Simulation of Natural Convection in Concentric Annuli between an Outer Inclined Square Enclosure and an Inner Horizontal Cylinder
In this work, the natural convection in a concentric
annulus between a cold outer inclined square enclosure and heated
inner circular cylinder is simulated for two-dimensional steady
state. The Boussinesq approximation was applied to model the
buoyancy-driven effect and the governing equations were solved
using the time marching approach staggered by body fitted
coordinates. The coordinate transformation from the physical
domain to the computational domain is set up by an analytical
expression. Numerical results for Rayleigh numbers 103 , 104 , 105
and 106, aspect ratios 1.5 , 3.0 and 4.5 for seven different
inclination angles for the outer square enclosure 0o , -30o
, -45o
,
-60o , -90o , -135o , -180o are presented as well. The computed flow
and temperature fields were demonstrated in the form of
streamlines, isotherms and Nusselt numbers variation. It is found
that both the aspect ratio and the Rayleigh number are critical to the
patterns of flow and thermal fields. At all Rayleigh numbers angle
of inclination has nominal effect on heat transfer.
[1] Shu, C., and Zhu, Y.D., Efficient computational of natural convection
in a concentric annulus between an outer square cylinder and inner
circular cylinder, Int. J. Numer. Meth. Fluid 38 (2002) 429-445.
[2] Kim, B.S., Lee, D.S., Ha, M.Y., and Yoon, H.S., A numerical study
of natural convection in a square enclosure with a circular cylinder at
different vertical locations, Int. J. heat and mass transfer 51 (2008)
1888-1906.
[3] Hyun Sik Yoon, Man Yeong Ha, ByungSoo Kim and Dong Hun Yu,
Effect of the position of a circular cylinder in a square enclosure on
natural convection at Rayleigh number of 107, American Institute of
Physics, PHYSICS OF FLUIDS 21 (047101) (2009).
[4] Hakan F. Oztop, Zepu Zhao and BoYu, Fluid flow due to combined
convection in lid-driven enclosure having a circular body,
International Journal of Heat and Fluid Flow 30 (2009) 886-901.
[5] J.M. Lee, M.Y. Ha and H.S. Yoon, Natural convection in a square
enclosure with a circular cylinder at different horizontal and diagonal
locations, International Journal of Heat and Mass Transfer 53 (2010)
5905-5919.
[6] Salam Hadi Hussain and Ahmed Kadhim Hussein, Numerical
investigation of natural convection phenomena in a uniformly heated
circular cylinder immersed in square enclosure filled with air at
different vertical locations, International Communications in Heat and
Mass Transfer 37 (2010) 1115 -1126.
[7] TalalKassem, Numerical study of the natural convection process in the
parabolic-cylindrical solar collector, The Ninth Arab International
Conference on Solar Energy (AICSE-9), Kingdom of Bahrain,
Desalination 209 (2007) 144-150.
[8] C. Shu ,Q.Yao , K. S. Yao and Y. D. Zhu , Numerical analysis of flow
and thermal fields ia arbitrary eccentric annulus by differential
quadrature method, Heat and Mass Transfer 38 (2002) 597-608.
[9] Arnab Kumar De and AmareshDalal , A numerical study of natural
convection around a square horizontal heated cylinder placed in an
enclosure, International Journal of heat mass transfer 49 (2006) 4608-
4623.
[10]WenRuey Chen, Natural convection heat transfer between inner sphere
and outer vertically eccentric cylinder, International Journal of Heat
and Mass Transfer 53 (2010) 5147-5155.
[11] XuXu, Gonggang Sun, Zitao Yu, Yacai Hu, Liwu Fan, Kefa Cen,
Numerical investigation of laminar natural convective heat transfer
from a horizontal triangular cylinder to its concentric cylindrical
enclosure, International Journal of Heat and Mass Transfer 52 (2009)
3176-3186.
[12] Zi-Tao Yu, Li-Wu Fan, Ya-Cai Hu and Ke-Fa Cen, Prandtl number
dependence of laminar natural convection heat transfer in a horizontal
cylindrical enclosure with an inner coaxial triangular cylinder,
International Journal of Heat and Mass Transfer 53 (2010) 1333-
1340.
[13] Manab Kumar Das and K . Saran Kumar Reddy, Conjugate natural
convection heat transfer in an inclined square cavity containing a
conducting block, International Journal of Heat and Mass Transfer 49
(2006) 4987-5000.
[14] YasinVarol, Hakan F. Oztop, AhmetKoca and FilizOzgen, Natural
convection and fluid flow in inclined enclosure with a corner heater,
Applied Thermal Engineering 29 (2009) 340-350.
[15] H.F. Nouanegue, A. Muftuoglu, E. Bilgen, Heat transfer by natural
convection, conduction and radiation in an inclined square enclosure
bounded with a solid wall, International Journal of Thermal Sciences
48 (2009) 871-880.
[16] F.A. Munir, N.A.C. Sidik and N.I.N. Ibrahim, Numerical Simulation
of Natural Convection in an Inclined Square Cavity, Journal of
Applied Sciences 11 (2) (2011) 373-378.
