0
Research Papers: Natural and Mixed Convection

Buoyancy Induced Convection From Biheaters in a Cavity: A Numerical Study

[+] Author and Article Information
Asis Giri

Department of Mechanical Engineering,
North Eastern Regional Institute of Science
and Technology,
Itanagar 791109, India
e-mail: measisgiri@rediffmail.com

Swastika Patel

Department of Mechanical Engineering,
North Eastern Regional Institute of Science
and Technology,
Itanagar 791109, India

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received October 2, 2016; final manuscript received April 26, 2018; published online June 7, 2018. Assoc. Editor: Antonio Barletta.

J. Heat Transfer 140(10), 102501 (Jun 07, 2018) (12 pages) Paper No: HT-16-1619; doi: 10.1115/1.4040140 History: Received October 02, 2016; Revised April 26, 2018

A computational study of natural convection from biheaters of finite thickness and finite conductivity placed on a finite thickness and a finite conductive bottom plate of a cavity is performed under constant heat input condition. Cavity is cooled by the sidewalls, while the top and backside of the bottom plate are insulated. Streamline, isotherms, and local heat flux distribution of the sidewalls are discussed. Base Grashof number is chosen as 2.5 × 106. Biheater maintains a nondimensional distance of 0.4 between them. The left heater is placed at a nondimensional distance of 0.2 from the left wall. Heater length ratio is varied from 0.4 to 1.7, while heater strength ratio is varied from 0.25 to 7.0. Optimum operating temperature condition is found from the analysis.

FIGURES IN THIS ARTICLE
<>
Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.

References

Papanicolaou, E. , and Gopalakrishna, S. , 1995, “ Natural Convection in Shallow, Horizontal Layers Encountered in Electronic Cooling,” ASME J. Electron. Packag., 117(4), pp. 307–316. [CrossRef]
Ortega, A. , and Lall, B. S. , 1996, “ Natural Convection Air Cooling of a Discrete Source on a Conducting Board in a Shallow Horizontal Enclosure,” 12th Annual IEEE Semiconductor Thermal Measurement and Management Symposium (SEMI-THERM), Austin, TX, Mar. 5–7, pp. 201–213.
Sezai, I. , and Mohammad, A. A. , 2000, “ Natural Convection From a Discrete Heat Source on the Bottom of a Horizontal Enclosure,” Int. J. Heat Mass Transfer, 43(13), pp. 2257–2266. [CrossRef]
Deng, Q. H. , Tang, G. F. , and Li, Y. , 2002a, “ Interaction Between Discrete Heat Sources in Horizontal Natural Convection Enclosures,” Int. J. Heat Mass Transfer, 45(26), pp. 5117–5132. [CrossRef]
Deng, Q. H. , Tang, G. F. , and Li, Y. , 2002b, “ A Combined Temperature Scale for Analyzing Natural Convection in Rectangular Enclosures With Discrete Wall Heat Sources,” Int. J. Heat Mass Transfer, 45(16), pp. 3437–3446. [CrossRef]
Calcagni, B. , Marsili, F. , and Paroncini, M. , 2005, “ Natural Convective Heat Transfer in Square Enclosures Heated From below,” Appl. Therm. Eng., 25(16), pp. 2522–2531. [CrossRef]
Sharif, M. A. R. , and Mohammad, T. R. , 2005, “ Natural Convection in Cavities With Constant Flux Heating at the Bottom Wall and Isothermal Cooling From the Sidewalls,” Int. J. Therm. Sci., 44(9), pp. 865–878. [CrossRef]
Ichimiya, K. , and Saiki, H. , 2005, “ Behavior of Thermal Plumes From Two-Heat Sources in an Enclosure,” Int. J. Heat Mass Transfer, 48(16), pp. 3461–3468. [CrossRef]
Oosthuizen, P. H. , and Paul, J. T. , 2005, “ Natural Convection in a Rectangular Enclosure With Two Heated Sections on the Lower Surface,” Int. J. Heat Fluid Flow, 26(4), pp. 587–596. [CrossRef]
Dalal, A. , and Das, M. K. , 2006, “ Natural Convection in a Rectangular Cavity Heated From Below and Uniformly Cooled From the Top and Both Sides,” Numer. Heat Transfer, Part A, 49, pp. 301–322. [CrossRef]
Bazylak, A. , Djilali, N. , and Sinton, D. , 2006, “ Natural Convection in an Enclosure With Distributed Heat Sources,” Numer. Heat Transfer, Part A, 49(7), pp. 655–667. [CrossRef]
Cheikh, N. B. , Beya, B. B. , and Lili, T. , 2006, “ Influence of Thermal Boundary Conditions on Natural Convection in a Square Enclosure Partially Heated From Below,” Int. Commun. Heat Mass Transfer, 34(3), pp. 369–379. [CrossRef]
Zhao, F. Y. , Tang, G. F. , and Liu, D. , 2006, “ Conjugate Natural Convection in Enclosures With External and Internal Heat Sources,” Int. J. Heat Mass Transfer, 44(3–4), pp. 148–165.
Chen, T. H. , and Chen, L. Y. , 2007, “ Study of Buoyancy-Induced Flows Subjected to Partially Heated Sources on the Left and Bottom Walls in a Square Enclosure,” Int. J. Therm. Sci., 46(12), pp. 1219–1231. [CrossRef]
Kuznetsov, G. V. , and Sheremet, M. A. , 2010, “ Conjugate Natural Convection in a Closed Domain Containing a Heat-Releasing Element With a Constant Heat-Release Intensity,” J. App. Mech. Tech. Phys., 51(5), pp. 699–712. [CrossRef]
Kuznetsov, G. V. , and Sheremet, M. A. , 2011, “ Conjugate Natural Convection in an Enclosure With a Heat Source of Constant Heat Transfer Rate,” Int. J. Heat Mass Transfer, 54(1–3), pp. 260–268. [CrossRef]
Banerjee, S. , Mukhopadhyay, A. , Sen, S. , and Ganguli, R. , 2008, “ Natural Convection in a Bi-Heater Configuration of Passive Electronic Cooling,” Int. J. Therm. Sci., 47(11), pp. 1516–1527. [CrossRef]
Mukhopadhyay, A. , 2010, “ Analysis of Entropy Generation Due to Natural Convection in Square Enclosures With Multiple Discrete Heat Sources,” Int. Comm. Heat Mass Transfer, 37(7), pp. 867–872. [CrossRef]
Patankar, S. V. , 1980, Numerical Heat Transfer and Fluid Flow, Hemisphere, Washington, DC.
de Vahl Davis, G. , 1983, “ Natural Convection of Air in a Square Cavity: A Bench-Mark Numerical Solution,” Int. J. Num. Methods Fluids, 3(3), pp. 249–264. [CrossRef]
Rao, G. M. , and Narasimham, G. S. V. L. , 2007, “ Laminar Conjugate Mixed Convection in a Vertical Channel With Heat Generating Components,” Int. J. Heat Mass Transfer, 50(17–18), pp. 3561–3574. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Schematic of physical domain

