Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-10T16:21:02.114Z Has data issue: false hasContentIssue false
  • English
  • Français

Natural Convection Cooling of an Array of Flush Mounted Discrete Heaters Inside a 3D Cavity

Part of: Incompressible viscous fluids Thermodynamics and heat transfer Basic methods in fluid mechanics Diffusion and convection

Published online by Cambridge University Press:  17 January 2017

V. P. M. Senthil Nayaki ,
S. Saravanan ,
X. D. Niu  and
P. Kandaswamy
V. P. M. Senthil Nayaki
Affiliation:
Department of Mathematics, Bharathiar University, Coimbatore 641 046, Tamil Nadu, India Department of Mathematics, KPR Institute of Engineering and Technology, Coimbatore 641407, Tamil Nadu, India
S. Saravanan*
Affiliation:
Department of Mathematics, Bharathiar University, Coimbatore 641 046, Tamil Nadu, India
X. D. Niu
Affiliation:
College of Engineering, Shantou University, Shantou, Guangdong 515063, China
P. Kandaswamy
Affiliation:
Research Center for Energy Conversion System, Doshisha University, Kyoto 610-0394, Japan
*
*Corresponding author. Email:drsshravan@gmail.com (S. Saravanan)
Get access

Abstract

An investigation of natural convective flow and heat transfer inside a three dimensional rectangular cavity containing an array of discrete heat sources is carried out. The array consists of a row and columnwise regular arrangement of identical square shaped isoflux discrete heaters and is flush mounted on a vertical wall of the cavity. A symmetrical isothermal sink condition is maintained by cooling the cavity uniformly from either the opposite wall or the side walls or the top and bottom walls. The other walls of the cavity are maintained adiabatic. A finite volume method based on the SIMPLE algorithm and the power law scheme is used to solve the conservation equations. The parametric study covers the influence of pertinent parameters such as the Rayleigh number, the Prandtl number, side aspect ratio of the cavity and cavity heater ratio. A detailed fluid flow and heat transfer characteristics for the three cases are reported in terms of isothermal and velocity vector plots and Nusselt numbers. In general it is found that the overall heat transfer rate within the cavity for Ra=107 is maximum when the side aspect ratio of the cavity lies between 1.5 and 2. A more complex and peculiar flow pattern is observed in the presence of top and bottom cold walls which in turn introduces hot spots on the adiabatic walls. Their location and size are highly sensitive to the side aspect ratio of the cavity and hence offers more effective ways for passive heat removal.

Keywords

Natural convectionrectangular cavityarray heatersheat removalelectronic equipment cooling

