Publication Cover
Numerical Heat Transfer, Part A: Applications
An International Journal of Computation and Methodology
Volume 77, 2020 - Issue 6
174
Views
4
CrossRef citations to date
0
Altmetric
Original Articles

Prandtl number scalings for unsteady natural convection boundary-layer flow on an evenly heated vertical plate in a homogeneous Pr > 1 fluid

ORCID Icon &
Pages 619-631 | Received 11 Sep 2019, Accepted 27 Dec 2019, Published online: 21 Jan 2020

References

  • Y. Jaluria, Natural Convection Heat and Mass Transfer. Oxford: Pergamon, 1980.
  • B. Gebhart, Y. Jaluria, R. L. Mahajan, and B. Sammakia, Buoyancy-Induced Flows and Transport. New York, USA: Hemisphere Publishing Corporation, 1988.
  • A. Bejan, Convection Heat Transfer, 2nd ed. New York: John Wiley & Sons, 1995.
  • A. Faghri, Y. Zhang, and, and J. Howell, Advanced Heat and Mass Transfer. Columbia, MO: Global Digital Press, 2010.
  • J. C. Cheng, Y. L. Tsay, and C. H. Yang, “Characteristics and enhancement of heat transfer from heat-generating blocks mounted on back wall of a 3D cabinet to an ambient natural convective air stream,” Numer. Heat Transf. A Appl., vol. 74, no. 9, pp. 1503–1537, 2018. DOI: 10.1080/10407782.2018.1525159.
  • L. Zhang, Y. Huang, G. Yang, and J. Wu, “Numerical simulation of conjugate turbulent mixed convection in an open cavity: evaluation of different wall heat conduction models,” Numer. Heat Transf. A Appl., vol. 74, no. 5, pp. 1244–1264, 2018. DOI: 10.1080/10407782.2018.1517554.
  • M. Qiao, F. Xu, and S. C. Saha, “Scaling analysis and numerical simulation of natural convection from a duct,” Numer. Heat Transf. A Appl., vol. 72, no. 5, pp. 355–371, 2017. DOI: 10.1080/10407782.2017.1376942.
  • B. Zamora and A. S. Kaiser, “Influence of the shape, thermal radiation, and variable properties on the turbulent buoyancy-driven airflow inside cavities with Trombe wall geometry,” Numer. Heat Transf. A: Appl., vol. 73, no. 5, pp. 307–331, 2018. DOI: 10.1080/10407782.2018.1439236.
  • W. He, G. Qin, Y. Wang, and Z. Bao, “A segregated spectral element method for thermomagnetic convection of paramagnetic fluid in rectangular enclosures with sinusoidal temperature distribution on one side wall,” Numer. Heat Transf. A Appl., vol. 76, no. 2, pp. 51–72, 2019. DOI: 10.1080/10407782.2019.1615787.
  • 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.
  • W. Lin and S. W. Armfield, “Scalings for unsteady natural convection boundary layers on an evenly heated plate with time-dependent heat flux,” Phys. Rev. E, vol. 88, no. 6, pp. 063013, 2013. DOI: 10.1103/PhysRevE.88.063013.
  • W. Lin and S. W. Armfield, “Scalings for unsteady natural convection boundary layers on a vertical plate at time-dependent temperature,” Int. J. Therm. Sci., vol. 111, pp. 78–99, 2017. DOI: 10.1016/j.ijthermalsci.2016.08.008.
  • W. Lin and S. W. Armfield, “Natural convection boundary-layer flow on an evenly heated vertical plate with time-varying heating flux in a stratified Pr < 1 fluid,” Numer. Heat Transf. A: Appl., vol. 76, no. 6, pp. 393–419, 2019.
  • M. Corcione, M. Cianfrini, and A. Quintino, “Temperature effects on the enhanced or deteriorated buoyancy-driven heat transfer in differentially heated enclosures filled with nanofluids,” Numer. Heat Transf. A: Appl., vol. 70, no. 3, pp. 223–241, 2016. DOI: 10.1080/10407782.2016.1173461.
  • I. Amber and T. S. O’Donovan, “A numerical simulation of heat transfer in an enclosure with a nonlinear heat source,” Numer. Heat Transf. A Appl., vol. 71, no. 11, pp. 1081–1093, 2017. DOI: 10.1080/10407782.2017.1330093.
