numer. Heat Transf. A, 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, vol. 70, no. 3, pp. 310–329, 2016. DOI: 10.1080/10407782.2016.1173474.
   Web of Science ®Google Scholar
• A. I. Alsabery, A. J. Chamkha, I. Hashim, and P. G. Siddheshwar, “Effects of nonuniform heating and wall conduction on natural convection in a square porous cavity using LTNE model,” J. Heat Transf., vol. 139, no. 12, pp. 122008–122001, 2017.
   Web of Science ®Google Scholar
• A. I. Alsabery, A. J. Chamkha, H. Saleh, I. Hashim, and B. Chanane, “Effects of finite wall thickness and sinusoidal heating on convection in nanofluid-saturated local thermal non-equilibrium porous cavity,” Phys. A, vol. 470, pp. 20–38, 2017. DOI: 10.1016/j.physa.2016.11.107.
   Web of Science ®Google Scholar
• D. S. Cimpean, C. Revnic, and I. Pop, “Natural convection in a square inclined cavity filled with a porous medium with sinusoidal temperature distribution on both side walls,” Transp. Porous Media, vol. 129, no. 389, pp. 1–14, 2019.
   Google Scholar
• A. Kumar, and P. Bera, “Natural convection in an anisotropic porous enclosure due to nonuniform heating from the bottom wall,” J. Heat Transf., vol. 131, no. 7, pp. 072601–072601, 2009.
   Web of Science ®Google Scholar
• M. K. Khandelwal, P. Bera, and A. Chakrabati, “Influence of periodicity of sinusoidal bottom boundary condition on the natural convection in porous enclosure,” Int. J. Heat Mass Transf., vol. 55, no. 11/12, pp. 2889–2900, 2012. DOI: 10.1016/j.ijheatmasstransfer.2012.02.028.
   Web of Science ®Google Scholar
• R. A. Wooding, “Large scale geothermal field parameters and convection theory” Second workshop geothermal reservoir engineering, Stanford University, Stanford, December 1–3, 1976, pp. 339–345.
   Google Scholar
• P. A. Tyvand, and L. Storsletten, “Onset of convection in an anisotropic porous medium with oblique principal axes,” J. Fluid Mech., vol. 226, no. 1, pp. 371–382, 1991. DOI: 10.1017/S0022112091002422.
   Google Scholar
• L. Storesletten, “Natural convection in a horizontal porous layer with anisotropic thermal diffusivity,” Transp. Porous Media, vol. 12, no. 1, pp. 19–29, 1993. DOI: 10.1007/BF00616359.
   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
• F. Wu, G. Wang, and W. Zhou, “A thermal nonequilibrium approach to natural convection in a square enclosure due to the partially cooled sidewalls of the enclosure,” Numer. Heat Transf., A, vol. 67, no. 7, pp. 771–790, 2015. DOI: 10.1080/10407782.2014.949189.
   Web of Science ®Google Scholar
• F. Wu, W. Zhou, G. Wang, X. Ma, and Y. Wang, “Numerical simulation of natural convection in a porous cavity with linearly temperature distributions under the local thermal nonequilibrium condition,” Numer. Heat Transf., A, vol. 68, no. 12, pp. 1394–1415, 2015. DOI: 10.1080/10407782.2015.1052316.
   Web of Science ®Google Scholar
• J. P. Holman, Heat Transfer. New Delhi, India: Mc Graw-Hill, 2010.
   Google Scholar
• S. V. Patankar, Numerical Heat Transfer and Fluid Flow. New Delhi, India: Hemisphere Publishing Corporation, 1980.
   Google Scholar
• G. Degan, and P. Vasseur, “Natural convection in a vertical slot filled with an anisotropic porous medium with oblique principal axes,” Numer. Heat Transf. A, vol. 30, no. 4, pp. 397–412, 1996. DOI: 10.1080/10407789608913847.
   Web of Science ®Google Scholar
• P. Bera, V. Eswaran, and P. Singh, “Numerical study of heat and mass transfer in an anisotropic porous enclosure due to constant heating and cooling,” Numer. Heat Transf. A, vol. 34, no. 8, pp. 887–905, 1998. DOI: 10.1080/10407789808914021.
   Web of Science ®Google Scholar