International Scientific Journal


This paper presents an analytical and numerical computation of laminar natural convection in a collection of vertical upright-angled triangular cavities filled with air. The vertical wall is heated with a uniform heat flux; the inclined wall is cooled with a uniform temperature; while the upper horizontal wall is assumed thermally insulated. The defining aperture angle φ is located at the lower vertex between the vertical and inclined walls. The finite element method is implemented to perform the computational analysis of the conservation equations for three aperture angles φ (= 15º, 30º and 45º) and height-based modified Rayleigh numbers ranging from a low Ra = 0 (pure conduction) to a high 109. Numerical results are reported for the velocity and temperature fields as well as the Nusselt numbers at the heated vertical wall. The numerical computations are also focused on the determination of the value of the maximum or critical temperature along the hot vertical wall and its dependence with the modified Rayleigh number and the aperture angle.
PAPER REVISED: 2014-01-28
PAPER ACCEPTED: 2014-02-24
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2016, VOLUME 20, ISSUE Issue 5, PAGES [1407 - 1420]
  1. Incropera, F., DeWitt, D.P., Introduction to Heat Transfer, 4th ed., John Wiley & Sons, Hoboken, NJ, 2002, pp. 524-530
  2. Çengel, Y.A., Heat Transfer: A Practical Approach, 2nd ed., McGraw-Hill, New York, 2003, pp. 477-486
  3. Raithby, G.D., Hollands, K.G.T., Natural Convection, in: Handbook of Heat Transfer (Eds. W.M. Rohsenow, J. Hartnett, Y. Cho), 3rd ed., Mc Graw-Hill, New York, 1998
  4. Jaluria, Y., Natural Convection, in: Heat Transfer Handbook (Eds. A. Bejan, A.D. Kraus), Wiley, New York, 2003
  5. Holtzman, G.A., Hill, R.W., Ball K.S., Laminar Natural Convection in Isosceles Triangular Enclosures Heated from Below and Symmetrically Cooled from Above, Journal of Heat Transfer, 122 (2000), 3, pp. 485-491
  6. Del Campo, .E.M, Sen, M., Ramos, E., Analysis of Laminar Convection in a Triangular Enclosure, Numerical Heat Transfer Part A, 13 (1988), 3, pp. 353-372.
  7. Elicer-Cortés, J.C., Kim-Son, D., Natural Convection in a Dihedral Cavity: Influence of the Angle and the Temperature of the Walls on the Mean Thermal Field, Experimental Heat Transfer, 6 (1993), 3, pp. 205-213
  8. Ridouane, E.H., Chang, J.Y., Campo, A., Natural Convection Patterns in Right-Angled Triangular Cavities with Heated Vertical Sides and Cooled Hypotenuses, Journal of Heat Transfer, 127 (2005), 10, pp. 1181-1186
  9. Sieres, J., Campo, A., Ridouane, E.H., Fernández-Seara, J., Effect of Surface Radiation on Buoyant Convection in Vertical Triangular Cavities with Variable Aperture Angles, International Journal of Heat and Mass Transfer, 50 (2007), 25-26, pp. 5139-5149
  10. Saha, S.C., Khan, M.M.K., A Review of Natural Convection and Heat Transfer in Attic-Shaped Space, Energy and Buildings, 43 (2011), 10, pp. 2564-2571
  11. Kaluri, R.S., Anandalakshmi, R., Basak, T., Bejan's Heatline Analysis of Natural Convection in Right-Angled Triangular Enclosures: Effects of Aspect-Ratio and Thermal Boundary Conditions, International Journal of Thermal Sciences, 49 (2010), 9, pp. 1576-1592
  12. Simons, R.E., Antonetti, V.W., Nakayama, W., Oktay, S., Heat Transfer in Electronic Packages, in: Microelectronics Packaging Handbook (Eds. R.R. Tummala, E.J. Rymaszewski, A.G. Klopfenstein), 2nd ed., Chapman and Hall, New York, 1997, pp. 1-315 to 1-403
  13. Bar-Cohen, A., Watwe, A.A., Prasher, R.S., Heat Transfer in Electronic Equipment, in: Heat Transfer Handbook (Eds. A. Bejan, A.D. Kraus), Wiley, New York, 2003
  14. Chu, R.C., The Challenges of Electronic Cooling: Past, Current and Future, Journal of Electronic Packaging, 126 (2004), 4, pp. 491-500
  15. COMSOL, Inc., COMSOL Multiphysics User's Guide, Version 3.5, Burlington, MA, 2008.
  16. Davis, T.A., Algorithm 832: UMFPACK V4.3-An Unsymmetric-Pattern Multifrontal Method, ACM Transactions on Mathematical Software, 30 (2004), pp. 196-199
  17. Lemmon, E.W., Huber, M.L., McLinden, M.O., NIST Standard Reference Database 23: Reference Fluid Thermodynamic and Transport Properties-REFPROP, Version 9.0. National Institute of Standards and Technology, Standard Reference Data Program, Gaithersburg, 2010
  18. Wang, Z., Mayinger, F., Natural Convection Heat Transfer in the PCB's Array of Electronic Equipments, Proceedings (Ed. B. Sunden), 1st Baltic Heat Transfer Conference, Göteborg, Sweden, 1991, pp. 841-854

© 2022 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence