Publication Cover
Numerical Heat Transfer, Part A: Applications
An International Journal of Computation and Methodology
Volume 74, 2018 - Issue 3
169
Views
5
CrossRef citations to date
0
Altmetric
Articles

Single domain integral transform analysis of natural convection in cavities partially filled with heat generating porous medium

, & ORCID Icon
Pages 1068-1086 | Received 27 Apr 2018, Accepted 08 Aug 2018, Published online: 08 Oct 2018

References

  • F. Arpino, G. Cortellessa, and A. Mauro, “Transient thermal analysis of natural convection in porous and partially porous cavities,” Numer. Heat Transf. Part A Appl., vol. 67, no. 6, pp. 605–631, 2015. DOI:10.1080/10407782.2014.949133.
  • A. Tahmasebi, M. Mahdavi, and M. Ghalambaz, “Local thermal nonequilibrium conjugate natural convection heat transfer of nanofluids in a cavity partially filled with porous media using Buongiorno’s model,” Numer. Heat Transf. Part A Appl., vol. 73, no. 4, pp. 254–276, 2018. DOI:10.1080/10407782.2017.1422632.
  • G. S. Beavers and D. D. Joseph, “Boundary conditions at a naturally permeable wall,” J. Fluid Mech., vol. 30, no. 01, pp. 197–207, 1967. DOI:10.1017/S0022112067001375.
  • D. A. Nield, “Onset of convection in a fluid layer overlying a layer of a porous medium,” J. Fluid Mech., vol. 81, no. 03, pp. 513–522, 1977. DOI:10.1017/S0022112077002195.
  • D. Poulikakos, A. Bejan, B. Selimos, and K. R. Blake, “High Rayleigh number in a fluid overlying a porous bed,” Int. J. Heat Fluid Flow, vol. 7, no. 2, pp. 109–116, 1986. DOI:10.1016/0142-727X(86)90056-1.
  • H. C. Brinkman, “A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles,” Appl. Sci. Res., vol. 1, no. 1, pp. 27–34, 1949. DOI:10.1007/BF02120313.
  • S. Whitaker, “Flow in porous media I: a theoretical derivation of Darcy’s law,” Transp. Porous Media, vol. 1, no. 1, pp. 3–25, 1986. DOI:10.1007/BF01036523.
  • J. A. Ochoa-Tapia and S. Whitaker, “Momentum transfer at the boundary between a porous medium and a homogeneous fluid-I. Theoretical development,” Int. J. Heat Mass Transf., vol. 38, no. 14, pp. 2635–2646, 1995. DOI:10.1016/0017-9310(94)00346-W.
  • J. A. Ochoa-Tapia and S. Whitaker, “Momentum transfer at the boundary between a porous medium and a homogeneous fluid-II. Comparison with experiment,” Int. J. Heat Mass Transf., vol. 38, no. 14, pp. 2647–2655, 1995. DOI:10.1016/0017-9310(94)00347-X.
  • G. Neale and W. Nader, “Practical significance of Brinkman extension of Darcy’s law: coupled parallel flows within a channel and a boundary porous medium,” Can. J. Chem. Eng., vol. 52, no. 4, pp. 475–478, 1974. DOI:10.1002/cjce.5450520407.
  • R. M. Cotta, Integral Transforms in Computational Heat and Fluid Flow, 1st ed. Boca Raton, FL: CRC Press, 1993.
  • R. M. Cotta and M. D. Mikhailov, Heat Conduction: Lumped Analysis, Integral Transforms, Symbolic Computation, 1st ed., Chichester, UK: Wiley Interscience, 1997.
  • R. M. Cotta, The Integral Transform Method in Thermal, Fluid Sciences and Engineering, 1st ed., New York, NY: Begell House, 1998.
  • R. M. Cotta and M. D. Mikhailov, “Hybrid methods and symbolic computations,” in Handbook of Numerical Heat Transfer, 2nd ed., Chapter 16, W. J. Minkowycz, E. M. Sparrow, and J. Y. Murthy, Eds. New York: John Wiley, 2006, pp. 493–522.
  • R. M. Cotta, D. C. Knupp, and C. P. Naveira-Cotta, Analytical Heat and Fluid Flow in Microchannels and Microsystems, 1st ed. New York, NY: Springer, 2016.
