Abstract
In the present study, a finite volume computational procedure and a full multigrid technique are used to investigate laminar natural convection in partially heated cubic enclosures. Effects of heated strip disposition in the enclosure on the heat transfer rate are studied. Results are presented in the form of flow lines, isotherms plots, average Nusselt numbers, and average temperature on the heat source surface. Statistical distributions of temperature and average velocity fields and their root-mean-square values are presented and discussed.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
S. Ostrach, “Natural Convection in Enclosures,” J. Heat Transfer 110(4b), 1175–1190 (1988).
A. K. da Silva, S. Lorente, and A. Bejan, “Optimal Distribution of Discrete Heat Sources on a Wall with Natural Convection,” Int. J. Heat Mass Transfer 47, 203–214 (2004).
T. H. Chen and L. Y. Chen, “Study of Buoyancy-Induced Flows Subjected to Partially Heated Sources on the Left and Bottom Walls in a Square Enclosure,” Int. J. Thermal Sci. 46, 1219–1231 (2007).
N. Ben-Cheikh, B. Ben-Beya, and T. Lili, “Influence of Thermal Boundary Conditions on Natural Convection in a Square Enclosure Partially Heated from Below,” Int. Comm. Heat Mass Transfer 34, 369–379 (2007).
Y. Varol, H. F. Oztop, and A. Koca, “Entropy Production due to Free Convection in Partially Heated Isosceles Triangular Enclosures,” Appl. Thermal Eng. 28, 1502–1513 (2008).
H. F. Oztop and E. Abu-Nada, “Numerical Study of Natural Convection in Partially Heated Rectangular Enclosures Filled with Nanofluids,” Int. J. Heat Fluid Flow 29, 1326–1336 (2008).
N. Nithyadevi and R. J. Yang, “Double Diffusive Natural Convection in a Partially Heated Enclosure with Soret and Dufour Effects,” Int. J. Heat Fluid Flow 30, 902–910 (2009).
Aswatha, C. J. Gangadhara Gowda, S. N. Sridhara, and K. N. Seetharamu, “Effect of Different Thermal Boundary Conditions at Bottom Wall on Natural Convection in Cavities,” J. Eng. Sci. Technol. 6(1), 109–130 (2011).
P. Alam, A. Kumar, S. Kapoor, and S. R. Ansari, “Numerical Investigation of Natural Convection in a Rectangular Enclosure due to Partial Heating and Cooling at Vertical Walls,” Comm. Nonlinear Sci. Numer. Simulat. 17, 2403–2414 (2012).
I. Sezai and A. A. Mohamad, “Natural Convection from a Discrete Heat Source on the Bottom of a Horizontal Enclosure,” Int. J. Heat Mass Transfer 43, 2257–2266 (2000).
R. L. Frederick and F. Quiroz, “On the Transition from Conduction to Convection Regime in a Cubical Enclosure with a Partially Heated Wall,” Int. J. Heat Mass Transfer 44, 1699–1709 (2001).
S. K. W. Tou and X. F. Zhang, “Three-Dimensional Numerical Simulation of Natural Convection in an Inclined Liquid-Filled Enclosure with an Array of Discrete Heaters,” Int. J. Heat Mass Transfer 46, 127–138 (2003).
P. H. Oosthuizen and J. T. Paul, “Natural Convection in a Rectangular Enclosure with Two Heated Sections on the Lower Surface,” Int. J. Heat Fluid Flow 26, 587–596 (2005).
A. K. Sharma, K. Velusamy, and C. Balaji, “Turbulent Natural Convection in an Enclosure with Localized Heating from Below,” Int. J. Thermal Sci. 46, 1232–1241 (2007).
N. Ben-Cheikh, A. Campo, N. Ouertatani, and T. Lili, “Three-Dimensional Study of Hheat and Fluid Flow of Air and Dielectric Liquids Filling Containers Partially Heated from Below and Entirely Cooled from Above,” Int. Comm. Heat Mass Transfer 37, 449–456 (2010).
Z. Bocu and Z. Altac, “Laminar Natural Convection Heat Transfer and Air Flow in Three-Dimensional Rectangular Enclosures with Pin Arrays Attached to Hot Wall,” Appl. Thermal Eng. 31, 3189–3195 (2011).
V. I. Terekhov and A. L. Ekaid, “Three-Dimensional Laminar Convection in a Parallelepiped with Heating of Two Side Walls,” High Temperature 49(6), 874–880 (2011).
S. V. Patankar, Numerical Heat Transfer and Fluid Flow (McGraw-Hill, New York, 1980).
Y. Achdou and J. L. Guermond, “Convergence Analysis of a Finite Element Projection Lagrange-Galerkin Method for the Incompressible Navier-Stokes Equations,” SIAM J. Numer. Anal. 37(3), 799–826 (2000).
B. P. Leonard, “A Stable and Accurate Convective Modelling Procedure Based on Quadratic up Stream Interpolation,” Comput. Methods Appl. Mech. Eng. 19, 59–98 (1979).
B. P. Leonard, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods (SIAM, Philadelphia, 1994).
N. Ben-Cheikh, B. Ben-Beya, and T. Lili, “Benchmark Solution for Time-Dependent Natural Convection Flows with an Accelerated Full-Multigrid Method,” Numer. Heat Transfer. Part B: Fundamentals 52, 131–151 (2007).
M. A. R. Sharif and T. R. Mohammad, “Natural Convection in Cavities with Constant Flux Heating at the Bottom Wall and Isothermal Cooling from the Sidewalls,” Int. J. Thermal Sci. 44, 865–878 (2005).
G. Saha, S. Saha, M. Q. Islam, and M. A. R. Akhanda, “Natural Convection in Enclosure with Discrete Isothermal Heating from Below,” J. Naval Arch. Marine Eng. 4, 1–13 (2007).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © S. Mellah, N. Ben-Cheikh, B. Ben-Beya, T. Lili.
__________
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 56, No. 2, pp. 106–116, March–April, 2015.
Rights and permissions
About this article
Cite this article
Mellah, S., Ben-Cheikh, N., Ben-Beya, B. et al. Laminar natural convection heat transfer and air flow in three-dimensional cubic enclosures with a partially heated wall. J Appl Mech Tech Phy 56, 257–266 (2015). https://doi.org/10.1134/S002189441502011X
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S002189441502011X