Cover
Vol. 14 No. 2 (2014)

Published: June 30, 2014

Pages: 216-228

Original Article

Transient Buoyancy- Driven Laminar Convection in an Inclined Three- Dimensional Trapezoidal Enclosure.

Ahmed Kadhim Hussein 1 Kolsi Lioua 2 Hussain H. Al-Kayiem 3
1 Department of Mechanical Engineering University of Babylon College of Engineering
2 Department of Energy Engineering University Monastir , Tunisia College of Engineering
3 Department of Mechanical Engineering University of Teknologi PETRONAS , 31750 Tronoh , Perak , Malaysia College of Engineering
History
  • Received: March 30, 2014
  • Available Online: June 30, 2014
DOI

https://doi.org/10.33971/bjes.14.2.22

Abstract

Numerical analysis of transient laminar three- dimensional buoyancy-driven convection in an inclined three- dimensional trapezoidal air-filled enclosure was investigated in this paper. The right and left sidewalls of the enclosure are kept at constant cold temperatures. The bottom wall is maintained at a constant hot temperature , while the top wall is considered adiabatic. Numerical investigation is performed for Rayleigh numbers varied as 10 3 ≤ Ra ≤ 10 5 , while the trapezoidal enclosure inclination angle is varied as 0° ≤  ≤ 180°. Prandtl number is considered constant at Pr = 0.71. Flow and thermal fields are presented in both two and three- dimensional pattern. Also, both local and average Nusselt numbers are calculated and discussed. The results show that when the Rayleigh number increases, the flow patterns are changed especially in three-dimensional results and the flow circulation increases. The minimum average Nusselt number inside the trapezoidal cavity corresponds to the highest    180 ].While, the average Nusselt inclination angle [i.e.,    30 . Moreover, number reaches its maximum value at when the Rayleigh number increases the average Nusselt number increases as expected.

Keywords

References

  1. Turan, O., Poole, R. and Chakraborty, N. Aspect ratio effects in laminar natural convection of Bingham fluids in rectangular enclosures with differentially heated side walls, Journal of Non-Newtonian Fluid Mechanics ,Vol.166 , 2011, pp : 208-230.
  2. Turan, O., Poole, R. and Chakraborty, N. Influences of boundary conditions on laminar natural convection in rectangular enclosures with differentially heated side walls , International Journal of Heat and Fluid Flow ,Vol. 33 , 2012, pp : 131-146.
  3. Lam, S., Gani, R. and Simons, J. Experimental and numerical studies of natural convection in trapezoidal cavities , ASME Journal of Heat Transfer, Vol. 111,1989, pp: 372–377.
  4. Kumar, S. Natural convective heat transfer in trapezoidal enclosure of box-type solar cooker , Renewable Energy, Vol. 29, 2004, pp : 211-222.
  5. Basak, T., Roy, S. , Singh , A. and Pandey, B. Natural convection flow simulation for various angles in a trapezoidal enclosure with linearly heated side wall(s) , International Journal of Heat and Mass Transfer, Vol. 52, 2009, pp : 4413-4425.
  6. Lasfer, K., Bouzaiane, M. and Lili , T. Numerical study of laminar natural convection in a side-heated trapezoidal cavity at various inclined heated sidewalls , Heat Transfer Engineering ,Vol.31, No.5, 2010, pp : 362-373.
  7. Basak, T., Ramakrishna , D. , Roy, S. , Matta , A. and Pop, I. A comprehensive heatline based approach for natural convection flows in trapezoidal enclosures: Effect of various walls heating , International Journal of Thermal Sciences, Vol. 50, 2011, pp : 1385-1404.
  8. Sahoo, S., Singh, S. and Banerjee,R. Analysis of heat losses from a trapezoidal cavity used for Linear Fresnel Reflector system , Solar Energy ,Vol. 86 , 2012, pp: 1313- 1322.
  9. Natarajan, S. , Reddy , K. and Mallick , T. Heat loss characteristics of trapezoidal cavity receiver for solar linear concentrating system , Applied Energy , Vol. 93, 2012 , pp : 523-531.
  10. Mustafa, A. and Ghani , I. Natural convection in trapezoidal enclosure heated partially from below , Al- Khwarizmi Engineering Journal , Vol.8, No.1 2012 , pp : 76-85.
  11. Da silva, A., Fontana , E. , Mariani , V. and Marcondes, F. Numerical investigation of several physical and geometric parameters in the natural convection into trapezoidal cavities , International Journal of Heat and Mass Transfer , Vol. 55 , 2012, pp: 6808-6818.
  12. Tracy, N. and Crunkleton, D. Oscillatory natural convection in trapezoidal enclosures , International Journal of Heat and Mass Transfer ,Vol. 55, 2012, pp : 4498-4510.
  13. Hiller , W., Koch,S. , Kowalewski ,T. and Stella , F. Onset of natural convection in a cube , International Journal of Heat and Mass Transfer, Vol. 13 , 1993, pp: 3251-3263.
  14. Frederick , R. Natural convection heat transfer in a cubical enclosure with two active sectors on one vertical wall , International Communications in Heat and Mass Transfer , Vol. 24 , No.4 , 1997, pp: 507-520.
  15. Frederick , R. and Moraga , S. Three-dimensional natural convection in finned cubical enclosures , International Journal of Heat and Fluid Flow , Vol. 28 , 2007, pp: 289-298.
  16. Oosthuizen, P., Kalendar, A. and Simko , T. Three- dimensional natural convective flow in a rectangular enclosure with a rectangular heated section on one vertical wall and a cooled horizontal upper wall , 5th European Thermal-Sciences Conference, 2008, Netherlands , pp: 1-8.
  17. Bocu, Z. and Altac ,Z. Laminar natural convection heat transfer and air flow in three-dimensional rectangular enclosures with pin arrays attached to hot wall , Applied Thermal Engineering, Vol. 31, 2011, pp: 3189-3195.
  18. Da silva, A. and Gosselin, L. On the thermal performance of an internally finned 3D cubic enclosure in natural convection , International Journal of Thermal Sciences,Vol. 44, 2005, pp : 540-546.
  19. Bennett, B. and Hsueh, J. Natural convection in a cubic cavity : implicit numerical solution of two benchmark problems , Numerical Heat Transfer, Part A ,Vol.50, 2006, pp : 99-107.
  20. Lo, D. and Leu, S. DQ analysis of 3D natural convection in an inclined cavity using an velocity-vorticity formulation , Proceedings of World Academy of Science, Engineering and Technology ,Vol. 36, 2008, pp : 370–375.
  21. Ghachem, K. , Kolsi , L. , Mâatki , C. , Hussein , A. and Borjini, M. Numerical simulation of three-dimensional double diffusive free convection flow and irreversibility studies in a solar distiller , International Communications in Heat and Mass Transfer, Vol.39, 2012, pp: 869-876.
  22. Basak,T., Roy, S., Singh,A. and Pop,I. Finite element simulation of natural convection flow in a trapezoidal enclosure filled with porous medium due to uniform and non-uniform heating, International Journal of Heat and Mass Transfer ,Vol. 52, 2009, pp : 70–78.