  • R. M. Cotta, D. C. Knupp, and J. N. N. Quaresma, “Analytical methods in heat transfer,” in Handbook of Thermal Science and Engineering, 1st ed., Chapter 1, Francis A. Kulacki, Eds. Switzerland: Springer International Publishing, 2017. DOI:10.1007/978-3-319-32003-8_2-1
  • M. A. Leal, J. S. Perez Guerrero, and R. M. Cotta, “Natural convection inside two-dimensional cavities: the integral transform method,” Commun. Numer. Meth. Eng., vol. 15, no. 2, pp. 113–125, 1999.
  • M. A. Leal, H. A. Machado, and R. M. Cotta, “Integral transform solutions of transient natural convection in enclosures with variable fluid properties,” Int. J. Heat Mass Transfer, vol. 43, no. 21, pp. 3977–3990, 2000. DOI:10.1016/S0017-9310(00)00023-5.
  • C. F. T. Matt, J. N. N. Quaresma, and R. M. Cotta, “Analysis of magnetohydrodynamic natural convection in closed cavities through integral transforms,” Int. J. Heat Mass Transf, vol. 113, pp. 502–513, 2017. DOI:10.1016/j.ijheatmasstransfer.2017.05.043.
  • S. C. Hirata, B. Goyeau, D. Gobin, M. Carr, and R. M. Cotta, “Linear stability of natural convection in superposed fluid and porous layers: influence of the interfacial modelling,” Int. J. Heat Mass Transf, vol. 50, no. 7–8, pp. 1356–1367, 2007. DOI:10.1016/j.ijheatmasstransfer.2006.09.038.
  • S. C. Hirata, B. Goyeau, D. Gobin, M. Chandesris, and D. Jamet, “Stability of natural convection in superposed fluid and porous layers: Equivalence of the one- and two-domain approaches,” Int. J. Heat Mass Transf, vol. 52, no. 1–2, pp. 533–536, 2009. DOI:10.1016/j.ijheatmasstransfer.2008.07.045.
  • C. Baohua and R. M. Cotta, “Integral transform analysis of natural convection in porous enclosures,” Int. J. Num. Meth. Fluids, vol. 17, no. 9, pp. 787–801, 1993.
  • L. S. De. B. Alves and R. M. Cotta, “Transient natural convection inside porous cavities: hybrid numerical-analytical solution and mixed symbolic-numerical computation,” Num. Heat Transfer, Part A—Appl., vol. 38, no. 1, pp. 89–110, 2000.
  • H. Luz Neto, J. N. N. Quaresma, and R. M. Cotta, “Natural convection in three-dimensional porous cavities: integral transform method,” Int. J. Heat Mass Transfer, vol. 45, no. 14, pp. 3013–3032, 2002.
  • G. G. C. Lima, C. A. C. Santos, A. Haag, and R. M. Cotta, “Integral transform solution of internal flow problems based on Navier-Stokes Equations and primitive variables formulation,” Int. J. Num. Meth. Eng, vol. 69, no. 3, pp. 544–561, 2007. DOI:10.1002/nme.1780.
  • J. S. Perez-Guerrero and R. M. Cotta, “Integral transform solution for the lid-driven cavity flow problem in streamfunction-only formulation,” Int. J. Num. Meth. Fluids, vol. 15, no. 4, pp. 399–409, 1992. DOI:10.1002/fld.1650150403.
  • J. S. Perez-Guerrero and R. M. Cotta, “Benchmark integral transform results for flow over a backward-facing step,” Comput. Fluids, vol. 25, no. 5, pp. 527–540, 1996. DOI:10.1016/0045-7930(96)00005-9.
  • J. S. Perez-Guerrero, J. N. N. Quaresma, and R. M. Cotta, “Simulation of laminar flow inside ducts of irregular geometry using integral transforms,” Comput. Mech., vol. 25, no. 4, pp. 413–420, 2000. DOI:10.1007/s004660050488.
  • R. Ramos, J. S. Perez-Guerrero, and R. M. Cotta, “Stratified flow over a backward facing step: hybrid solution by integral transforms,” Int. J. Num. Meth. Fluids, vol. 35, no. 2, pp. 173–197, 2001.
  • C. A. M. Silva, E. N. Macedo, J. N. N. Quaresma, L. M. Pereira, and R. M. Cotta, “Integral transform solution of the Navier-Stokes equations in full cylindrical regions with streamfunction formulation,” Int. J. Num. Meth. Biomedical Eng., vol. 26, no. 11, pp. 1417–1434, 2010.
  • D. C. Knupp, R. M. Cotta, and C. P. Naveira-Cotta, “Heat transfer in microchannels with upstream–downstream regions coupling and wall conjugation effects,” Numer. Heat Transf. Part B Fundam., vol. 64, no. 5, pp. 365–387, 2013. DOI:10.1080/10407790.2013.810535.