[1] Shu, C., and Zhu, Y.D., Efficient computational of natural convection
in a concentric annulus between an outer square cylinder and inner
circular cylinder, Int. J. Numer. Meth. Fluid 38 (2002) 429-445.
[2] Kim, B.S., Lee, D.S., Ha, M.Y., and Yoon, H.S., A numerical study
of natural convection in a square enclosure with a circular cylinder at
different vertical locations, Int. J. heat and mass transfer 51 (2008)
1888-1906.
[3] Hyun Sik Yoon, Man Yeong Ha, ByungSoo Kim and Dong Hun Yu,
Effect of the position of a circular cylinder in a square enclosure on
natural convection at Rayleigh number of 107, American Institute of
Physics, PHYSICS OF FLUIDS 21 (047101) (2009).
[4] Hakan F. Oztop, Zepu Zhao and BoYu, Fluid flow due to combined
convection in lid-driven enclosure having a circular body,
International Journal of Heat and Fluid Flow 30 (2009) 886-901.
[5] J.M. Lee, M.Y. Ha and H.S. Yoon, Natural convection in a square
enclosure with a circular cylinder at different horizontal and diagonal
locations, International Journal of Heat and Mass Transfer 53 (2010)
5905-5919.
[6] Salam Hadi Hussain and Ahmed Kadhim Hussein, Numerical
investigation of natural convection phenomena in a uniformly heated
circular cylinder immersed in square enclosure filled with air at
different vertical locations, International Communications in Heat and
Mass Transfer 37 (2010) 1115 -1126.
[7] TalalKassem, Numerical study of the natural convection process in the
parabolic-cylindrical solar collector, The Ninth Arab International
Conference on Solar Energy (AICSE-9), Kingdom of Bahrain,
Desalination 209 (2007) 144-150.
[8] C. Shu ,Q.Yao , K. S. Yao and Y. D. Zhu , Numerical analysis of flow
and thermal fields ia arbitrary eccentric annulus by differential
quadrature method, Heat and Mass Transfer 38 (2002) 597-608.
[9] Arnab Kumar De and AmareshDalal , A numerical study of natural
convection around a square horizontal heated cylinder placed in an
enclosure, International Journal of heat mass transfer 49 (2006) 4608-
4623.
[10]WenRuey Chen, Natural convection heat transfer between inner sphere
and outer vertically eccentric cylinder, International Journal of Heat
and Mass Transfer 53 (2010) 5147-5155.
[11] XuXu, Gonggang Sun, Zitao Yu, Yacai Hu, Liwu Fan, Kefa Cen,
Numerical investigation of laminar natural convective heat transfer
from a horizontal triangular cylinder to its concentric cylindrical
enclosure, International Journal of Heat and Mass Transfer 52 (2009)
3176-3186.
[12] Zi-Tao Yu, Li-Wu Fan, Ya-Cai Hu and Ke-Fa Cen, Prandtl number
dependence of laminar natural convection heat transfer in a horizontal
cylindrical enclosure with an inner coaxial triangular cylinder,
International Journal of Heat and Mass Transfer 53 (2010) 1333-
1340.
[13] Manab Kumar Das and K . Saran Kumar Reddy, Conjugate natural
convection heat transfer in an inclined square cavity containing a
conducting block, International Journal of Heat and Mass Transfer 49
(2006) 4987-5000.
[14] YasinVarol, Hakan F. Oztop, AhmetKoca and FilizOzgen, Natural
convection and fluid flow in inclined enclosure with a corner heater,
Applied Thermal Engineering 29 (2009) 340-350.
[15] H.F. Nouanegue, A. Muftuoglu, E. Bilgen, Heat transfer by natural
convection, conduction and radiation in an inclined square enclosure
bounded with a solid wall, International Journal of Thermal Sciences
48 (2009) 871-880.
[16] F.A. Munir, N.A.C. Sidik and N.I.N. Ibrahim, Numerical Simulation
of Natural Convection in an Inclined Square Cavity, Journal of
Applied Sciences 11 (2) (2011) 373-378.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:49320", author = "Sattar Al-Jabair and Laith J. Habeeb", title = "Simulation of Natural Convection in Concentric Annuli between an Outer Inclined Square Enclosure and an Inner Horizontal Cylinder", abstract = "In this work, the natural convection in a concentric
annulus between a cold outer inclined square enclosure and heated
inner circular cylinder is simulated for two-dimensional steady
state. The Boussinesq approximation was applied to model the
buoyancy-driven effect and the governing equations were solved
using the time marching approach staggered by body fitted
coordinates. The coordinate transformation from the physical
domain to the computational domain is set up by an analytical
expression. Numerical results for Rayleigh numbers 103 , 104 , 105
and 106, aspect ratios 1.5 , 3.0 and 4.5 for seven different
inclination angles for the outer square enclosure 0o , -30o
, -45o
,
-60o , -90o , -135o , -180o are presented as well. The computed flow
and temperature fields were demonstrated in the form of
streamlines, isotherms and Nusselt numbers variation. It is found
that both the aspect ratio and the Rayleigh number are critical to the
patterns of flow and thermal fields. At all Rayleigh numbers angle
of inclination has nominal effect on heat transfer.", keywords = "natural convection, concentric annulus, square
inclined enclosure", volume = "6", number = "9", pages = "1811-9", }