MSC classification

Secondary: 76R05: Forced convection 76D55: Flow control and optimization 76M12: Finite volume methods 80A20: Heat and mass transfer, heat flow
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 9 , Issue 3 , June 2017 , pp. 698 - 721
Copyright
Copyright © Global-Science Press 2017 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Ostrach, S., Natural convection in enclosures, ASME J. Heat Transfer, 110 (1988), pp. 1175–1190.CrossRefGoogle Scholar
[2] Chu, R. C., The challenges of electronic cooling: past, current and future, ASME J. Elect. Package, 126 (2004), pp. 491–500.CrossRefGoogle Scholar
[3] Chen, P. H., Chang, S. W. and Chiang, H. F., High power electronic component: review, Recent Patents Eng., 2 (2008), pp. 174–188.CrossRefGoogle Scholar
[4] Chu, H. H. S., Churchill, S. W. and Patterson, C. V. S., The effect of heater size, location, aspect ratio, and boundary conditions on two-dimensional, laminar, natural convection in rectangular channels, ASME J. Heat Transfer, 98 (1976), pp. 194–201.Google Scholar
[5] Turner, B. L. and Flack, R. D., The experimental measurement of natural convective heat transfer in rectangular enclosures with concentrated energy sources, ASME J. Heat Transfer, 102 (1980), pp. 236–241.Google Scholar
[6] Ho, C. J. and Chang, J. Y., A study of natural convection heat transfer in a vertical rectangular enclosure with two-dimensional discrete heating: effect of aspect ratio, Int. J. Heat Mass Transfer, 37(6) (1994), pp. 917–925.Google Scholar
[7] Liu, Y. and Phan-Thien, N., An optimum spacing problem for three chips mounted on a vertical substrate in an enclosure, Numer. Heat Trans. A, 37 (2000), pp. 613–630.Google Scholar
[8] Bae, J. H. and Hyun, J. M., Time dependent buoyant convection in an enclosure with discrete heat sources, Int. J. Therm. Sci., 43 (2004), pp. 3–11.CrossRefGoogle Scholar
[9] Ben Nasr, K., Chouikh, R., Kerkeni, C. and Guizani, A., Numerical study of the natural convection in cavity heated from the lower corner and cooled from the ceiling, Appl. Therm. Eng., 26 (2006), pp. 772–775.Google Scholar
[10] Chen, T. H. and Chen, L. Y., 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 (2007), pp. 1219–1231.CrossRefGoogle Scholar
[11] Webb, B. W. and Bergman, T. L., Three-dimensional natural convection from vertical heated plates with adjoining cool surfaces, ASME J. Heat Transfer, 114 (1992), pp. 115–120.Google Scholar
[12] Frederick, R. L. and Quiroz, F., On the transition from conduction to convection regime in a cubical enclosure with a partially heated wall, Int. J. Heat Mass Transfer, 44 (2001), pp. 1699–1709.Google Scholar
[13] Frederick, R. L. and Berbakow, O., Natural convection in cubical enclosures with thermal sources on adjacent vertical walls, Numer. Heat Trans. A, 41 (2002), pp. 331–340.Google Scholar
[14] Chuang, S., Chiang, J. and Kuo, Y., Numerical simulation of heat transfer in a three-dimensional enclosure with three chips in various position arrangements, Heat Transfer Eng., 24(2) (2003), pp. 42–59.Google Scholar
[15] Zhang, W., Huang, Z., Zhang, C. and Xi, G., Numerical study on conjugate, conduction-convection in a cubic enclosure submitted to time-periodic sidewall temperature, ASME J. Heat Transfer, 135 (2013), 022504.Google Scholar
[16] Joshi, Y. K., Liquid cooling of high-performance microcomponents and microsystems miniature flow loops for thermal management, Adv. Package, 13 (2004), pp. 35–36.Google Scholar
[17] Bar-Cohen, A., Thermal management of electronic components with dielectric liquids, ASME/JSME Thermal Engineering Joint Conference, 2 (1991), pp. xv–xxxix.Google Scholar
[18] Joshi, Y. and Paje, R. A., Natural convection cooling of a ceramic substrate mounted leadless chip carrier in dielectric liquids, Int. Commun. Heat Mass Transfer, 18 (1991), pp. 39–47.Google Scholar
[19] Joshi, Y., Haukenes, L. O. and Sathe, S. B., Natural convection liquid immersion cooling of a heat source flush mounted on a conducting substrate in a square enclosure, Int. J. Heat Mass Transfer, 36(2) (1993), pp. 249–263.Google Scholar
[20] Madhavan, P. N. and Sastri, V. M. K., Conjugate natural convection cooling of protruding heat sources mounted on a substrate placed inside an enclosure: A parametric study, Comput. Methods Appl. Mech. Eng., 188 (2000), pp. 187–202.Google Scholar
[21] Keyhani, M., Prasad, V. and Cox, R., An experimental study of natural convection in a vertical cavity with discrete heat sources, ASME J. Heat Transfer, 110 (1988), pp. 616–624.Google Scholar
[22] Keyhani, M., Chen, L. and Pitts, D. R., The aspect ratio effect on natural convection in an enclosure with protruding heat sources, ASME J. Heat Transfer, 113 (1991), pp. 883–891.Google Scholar
[23] Polentini, M. S., Ramadhyani, S. and Incropera, F. P., Single-phase thermosyphon cooling of an array of discrete heat sources in a rectangular cavity, Int. J. Heat Mass Transfer, 36(16) (1993), pp. 3983–3996.CrossRefGoogle Scholar