Grahic Jump Location
Fig. 4

((a.1), (b.1), (c.1)) Streamline; ((a.2), (b.2), (c.2)) Isotherms; ((a.3), (b.3), (c.3)) local heat flux on left and right cold walls at εr=1 and h* = 0.05 for different qr: (a.1) εr = 1.0, qr = 0.4, h* = 0.05; (a.2) εr = 1.0, qr = 0.4, h* = 0.05; (a.3) εr = 1.0, qr = 0.4, h* = 0.05; (b.1) εr = 1.0, qr = 0.5, h* = 0.05; (b.2) εr = 1.0, qr = 0.5, h* = 0.05; (b.3) εr = 1.0, qr = 0.5, h* = 0.05; (c.1) εr = 1.0, qr = 1.0, h* = 0.05; (c.2) εr = 1.0, qr = 1.0, h* = 0.05; and (c.3) εr = 1.0, qr = 1.0, h* = 0.05

Grahic Jump Location
Fig. 2

Computational domain with the arrangement of computational grid

Grahic Jump Location
Fig. 3

Numerical simulation obtained from the present code in the case of Banerjee et al. [17] for the parameters of Grb = 1 × 106,εr=1,w1*=0.2 and W* = 0.5, ((a.1), (b.1), (c.1)) streamfunction; ((a.2), (b.2), (c.2)) isotherms

Grahic Jump Location
Fig. 5

((a.1), (b.1), (c.1)) Streamline; ((a.2), (b.2), (c.2)) Isotherms; ((a.3), (b.3), (c.3)) local heat flux on left and right cold walls at qr=1 and h* = 0.05 for different εr : (a.1) qr = 1.0, εr = 0.4, h* = 0.05; (a.2) qr = 1.0, εr = 0.4, h* = 0.05; (a.3) qr = 1.0, εr = 0.4, h* = 0.05; (b.1) qr = 1.0, εr = 0.75, h* = 0.05; (b.2) qr = 1.0, εr = 0.75, h* = 0.05; (b.3) qr = 1.0, εr = 0.75, h* = 0.05; (c.1) qr = 1.0, εr = 1.7, h* = 0.05; (c.2) qr = 1.0, εr = 1.7, h* = 0.05; and (c.3) qr = 1.0, εr = 1.7, h* = 0.05

Grahic Jump Location
Fig. 6

Local Nusselt number variation on the base and chip surfaces for εr=1.0 and various qr (a) h = 0.05 and (b) h = 0.008

Grahic Jump Location
Fig. 7

Local Nusselt number variation on the base and chip surfaces for qr=1.0 and various εr (a) h = 0.05 and (b) h = 0.008

Grahic Jump Location
Fig. 8

Variation of Grθmax the left and right heaters versus heater length ratio at h* = 0.05 for different heater strength ratios: (a) qr=0.5, (b) qr=1.0, and (c) qr=2.0

Grahic Jump Location
Fig. 9

Variation of Grθmax the left and right heaters versus heater length ratio at h* = 0.008 for different heater strength ratios: (a) qr=0.5, (b) qr=1.0, and (c) qr=2.0

Grahic Jump Location
Fig. 10

Variation of Grθmax the left and right heaters versus heater strength ratio at h* = 0.05 for different heater length ratios: (a) εr=0.5, (b) εr=1.0, and (c) εr=1.5

Grahic Jump Location
Fig. 11

Variation of Grθmax the left and right heaters versus heater strength ratio at h* = 0.008 for different heater strength ratios: (a) εr=0.5, (b) εr=1.0, and (c) εr=1.5

Grahic Jump Location
Fig. 12

Variation of (a) the common maximum temperatures of the heaters and (b) heater strength ratio versus heater length ratio corresponding to common maximum temperatures of the heaters

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