0
Research Papers: Natural and Mixed Convection

Numerical Study on Conjugate Conduction–Convection in a Cubic Enclosure Submitted to Time-Periodic Sidewall Temperature

[+] Author and Article Information
Guang Xi

Professor
e-mail: xiguang@mail.xjtu.edu.cn
Department of Fluid Machinery and Engineering,
School of Energy and Power Engineering,
Xi'an Jiaotong University,
No. 28 West Xianning Road,
Xi'an 710049, Shaanxi, P.R. China

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the Journal of Heat Transfer. Manuscript received May 9, 2012; final manuscript received September 20, 2012; published online December 28, 2012. Assoc. Editor: Darrell W. Pepper.

J. Heat Transfer 135(2), 022504 (Dec 28, 2012) (10 pages) Paper No: HT-12-1213; doi: 10.1115/1.4007738 History: Received May 09, 2012; Revised September 20, 2012

The laminar conjugate conduction-natural convection heat transfer in a cubic enclosure of finite thickness conductive walls and central cavity filled with fluid is comprehensively studied by using recently developed high accuracy temporal-spatial multidomain pseudospectral method. The enclosure is assumed to have one sidewall submitted to time-periodic pulsating temperature and the opposing sidewall constant temperature, and the top, bottom and two lateral sidewalls are adiabatic. The present study is devoted to explore the fluid mechanics and heat transfer mechanisms of the time-periodic conjugate conduction-natural convection in the enclosure, with particular highlights on the heat transfer resonance and back heat transfer phenomena, the perturbation propagation patterns and the three-dimensional characteristics. The computations are performed for wide ranges of controlling parameters of engineering significance, i.e., the dimensionless wall thickness 0 ≤ s ≤ 0.10, the solid–fluid thermal conductivity ratio 10 ≤ k ≤ 50 and diffusivity ratio 0.001 ≤ a ≤ 0.1, and the sidewall temperature pulsating period 1 ≤ P ≤ 103. Numerical results reveal that the time-periodic fluid flow and conjugate heat transfer performances of the enclosure system are greatly affected by the conductive walls and complexly dependent on the controlling parameters. The thickness and thermophysical properties of the conductive walls, together with the pulsating period of the sidewall temperature, govern the sidewall temperature disturbance propagation patterns (amplitude, phase position and speed) within the enclosure. The heat transfer resonance only appears in cases of large diffusivity ratio, but the variation of period-averaged heat transfer rate with respect to the pulsating period is quite different from that of the zero wall thickness enclosure. The back heat transfer exists in region close to the corners formed by either the top or bottom walls and the enclosure hot sidewall, and the former is more remarkable in both scale and duration and is gradually disappearing as the pulsating period increases.

FIGURES IN THIS ARTICLE
<>
Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.