  • D. C. Knupp, C. P. Naveira-Cotta, and R. M. Cotta, “Conjugated convection-conduction analysis in microchannels with axial diffusion effects and a single domain formulation,” J. Heat Transfer, vol. 135, no. 9, pp. 091401, 2013. DOI:10.1115/1.4024425.
  • D. C. Knupp, C. P. Naveira-Cotta, and R. M. Cotta, “Theoretical–experimental analysis of conjugated heat transfer in nanocomposite heat spreaders with multiple microchannels,” Int. J. Heat Mass Transf., vol. 74, pp. 306–318, 2014. DOI:10.1016/j.ijheatmasstransfer.2014.03.005.
  • D. C. Knupp, R. M. Cotta, C. P. Naveira-Cotta, and S. Kakaç, “Transient conjugated heat transfer in microchannels: Integral transforms with single domain formulation,” Int. J. Therm. Sci., vol. 88, pp. 248–257, 2015. DOI:10.1016/j.ijthermalsci.2014.04.017.
  • D. C. Knupp, R. M. Cotta, and C. P. Naveira-Cotta, “Fluid flow and conjugated heat transfer in arbitrarily shaped channels via single domain formulation and integral transforms,” Int. J. Heat Mass Transf., vol. 82, pp. 479–489, 2015. DOI:10.1016/j.ijheatmasstransfer.2014.11.007.
  • J. R. B. Souza et al., “Thermal analysis of anti-icing systems in aeronautical velocity sensors and structures,” J Braz. Soc. Mech. Sci. Eng., vol. 38, no. 5, pp. 1489–1509, 2016. DOI:10.1007/s40430-015-0449-7.
  • R. M. Cotta, C. P. Naveira-Cotta, D. C. Knupp, J. L. Z. Zotin, P. C. Pontes, and A. P. Almeida, “Recent advances in computational-analytical integral transforms for convection-diffusion problems,” Heat Mass Transfer, vol. 54, pp. 2475–2496, 2018. (Invited Paper). DOI:10.1007/s00231-017-2186-1.
  • K. M. Lisboa and R. M. Cotta, “Hybrid integral transforms for flow development in ducts partially filled with porous media,” Proc. R. Soc. A Math. Phys. Eng. Sci., vol. 474, no. 2209, p. 20170637, 2018. DOI:10.1098/rspa.2017.0637.
  • K. M. Lisboa and R. M. Cotta, “On the mass transport in membraneless flow batteries with flow-by configuration,” Int. J. Heat Mass Transf., vol. 122, pp. 954–966, 2018. DOI:10.1016/j.ijheatmasstransfer.2018.02.002.
  • M. Wang, H. Zhao, Y. Zhang, G. Su, W. Tian, and S. Qiu, “Research on the designed emergency passive residual heat removal system during the station blackout scenario for CPR1000,” Ann. Nucl. Energy, vol. 45, pp. 86–93, 2012. DOI:10.1016/j.anucene.2012.03.004.
  • A. Kaliatka, V. Ognerubov, and V. Vileiniskis, “Analysis of the processes in spent fuel pools of ignalina NPP in case of loss of heat removal,” Nucl. Eng. Des., vol. 240, no. 5, pp. 1073–1082, 2010. DOI:10.1016/j.nucengdes.2009.12.026.
  • T. C. Hung, V. K. Dhir, B. S. Pei, Y. S. Chen, and F. P. Tsai, “The development of a three-dimensional transient CFD model for predicting cooling ability of spent fuel pools,” Appl. Therm. Eng., vol. 50, no. 1, pp. 496–504, 2013. DOI:10.1016/j.applthermaleng.2012.06.042.
  • C. Ye, M. G. Zheng, M. L. Wang, R. H. Zhang, and Z. Q. Xiong, “The design and simulation of a new spent fuel pool passive cooling system,” Ann. Nucl. Energy, vol. 58, pp. 124–131, 2013. DOI:10.1016/j.anucene.2013.03.007.
  • L. Lima, N. Mangiavacchi, and L. Ferrari, “Stability analysis of passive cooling systems for nuclear spent fuel Pool,” J. Braz. Soc. Mech. Sci. Eng., vol. 39, no. 3, pp. 1019–1031, 2017. DOI:10.1007/s40430-016-0589-4.
  • U. Appenzeller, External spent fuel storage facility at the nuclear power plant in Gösgen, IAEA Technical Meeting on SNF storage options, 2–4 July 2013, Vienna, Austria.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.