EFFECT OF DISCRETE HEATER AT THE VERTICAL WALL OF THE CAVITY OVER THE HEAT TRANSFER AND ENTROPY GENERATION USING LBM

Abstract

In this paper Lattice Boltzmann Method (LBM) was employed for investigation the effect of the heater location on flow pattern, heat transfer and entropy generation in a cavity. A 2D thermal lattice Boltzmann model with 9 velocities, D2Q9, is used to solve the thermal flow problem. The simulations were performed for Rayleigh numbers from 103 to 106 at Pr = 0.71. The study was carried out for heater length of 0.4 side wall length which is located at the right side wall. Results are presented in the form of streamlines, temperature contours, Nusselt number and entropy generation curves. Results show that the location of heater has a great effect on the flow pattern and temperature fields in the enclosure and subsequently on entropy generation. The dimensionless entropy generation decreases at high Rayleigh number for all heater positions. The ratio of averaged Nusselt number and dimensionless entropy generation for heater located on vertical and horizontal walls was calculated. Results show that higher heat transfer was observed from the cold walls when the heater located on vertical wall. On the other hand, heat transfer increases from the heater surface when it located on the horizontal wall.

Keywords

Dates

  • Submission Date2009-04-22
  • Revision Date2009-11-17
  • Acceptance Date2010-03-12

