References
1. Crawford, L. and Lemlich, R. \Natural convection in
horizontal concentric cylindrical annuli", Industrial &
Engineering Chemistry Fundamentals, 1 pp. 260-264
(1962).
2. Mack, L.R. \Natural convection between horizontal
concentric cylinders for low Rayleigh numbers", Journal
of Mech. and Applied Mathematics, 21, pp. 223-241
(1968).
3. Kuehn, T.H. and Goldstein, R.L. \Correlating equations
for natural convection heat transfer between
horizontal circular cylinders", International Journal of
Heat and Mass Transfer, 19, pp. 1127-1134 (1976).
4. Projahn, U., Rieger, H., and Beer, H. \Numerical analysis
of laminar natural convection between concentric
and eccentric cylinders", Numerical Heat Transfer, 4,
pp. 131-146 (1981).
1196 G.R. Zendehbudi/Scientia Iranica, Transactions B: Mechanical Engineering 25 (2018) 1189{1196
5. Cho, C.H., Chang, K.S., and Park, K.H. \Numerical
simulation of natural convection in concentric and
eccentric horizontal cylindrical annuli", Transactions
of the ASME, 104, pp. 624-630 (1982).
6. Glakpe, E.K., Watkins Jr., C.B., and Cannon, J.N.
\Constant heat
ux solutions for natural convection
between concentric and eccentric horizontal cylinders",
Numerical Heat Transfer, 10, pp. 279-295 (1986).
7. Kumar, R. \Study of natural convection in horizontal
annuli", International Journal of Heat and Mass
Transfer, 31, pp. 1137-1148 (1988).
8. Vafai, K. and Desai, C.P. \Comparative analysis of
the nite element and nite di erence methods for
simulation of buoyancy induced
ow and heat transfer
in closed and open ended annular cavities", Numerical
Heat Transfer, Part A, 23, pp. 35-39 (1993).
9. Moukalled, F. and Acharya, S. \Natural convection in
the annulus between concentric horizontal circular and
square cylinders", Journal of Thermophysics and Heat
Transfer, 10, pp. 524-531 (1996).
10. Yoo, J.-S. \Natural convection in a narrow horizontal
cylindrical annulus", International Journal of Heat and
Mass Transfer, 41, pp. 3055-3073 (1998).
11. Francis Jr., N.D. and Itamura, M.T., CFD Calculation
of Internal Natural Convection in the Annulus
Between Horizontal Concentric Cylinders, Sandia National
Laboratories (2002).
12. Passerinil, A., Ruzicka, M., and Thater, G. \Natural
convection between two horizontal coaxial cylinders",
ZAMM, 84, pp. 3-16 (2004).
13. Ding, H., Shu, C., and Yeo, K.S. \Simulation of natural
convection in eccentric annuli between a square outer
cylinder and a circular inner cylinder using local MQDQ
method", Numerical Heat Transfer, 47, pp. 291-
313 (2005).
14. Padilla, E.L.M., Campregher, R., and Silveira-Neto, A.
\Numerical analysis of the natural convection in horizontal
annuli at low and moderate Ra", Engenharia
Trmica (Thermal Engineering), 5, pp. 58-65 (2006).
15. 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 di erent vertical
locations", International Journal of Heat and Mass
Transfer, 51, pp. 1888-1906 (2008).
16. Xu, X., Sun, G., Yu, Z., Hu, Y., Fan, L., and Cen, K.
\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, pp. 3176-3186
(2009).
17. Ataylmaz, S.O. \Experimental and numerical study of
natural convection heat transfer from horizontal concentric
cylinders", International Journal of Thermal
Sciences, 50, pp. 1472-1483 (2011).
18. Hu, Y., Niu, X.D., Shu, S., Yuan, H., and Li, M.
\Natural convection in a concentric annulus: a lattice
Boltzmann method study with boundary condition
enforced immersed boundary method", Advances in
Applied Mathematics and Mechanics, 5, pp. 321-336
(2013).
19. Patel, S.S., Min, M., Uga, K.C., and Lee, T. \A
spectral-element discontinuous Galerkin LBM for simulating
natural convection heat transfer in a horizontal
concentric annulus", Computers and Fluids, 95, pp.
197-209, (2014).
20. Yuan, X., Tavakkoli, F. and Vafai, K. \Analysis of
natural convection in horizontal concentric annuli of
varying inner shape", Numerical Heat Transfer, 68,
pp. 1155-1174 (2015).
21. Chorin., A. \A numerical method for solving incompressible
viscous
ow problems", Journal of Computational
Physics, 2, pp. 12-26 (1967).
22. Zendehbudi, G.R. \E ects of non-uniform wall properties
on stress distribution in an abdominal aortic
aneurysm, considering nonlinear constitutive equations",
Scientia Iranica, 21, pp. 620-627 (2014).
23. Bergman, T.L., Lavine, A.S., Incropera, F.P. and Dewitt,
D.P., Fundamentals of Heat and Mass Transfer,
John Wiley & Sons (2011).
24. Jiji, L.M., Heat Convection, Springer-Verlag Berlin
Heidelberg (2009).
25. Bejan, A., Convection Heat Transfer, John Wiley &
Sons (2000).
)