[24] Wroblewski, D. E. and Joshi, Y., Computations of liquid immersion cooling for a protruding heat sources in a cubical enclosure, Int. J. Heat Mass Transfer, 36(5) (1993), pp. 1201–1218.Google Scholar
[25] Wroblewski, D. E. and Joshi, Y., Liquid immersion cooling of a substrate-mounted protrusion in a three-dimensional enclosure: The effects of geometry and boundary conditions, ASME J. Heat Transfer, 116 (1994), pp. 112–119.Google Scholar
[26] Joshi, Y., Kelleher, M. D., Powell, M. and Torres, E. I., Natural convection heat transfer from an array of rectangular protrusions in an enclosure filled with dielectric liquid, ASME J. Electron. Package, 116 (1994), pp. 138–147.CrossRefGoogle Scholar
[27] Heindel, T. J., Ramadhyani, S. and Incropera, F. P., Conjugate natural convection from an array of discrete heat sources: Part 1: Two- and three-dimensional model validation, Int. J. Heat Fluid Flow, 16 (1995), pp. 501–510.Google Scholar
[28] Heindel, T. J., Incropera, F. P. and Ramadhyani, S., Conjugate natural convection from an array of discrete heat sources: Part 2: A numerical parametric study, Int. J. Heat Fluid Flow, 16 (1995), pp. 511–518.Google Scholar
[29] Heindel, T. J., Incropera, F. P. and Ramadhyani, S., Enhancement of natural convection heat transfer from an array of discrete heat sources, Int. J. Heat Mass Transfer, 39(3) (1996), pp. 479–490.CrossRefGoogle Scholar
[30] Heindel, T. J., Ramadhyani, S. and Incropera, F. P., Laminar natural convection in a discretely heated cavity: I-Assessment of three dimensional effects, ASME J. Heat Transfer, 117 (1995), pp. 902–909.Google Scholar
[31] Heindel, T. J., Incropera, F. P. and Ramadhyani, S., Laminar natural convection in a discretely heated cavity: II-Comparisons of experimental and theoretical results, ASME J. Heat Transfer, 117 (1995), pp. 910–917.CrossRefGoogle Scholar
[32] Mukutmoni, D., Joshi, Y. K. and Kelleher, M. D., Computations for a three-by-three array of protrusions cooled by liquid immersion: Effect of substrate thermal conductivity, ASME J. Heat Transfer, 117 (1995), pp. 294–300.Google Scholar
[33] Tou, S. K. W., Tso, C. P. and Zhang, X., 3-D numerical analysis of natural convective liquid cooling of a 3×3 heater array in rectangular enclosures, Int. J. Heat Mass Transfer, 42 (1999), pp. 3231–3244.Google Scholar
[34] Tso, C. P., Jin, L. F., Tou, S. K. W. and Zhang, X. F., Flow pattern evolution in natural convection cooling from an array of discrete heat sources in a rectangular cavity at various orientations, Int. J. Heat Mass Transfer, 47 (2004), pp. 4061–4073.CrossRefGoogle Scholar
[35] Kandaswamy, P., Senthil Nayaki, V. P. M., Purusothaman, A. and Saravanan, S., Natural convection in a rectangular enclosure with an array of discrete heat sources, Heat Trans. Res., (2014) (accepted).Google Scholar
[36] Bhowmik, H. and Tou, K. W., Experimental study of transient natural convection heat transfer from simulated electronic chips, Exp. Therm. Fluid Sci., 29 (2005), pp. 485–492.CrossRefGoogle Scholar
[37] Hopton, P. and Summers, J., Enclosed liquid natural convection as a means of transferring heat from microelectronics to cold plates, Proc. 29th Annual IEEE Semiconductor Thermal Measurement and Management Symposium, San Jose, USA, (2013), pp. 60–64.Google Scholar
[38] Habib, M. A., Said, S. A. M. and Ayinde, T., Characteristics of natural convection heat transfer in an array of discrete heat sources, Exp. Heat Transfer, 27 (2014), pp. 91–111.Google Scholar
[39] Mallinson, G. D. and De Vahl Davis, G., Three-dimensional natural convection in a box: A numerical study, J. Fluid Mech., 83(1) (1977), pp. 1–31.Google Scholar
[40] Fusegi, T., Hyun, J. M., Kuwahara, K. and Farouk, B., A numerical study of three dimensional natural convection in a differentially heated cubical enclosure, Int. J. Heat Mass Transfer, 34 (1991), pp. 1543–1557.Google Scholar
[41] Ozoe, H., Sato, N. and Churchill, S., Experimental confirmation of the three dimensional helical streaklines previously computed for natural convection in inclined rectangular enclosures, Int. Chem. Eng., 19 (1979), pp. 454–462.Google Scholar
[42] Patankar, S. V., Numerical Heat Transfer and Fluid Flow, Hemisphere Publishing, Corporation, Taylor and Francis Group, New York, 1980.Google Scholar
[43] Ogut, E. B., Natural convection of water-based nanofluids in an inclined enclosure with a heat source, Int. J. Therm. Sci., 48 (2009), pp. 2063–2073.CrossRefGoogle Scholar
[44] Tric, E., Labrosse, G. and Betrouni, M., A first incursion into the 3D structure of natural convection of air in a differentially heated cubic cavity, from accurate numerical solutions, Int. J. Heat Mass Transfer, 43 (2000), pp. 4043–4056.Google Scholar
[45] Park, K. A. and Bergles, A. E., Natural convection heat transfer characteristics of simulated microelectronic chips, ASME J. Heat Transfer, 109 (1987), pp. 90–96.Google Scholar
[46] Bar-Cohen, A., Direct liquid cooling of high flux micro and nano electronic components, Proc. IEEE, 94 (2006), pp. 1549–1570.Google Scholar