Abstract
Two-dimensional numerical simulations were used to analyze the temperature-driven natural convection phenomena in a square enclosure with an inner cylinder in the Rayleigh number range of Ra =105 ~ 106. The immersed boundary method based on the finite volume method (FVM) was applied to generate and treat inner cylinders, which remained at constant high temperature with no-slip boundary condition. The cylinder remained at a constant high temperature with no-slip boundary conditions. The detailed phenomena of natural convection were investigated according to the bottom wall temperature with a cold and isothermal top walls and adiabatic side walls. The numerical solutions at a Rayleigh number of 105 reached steady state once the solutions fully converged. When the Rayleigh number increased to 106, the solution showed unsteady characteristic depending on the bottom wall temperature. In addition, the distribution of the isotherms in the lower part of the enclosure depended on the temperature variation of the bottom wall and the Rayleigh number. These effects had a significant influence on the convection structure in the lower part of the enclosure and on the corresponding heat transfer on the walls. The convection structures in the enclosure changed significantly in several cases at 106 with a high bottom wall temperature.
Similar content being viewed by others
References
G. Cesini, M. Paroncini, G. Cortella and M. Manzan, Natural convection from a horizontal cylinder in a rectangular cavity, International Journal of Heat Mass Transfer, 42 (1999) 1801–1811.
H. Asan, Natural convection in an annulus between two isothermal concentric square ducts, International Communications in Heat Mass Transfer, 27 (2000) 367–376.
F. Moukalled and S. Acharya, Natural convection in the annulus between concentric horizontal circular and square cylinders, Journal of Thermophysics and Heat Transfer, 10 (1996) 524–531.
C. Shu and Y. D. Zhu, Efficient computation of natural convection in a concentric annulus between an outer square cylinder and an inner circular cylinder, International Journal for Numerical Methods in Fluids, 38 (2002) 429–445.
Y. Kamotani, L. W. Wang, S. Ostrach and H. D. Jiang, Experimental study of natural convection in shallow enclosures with horizontal temperature and concentration gradients, International Journal of Heat and Mass Transfer, 28 (1) (1985) 165–173.
M. Jami, A. Mezrhab, M. Bouzidi and P. Lallemand, Lattice Boltzmann method applied to the laminar natural convection in an enclosure with a heat-generating cylinder conducting body, International Journal of Thermal Science, 46 (2007) 38–47.
H. F. Oztop and E. Abu-Nada, Numerical study of natural convection in partially heated rectangular enclosures filled with nanofluids, International Journal of Heat and Fluid Flow, 29 (5) (2008) 1326–1336.
H. J. Lee, J. H. Doo, M. Y. Ha and H. S. Yoon, Effects of thermal boundary conditions on natural convection in a square enclosure with an inner circular cylinder locally heated from the bottom wall, International Journal of Heat and Mass Transfer, 65 (2013) 435–450.
E. Bilgen and R. Ben Yedder, Natural convection in enclosure with heating and cooling by sinusoidal temperature profiles on one side, International Journal of Heat and Mass Transfer, 50 (2007) 139–150.
S. H. Lee, Y. M. Seo, H. S. Yoon and M. Y. Ha, Threedimensional natural convection around an inner circular cylinder located in a cubic enclosure with sinusoidal thermal boundary condition, International Journal of Heat and Mass Transfer, 101 (2016) 807–823.
M. Kim, J. H. Doo, Y. G. Park, H. S. Yoon and M. Y. Ha, Natural convection in a square enclosure with a circular cylinder according to the bottom wall temperature variation, Journal of Mechanical Science and Technology, 28 (12) (2014) 5013–5025.
H. J. Lee, J. H. Doo, M. Y. Ha and H. S. Yoon, Effects of thermal boundary conditions on natural convection in a square enclosure with an inner circular cylinder locally heated from the bottom wall, International Journal of Heat and Mass Transfer, 65 (2013) 435–450.
H. S. Yoon, M. Y. Ha, B. S. Kim and D. H. Yu, Effect of the position of a circular cylinder in a square enclosure on natural convection at Rayleigh number of 107, Physics of Fluids, 21 (2009).
D. W. Kang, M. Y. Ha, H. S. Yoon and C. Choi, Bifurcation to unsteady natural convection in square enclosure with a circular cylinder at Rayleigh number of 107, International Journal of Heat and Mass Transfer, 64 (2013) 926–944.
J. Kim and P. Moin, Application of a fractional step method to incompressible Navier–Stokes equations, Journal of Computational Physics, 59 (1985) 308–323.
Y. Zang, R. L. Street and J. R. Koseff, A non-staggered grid, fractional step method for time-dependent incompressible Navier–Stokes equations in curvilinear coordinates, Journal of Computational Physics, 114 (1994) 18–33.
B. S. Kim, D. S. Lee, M. Y. Ha and H. S. Yoon, A numerical study of natural convection in a square enclosure with a cir-cular cylinder at different vertical locations, International Journal of Heat and Mass Transfer, 51 (2008) 1888–1906.
J. Kim, D. Kim and H. Choi, An immersed-boundary finite volume method for simulations of flow in complex geometries, Journal of Computational Physics, 171 (2001) 132–150.
Author information
Authors and Affiliations
Corresponding authors
Additional information
Recommended by Associate Editor Jungil Lee
Man Yeong Ha received his undergraduate degree from Pusan National University, S. Korea, in 1981, as well as a Master’s degree from then Korea Advanced Institute of Science and Technology, S. Korea, in 1983, and his Ph.D. degree from Pennsylvania State University, USA, in 1990. He is currently a Professor at the School of Mechanical Engineering at Pusan National University in Busan, S. Korea. He served as Editor of the Journal of Mechanical Science and Technology. His research interests are focused on thermal heat management, computational fluid dynamics, and the finite volume method using a hybrid scheme.
Jaehyun Park received his undergraduate degree from the University of Texas at San Antonio in 2013 and started attending Pusan National University for the integrated Ph.D. program under the supervision of Professor Man Yeong Ha. Jaehyun Park is now focusing on heat transfer enhancement using various methods such as fundamental natural convection and multiphase simulations.
Rights and permissions
About this article
Cite this article
Park, J., Kim, M., Mun, G.S. et al. Natural convection in a square enclosure with a circular cylinder with adiabatic side walls according to bottom wall temperature variation. J Mech Sci Technol 32, 3201–3211 (2018). https://doi.org/10.1007/s12206-018-0623-9
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12206-018-0623-9