References

de Vahl Davis, G., 1983, “Natural Convection of Air in a Square Cavity: A Benchmark Numerical Solution,” Int. J. Numer. Methods Fluids, 3, pp. 249–264. [CrossRef]
Mallinson, G. D., and de Vahl Davis, G., 1977, “Three-Dimensional Natural Convection in a Box: A Numerical Study,” J. Fluid Mech., 83, pp. 1–31. [CrossRef]
Lage, J. L., and Bejan, A., 1993, “The Resonance of Natural Convection in an Enclosure Heated Periodically From the Side,” Int. J. Heat Mass Transfer, 36, pp. 2027–2038. [CrossRef]
Kazmierczak, M., and Chinoda, Z., 1992, “Buoyancy-Driven Flow in an Enclosure With Time Periodic Boundary Conditions,” Int. J. Heat Mass Transfer, 35, pp. 1507–1518. [CrossRef]
Kwak, H. S., and Hyun, J. M., 1996, “Natural Convection in an Enclosure Having a Vertical Sidewall With Time-Varying Temperature,” J. Fluid Mech., 329, pp. 65–88. [CrossRef]
Kwak, H. S., Kuwahara, K., and Hyun, J. M., 1998, “Resonant Enhancement of Natural Convection Heat Transfer in a Square Enclosure,” Int. J. Heat Mass Transfer, 41, pp. 2837–2846. [CrossRef]
Xia, Q., Yang, K. T., and Mukutmoni, D., 1995, “Effect of Imposed Wall Temperature Oscillations on the Stability of Natural Convection in a Square Enclosure,” ASME J. Heat Transfer, 117, pp. 113–120. [CrossRef]
Abourida, B., Hasnaoui, M., and Douamna, S., 1999, “Transient Natural Convection in a Square Enclosure With Horizontal Walls Submitted to Periodic Temperatures,” Numer. Heat Transfer A, 36, pp. 737–750. [CrossRef]
Bae, J. H., Hyun, J. M., and Kwak, H. S., 2001, “Buoyant Convection in a Cavity With a Baffle Under Time-Periodic Wall Temperature,” Numer. Heat Transfer A, 39, pp. 723–736. [CrossRef]
Liu, D., Zhao, F. Y., and Tang, G. F., 2008, “Conjugate Heat Transfer in an Enclosure With a Centered Conducting Body Imposed Sinusoidal Temperature Profiles on One Side,” Numer. Heat Transfer A, 53, pp. 204–223. [CrossRef]
Kalabin, E. V., Kanashina, M. V., and Zubkov, P. T., 2005, “Heat Transfer From the Cold Wall of a Square Cavity to the Hot One by Oscillatory Natural Convection,” Numer. Heat Transfer A, 47, pp. 609–619. [CrossRef]
Kalabin, E. V., Kanashina, M. V., and Zubkov, P. T., 2005, “Natural-Convective Heat Transfer in a Square Cavity With Time-Varying Side-Wall Temperature,” Numer. Heat Transfer A, 47, pp. 621–631. [CrossRef]
Cheikh, N. B., Beya, B. B., and Lili, T., 2007, “Aspect Ratio Effect on Natural Convection Flow in a Cavity Submitted to a Periodical Temperature Boundary,” ASME J. Heat Transfer, 129, pp. 1060–1068. [CrossRef]
Ayachi, R. E., Raji, A., Hasnaoui, M., and Bahlaoui, A., 2008, “Combined Effect of Radiation and Natural Convection in a Square Cavity Differentially Heated With a Periodic Temperature,” Numer. Heat Transfer A, 53, pp. 1339–1356. [CrossRef]
Kim, K. H., and Hyun, J. M., 2004, “Buoyant Convection in a Cubical Enclosure Under Time-Periodic Magnetizing Force,” Int. J. Heat Mass Transfer, 47, pp. 5211–5218. [CrossRef]
Nithyadevi, N., Kandaswamy, P., and Malliga Sundari, S., 2009, “Magnetoconvection in a Square Cavity With Partially Active Vertical Walls: Time Periodic Boundary Condition,” Int. J. Heat Mass Transfer, 52, pp. 1945–1953. [CrossRef]
Narasimhan, A., and Reddy, B. V. K., 2011, “Resonance of Natural Convection Inside a Bidisperse Porous Medium Enclosure,” ASME J. Heat Transfer, 133, p. 042601. [CrossRef]
Ghasemi, B., and Aminossadati, S. M., 2010, “Periodic Natural Convection in a Nanofluid-Filled Enclosure With Oscillating Heat Flux,” Int. J. Therm. Sci., 49, pp. 1–9. [CrossRef]
Wang, Q. W., Yang, J., Zeng, M., and Wang, G., 2010, “Three-Dimensional Numerical Study of Natural Convection in an Inclined Porous Cavity With Time Sinusoidal Oscillating Boundary Conditions,” Int. J. Heat Fluid Flow, 31, pp. 70–82. [CrossRef]
Zhang, W., Zhang, C. H., and Xi, G., 2011, “Conjugate Conduction-Natural Convection in an Enclosure With Time-Periodic Sidewall Temperature and Inclination,” Int. J. Heat Fluid Flow, 32, pp. 52–64. [CrossRef]
Zhang, W., Xi, G., Zhang, C. H., and Huang, Z., 2011, “A High Accuracy Temporal-Spatial Pseudospectral Method for Time-Periodic Unsteady Fluid Flow and Heat Transfer Problems,” Int. J. Comput. Fluid Dyn., 25, pp. 191–206. [CrossRef]
Zhang, C. H., Zhang, W., and Xi, G., 2010, “A Pseudospectral Multidomain Method for Conjugate Conduction-Convection in Enclosures,” Numer. Heat Transfer B, 57, pp. 260–282. [CrossRef]
Peyret, R., 2002, Spectral Methods for Incompressible Viscous Flow, Springer, New York.
Misra, D., and Sarkar, A., 1997, “Finite Element Analysis of Conjugate Natural Convection in a Square Enclosure With a Conducting Vertical Wall,” Comput. Methods Appl. Mech. Eng, 141, pp. 205–219. [CrossRef]
Zhang, W., Huang, Z., Zhang, C. H., and Xi, G., 2012, “Conjugate Wall Conduction-Fluid Natural Convection in a Three-Dimensional Inclined Enclosure,” Numer. Heat Transfer A, 61, pp. 122–141. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Physical model and geometric configuration