DOI Reference

10.2298/TSCI1102423A

References

  1. Chu, H. H. and Churchill, S. W., The effect of heater size, location, aspect-ratio and boundary conditions on two-dimensional laminar natural convection in rectangular channels, Journal of Heat Transfer, Vol. 98, No. 2, (1976), pp. 194-201.
  2. Refai, A.G. and Yovanovich, M.M., Influence of Discrete Heat Source Location on Natural Convection Heat Transfer in a Vertical Square Enclosure, Journal of Electronic Packaging September, Vol. 113, No. 3, (1991), pp. 268-274.
  3. Refai, A.G. and Yovanovich, M.M., Numerical Study of Natural Convection from Discrete Heat Sources in a Vertical Square Enclosure, Journal of Thermophysics and Heat Transfer, Vol. 6, No. 1, January, 1992, pp. 121-127. AIAA Paper No. 90-0256, originally presented at AIAA 28th Aerospace Sciences Meeting, Reno, NV, January 8-11, 1990.
  4. Nelson, J.E.B., Balakrishnan, A.R., and Murthy, S.S., Experiments on stratified chilledwater tanks, Int. J. Refrig. 22 (3) (1999) 216-234.
  5. Ampofo, F. and Karayiannis, T.G., Experimental benchmark data for turbulent natural convection in an air filled square cavity, Int. J. Heat Mass Transfer 46 (19), (2003) pp. 3551-3572.
  6. Adeyinka, O.B. and Naterer, G.F., Experimental uncertainty of measured entropy production with pulsed laser PIV and planar laser induced fluorescence, Int. J.Heat Mass Transfer 48, (2005), pp. 1450-1461.
  7. Poujol, F.T., Natural convection of a high Prandtl number fluid in cavity, Int.Comm. Heat Mass Transfer 27 (1) (2000), pp. 109-118.
  8. Oliveski, R.D.C., Krenzinger, A. and Vielmo, H.A., Cooling of cylindrical vertical tank submitted to natural internal convection, Int. J. Heat Mass Transfer 46 (11) (2003), pp. 2015-2026.
  9. Basak, T., Roy, S. and Balakrishnan, A.R., Effects of thermal boundary conditions on natural convection flows within a square cavity, Int.J.Heat Mass Transfer 49, Issues 23-24, (2006), pp. 4525-4535
  10. Basak, T., Aravind, G. and Roy, S., Visualization of heat flow due to natural convection within triangular cavities using Bejan's heatline concept, Int.J.Heat Mass Transfer 52 (2009) pp. 2824-2833
  11. Beya, B. B. and Lili, T., Transient natural convection in 3D tilted enclosure heated from two opposite sides, International Communications in Heat and Mass Transfer 36 (2009) pp. 604-613
  12. Chen, S. and Doolen, G.D., Lattice Boltzmann method for fluid flows, Annu. Rev. Fluid Mech. 30, (1998), pp. 329-364.
  13. Succi, S., The Lattice Boltzmann Equation for Fluid Dynamics and Beyond, Clarendon Press, Oxford. 2001.
  14. Mohammad, A.A., Applied Lattice Boltzmann Method for Transport Phenomena Momentum Heat and Mass Transfer, The University of Calgary Press, 2007.
  15. Kao, P.H., Chen, Y.H. and Yang, R.J. Simulations of the macroscopic and mesoscopic natural convection flows within rectangular cavities, International Journal of Heat and Mass Transfer, 51 (2008), pp. 3776-3793
  16. Chopard, B. and Luthi, P.O., Lattice Boltzmann computations and applications to physics, Theor. Comput. Phys. 217 (1999), pp. 115-130.
  17. Nourgaliev, R.R., Dinh, T.N., Theofanous, T.G. and Joseph, D., The lattice Boltzmann equation method: theoretical interpretation, numerics and implications, Int. J. Multiphase Flow, 29 (2003), pp. 117-169.
  18. He, X., Chen, S. G.D., Doolen, A novel thermal model for the lattice Boltzmann method in incompressible limit, J. Comput. Phys. 146, (1998), pp. 282-300.
  19. Barrios, G., Rechtman, R., Rojas, J. and Tovar, R., The lattice Boltzmann equation for natural convection in a two-dimensional cavity with a partially heated wall, J. Fluid Mech., 522 (2005), pp. 91-100.
  20. Dixit, H.N. and Babu, V. Simulations of high Rayleigh number natural convection in a square cavity using the lattice Boltzmann method, Int. J. Heat Mass Transfer, 49, (2006), pp. 727-739.
  21. Annunziata D'Orazio, Massimo Corcione, Gian Piero Celata, Application to natural convection enclosed flows of a lattice Boltzmann BGK model coupled with a general purpose thermal boundary condition, International Journal of Thermal Sciences, 43 (2004), pp. 575-586.
  22. Mezrhab, A., Jami, M., Abid, C., Bouzidi, M. and Lallemand, P., Lattice-Boltzmann modelling of natural convection in an inclined square enclosure with partitions attached to its cold wall, International Journal of Heat and Fluid Flow, 27 (2006), pp. 456-465
  23. Jami, P., Mezrhab, A. and Bouzidi, M., Lallemand, Lattice Boltzmann method applied to the laminar natural convection in an enclosure with a heat-generating cylinder conducting body, International Journal of Thermal Sciences, 46 (2007), pp. 38-47
  24. Mohamad, A.A. , El-Ganaoui, M. and Bennacer, R., Lattice Boltzmann simulation of natural convection in an open ended cavity, Int. J. Thermal Sciences 48, Issue 10, (2009), pp. 1870-1875
  25. Peng, Y., Shu, C. and Chew, Y.T., A 3D incompressible thermal lattice Boltzmann model and its application to simulate natural convection in a cubic cavity, Journal of Computational Physics 193 (2003) pp.260-274
  26. Bejan A. Entropy generation through heat and fluid flow. New York: Wiley; 1982.
  27. Bejan A. Entropy generation minimization. New York: CRC Press; 1996.
  28. Bejan A. Advanced engineering thermodynamics, 2nd ed. New York: Wiley; 1997.
  29. Bejan A., Second-law analysis in heat transfer, Energy—The International Journal, 5 (1980), pp. 721-32.
  30. Bejan A., Second-law analysis in heat transfer and thermal design, Adv. Heat Transfer,15 (1982), pp. 1-58.
  31. Bejan A., Fundamentals of exergy analysis, entropy-generation minimization, and the generation of flow architecture, International Journal of Energy Research, 26 (2002), pp. 545-65.
  32. Demirel Y, Kahraman R., Thermodynamic analysis of convective heat transfer in an annular packed duct, International Journal of Heat and Fluid Flow, 21 (2000), pp. 442-8.
  33. Sahin AZ., A second-law comparison for optimum shape of duct subjected to constant wall temperature and laminar flow, J Heat Mass Transfer, 33 (1998), pp. 425-30.
  34. Narusawa U., The second-law analysis of mixed convection in rectangular ducts, J Heat Mass Transfer, 37 (1998), pp. 197-203.
  35. Mahmud S. and Fraser, RA., Thermodynamic analysis of flow and heat transfer inside a channel with two parallel plates, Exergy, 2 (2002), pp.140-6.
  36. Mahmud, S. and Fraser, RA., The second-law analysis in fundamental convective heat-transfer problems, Int. J. Therm. Sci. , 42 (2003),177-86.
  37. Aı¨boud-Saouli, S., Settou, N., Saouli, S. and Mezrab, N., Second-law analysis of laminar fluid flow in a heated channel with hydromagnetic and viscous dissipation effects, Applied Energy, 84 (2007), pp. 279-289
  38. Delavar, M. A., Farhadi, M. and Sedighi, K., Effect of the Heater Location on Heat Transfer and Entropy Generation in the Cavity Using the Lattice Boltzmann Method, Heat Transfer Research, 2009, Vol. 40, No. 6, pp:521-536
  39. Peng, Y., Shu, C. and Chew, Y.T., Simplified thermal lattice Boltzmann model for incompressible thermal flows, Phys. Rev. E 68, (2003), 026701.
  40. Shu, C., Niu, X.D. and Chew, Y.T., A lattice Boltzmann kinetic model for microflow and heat transfer, J. Stat. Phys. 121 (1-2), (2005), pp.239-255.
  41. Vahl Davis, G. D., Natural convection of air in a square cavity: a bench mark numerical solution, Int. J. Numer. Methods Fluids, 3 (1983), pp. 249-264.
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