  • Y. Billaud, D. Saury, and D. Lemonnier, “Numerical investigation of coupled natural convection and radiation in a differentially heated cubic cavity filled with humid air. Effects of the cavity size,” Numer. Heat Transf. A Appl., vol. 72, no. 7, pp. 495–518, 2017. DOI: 10.1080/10407782.2017.1386509.
  • W. Wang, J. Wu, and X. Feng, “A novel pressure-correction projection finite element method for incompressible natural convection problem with variable density,” Numer. Heat Transf. A Appl., vol. 74, no. 2, pp. 1001–1017, 2018. DOI: 10.1080/10407782.2018.1505093.
  • W. Lin, S. W. Armfield, J. C. Patterson, and C. Lei, “Prandtl number scaling of unsteady natural convection boundary layers for Pr > 1 fluids under isothermal heating,” Phys. Rev. E, vol. 79, no. 6, pp. 066313, 2009. DOI: 10.1103/PhysRevE.79.066313.
  • W. Lin, S. W. Armfield, and J. C. Patterson, “Unsteady natural convection boundary-layer flow of a linearly-stratified fluid with Pr < 1 on an evenly heated semi-infinite vertical plate,” Int. J. Heat Mass Transf., vol. 51, pp. 327–342, 2008.
  • W. Lin, S. W. Armfield, and J. C. Patterson, “Cooling of a Pr < 1 fluid in a rectangular container,” J. Fluid Mech., vol. 574, pp. 85–108, 2007.
  • L. Soucasse, P. Riviere, A. Soufiani, S. Xin, and P. Le Quere, “Transitional regimes of natural convection in a differentially heated cubical cavity under the effects of wall and molecular gas radiation,” Phys. Fluids, vol. 26, no. 2, pp. 024105, 2014. DOI: 10.1063/1.4864265.
  • F. Xu, J. C. Patterson, and C. Lei, “An experimental study of the coupled thermal boundary layers adjacent to a partition in a differentially heated cavity,” Exp. Therm. Fluid Sci., vol. 54, pp. 12–21, 2014. DOI: 10.1016/j.expthermflusci.2014.01.005.
  • S. C. Saha and M. M. K. Khan, “An improved boundary layer scaling with ramp heating on a sloping plate,” Int. J. Heat Mass Transf., vol. 55, no. 9–10, pp. 2268–2284, 2012. DOI: 10.1016/j.ijheatmasstransfer.2012.01.038.
  • J. Fohr and H. B. Moussa, “Heat conduction mass transfer in a cylindrical grain silo submitted to a periodical wall heat flux,” Int. J. Heat Mass Transf., vol. 37, no. 12, pp. 1699–1712, 1994. DOI: 10.1016/0017-9310(94)90060-4.
  • Q. W. Wang, J. Yang, M. Zeng, and G. Wang, “Three-dimensional numerical study of natural convection in an inclined porous cavity with time sinusoidal oscillating boundary conditions,” Int. J. Heat Fluid Flow, vol. 31, no. 1, pp. 70–82, 2010. DOI: 10.1016/j.ijheatfluidflow.2009.11.005.
  • S. Paolucci and Z. J. Zikoski, “Free convective flow from a heated vertical wall immersed in a thermally stratified environment,” Int. J. Heat Mass Transf., vol. 67, pp. 1062–1071, 2013. DOI: 10.1016/j.ijheatmasstransfer.2013.08.076.
  • W. Lin and S. W. Armfield, “Unified Prandtl number scaling for start-up and fully developed natural-convection boundary layers for both Pr≳1 and Pr≲1 fluids with isothermal heating,” Phys. Rev. E, vol. 86, pp. 066312, 2012.
  • S. W. Armfield, J. C. Patterson, and W. Lin, “Scaling investigation of the natural convection boundary layer on an evenly heated plate,” Int. J. Heat Mass Transf., vol. 50, no. 7–8, pp. 1592–1602, 2007.
  • J. C. Patterson, C. Lei, S. W. Armfield, and W. Lin, “Scaling of unsteady natural convection boundary layers with a non-instantaneous initiation,” Int. J. Therm. Sci., vol. 48, no. 10, pp. 1843–1852, 2009.
  • V. P. Carey and J. C. Mollendorf, “Measured variation of thermal boundary-layer thickness with Prandtl number for laminar natural convection from a vertical uniform-heat-flux surface,” Int. J. Heat Mass Transf., vol. 21, no. 4, pp. 481–488, 1978.

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.