Grahic Jump Location
Fig. 2

Heat transfer resonance for the zero wall thickness enclosure (s = 0)

Grahic Jump Location
Fig. 3

Heat transfer resonance for the finite wall thickness enclosure

Grahic Jump Location
Fig. 4

Pulsating amplitude of temperature along the centerline (y = z = 0)

Grahic Jump Location
Fig. 5

Temperature pulsations at three points on the centerline (y = z = 0) (s = 0.02, k = 10, a = 0.1)

Grahic Jump Location
Fig. 6

Temporal evolutions of temperature profile along the centerline (y = z = 0) (s = 0.02, k = 10, a = 0.1)

Grahic Jump Location
Fig. 7

Temporal evolution and spatial distribution of averaged Nusselt computed at the cavity hot sidewall (s = 0.02, k = 10, a = 0.1). Negative values for heat transfer from fluid to hot sidewall.

Grahic Jump Location
Fig. 8

Time-periodic distributions of temperature (contours) and velocity u (isolines) on the y = 0 cross section at equispaced time instants from (a) t = 0 to (m) t = 11P/12 (s = 0.02, k = 10, a = 0.1, P = 10). Temperature increment △θ = 0.1 with θ = 0 on the left (cold) sidewall; velocity u increment △u = 0.04 from −0.32 to 0.24 with solid lines for positive values that represents fluid moving from left (cold) to right (hot) sidewall.

Grahic Jump Location
Fig. 9

Time-periodic distributions of temperature (contours) and velocity u (isolines) on the y = 0 cross section at equispaced time instants from (a) t = 0 to (m) t = 11P/12 (s = 0.02, k = 10, a = 0.1, P = 800). Temperature increment △θ = 0.1 with θ = 0 on the left (cold) sidewall; velocity u increment △u = 0.04 from −0.24 to 0.20 with solid lines for positive values that represents fluid moving from left (cold) to right (hot) sidewall.

Grahic Jump Location
Fig. 10

Pulsating amplitude of temperature along the centerline (z = 0) at various constant-y cross sections (s = 0.02, k = 10, a = 0.1)

Grahic Jump Location
Fig. 11

Temporal evolutions of temperature and velocity u distributions along the z-direction centerline (x = 0), and temperature and velocity w distributions along the x-direction centerline (z = 0) at various constant-y cross sections (s = 0.02, k = 10, a = 0.1, P = 100)

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In