This paper addresses the problem of natural convection in H-Form cavity with differentially heated side walls having two circular adiabatic obstacles. To achieve accurate solutions of the equations system defining this study, the computational methods are founded on the finite element method (FEM). Numerical illustrations have been carried out and discussed for several Rayleigh numbers from 10 to 106. We show the impact of Rayleigh number as a crucial parameter on both the heat transfer and the fluid flow. We deduce an important finding with H-Form cavity, the Rayleigh number hasn't a strong effect on both the characteristics of the fluid flow and the temperature distribution for the values ranging from 10 to 104, unlike the case of square cavity. However, its effect starts to appear from Ra = 105. The achieved results are discussed and compared with preceding works in the literature to show their effectiveness.
REFERENCES
1.
G. De Vahl
Davis
and I. P.
Jones
, Natural convection in a square cavity: A comparison exercise
, Int. J. Meth. Fluids
3
, 227
–248
(1983
).2.
C.
Béghein
, F.
Haghighat
, and F.
Allard
, Numerical study of double-diffusive natural convection in a square cavity
, International Journal of Heat and Mass Transfer
35
(4
), 833
–846
(1992
).3.
F.
Xu
, J. C.
Patterson
, and Ch. W.
Lei
., Heat transfer through coupled thermal boundary layers induced by a suddenly generated temperature difference
, Int. J. Heat Mass Transfer
52
, 4966
–4975
(2009
).4.
S.A.M.
Mehryan
, Mohammad
Ghalambaz
, Muneer A.
Ismael
, and Ali J.
Chamkha
, Analysis of fluid-solid interaction in MHD natural convection in a square cavity equally partitioned by a vertical flexible membrane
, Journal of Magnetism and Magnetic Materials
424
, 161
–173
(2017
).5.
M.
Leporini
, F.
Corvaro
, B.
Marchetti
, F.
Polonara
, and M.
Benucci
, Experimental and numerical investigation of natural convection in tilted square cavity filled with air
, Experimental Thermal and Fluid Science
99
, 572
–583
(2018
).6.
A.
Mazgar
, F.
Hajji
, K.
Jarray
, and F.
Ben Nejma
, Conjugate non-Gray Gas Radiation Combined with Natural Convection inside a Square Cavity with Internal Heat Source: Entropy Generation
, Conference: 6ᵗʰ International Conference on Green Energy and Environmental Engineering GEEE-2019, April 27-29ᵗʰ
, 2019
, Tabarka, Tunisia
.7.
M. M.
Mousa
, Finite element investigation of stationary natural convection of light and heavy water in a vessel containing heated rods
, Z. Naturforsch
67a
, 421
–427
(2012
).8.
M. M.
Mousa
, Modeling of Laminar Buoyancy Convection in a Square Cavity Containing an Obstacle
, Bull. Malays. Math. Sci. Soc.
39
, 483
–498
(2016
).9.
V.
Nassehi
, and M.
Parvazinia
, Finite Element Method in Engineering
. Imp. College Press
, London
(2010
).10.
T.
Fusegi
, J. M.
Hyun
, K.
Kuwahara
, and B.
Farouk
, A numerical study of three-dimensional natural convection in a differentially heated cubical enclosure
, Int. J. Heat Mass Transf
34,
1543
–1557
(1991
).11.
G.
Barakos
, E.
Mitsoulis
, and D.
Assimacopoulos
, Natural convection flow in a square cavity revisited: laminar and turbulent models with wall functions
, Int. J. Numer. Methods Fluids
18
, 695
–719
(1994
).12.
A.
Bouaine
and M.
Rachik
, Modeling the impact of immigration and climatic conditions on the epidemic spreading based on cellular automata approach
, 46
, 36
–44
(2018
). 13.
T.
Basak
, S.
Roy
, and I.
Pop
, Heat flow analysis for natural convection within trapezoidal enclosures based on heatline concept
, Int. J. Heat Mass Transfer
52,
(2009
) 2471
–2483
.14.
R.S.
Kaluri
, R.
Anandalakshmi
, and T.
Basak
, Bejan's heatline analysis of natural convection in right- angled triangular enclosures: Effects of aspect ratio and thermal boundary conditions
, Int. J. Therm. Sci.
49,
1576
–1592
(2010
).15.
E. M.
Alawadhi
, Phase change process with free convection in a circular enclosure: numerical simulations
, Comput. Fluids
33,
1335
–1348
(2004
).16.
G. C.
Buscaglia
and E. A.
Dari
, Implementation of the Lagrange-Galerkin method for the incompressible Navier-Stokes equations
, Int. J. Numer. Methods Fluids
15
, 23
–36
(1992
).17.
B.
Gebhart
, Buoyancy-induced fluid motion characteristics of applications in technology: The 1979 Freeman Scholar Lecture
, ASME Trans. J. Fluid Eng.
101
, 5
–28
(1979
).18.
S.
Ostrach
, Natural convection in enclosures
, ASME Trans. J. Heat Transf
110
, 1175
–1190
(1988
).19.
T.
Basak
and K.G.
Ayappa
, Influence of internal convection during microwave thawing of cylinders
. AIChE J.
47
, 835
–850
(2001
).20.
T.
Basaka
, S.
Royb
, and Ch.
Thirumalesha
, Finite element analysis of natural convection in a triangular enclosure: effects of various thermal boundary conditions
. Chem. Eng. Sci.
62
, 2623
–2640
(2007
).21.
J. N.
Reddy
, An Introduction to the Finite Element Method
, McGraw-Hill
, NewYork
(1993
).22.
S.
Roy
and T.
Basak
, Finite element analysis of natural convection flows in a square cavity with non- uniformly heated wall(s
), Int. J. Eng. Sci.
43
, 668
–680
(2005
).23.
M.
Loukili
and S.
Mordane
, New contribution to stokes equations
, Advances and Applications in Fluis Mechanics
20
, 107
–116
(2017
).24.
M.
Loukili
and S.
Mordane
, New Numerical Investigation Using Meshless Methods Applied to the Linear Free Surface Water Waves
, Advances In Intelligent Sys. Comp.
765
, 337
–345
(2019
).25.
M.
Loukili
and S.
Mordane
, Numerical Analysis of an Absorbing Boundary Condition Applied to the Free Surface Water Waves Using the Method of Fundamental Solutions
, 8th International Conference on Modeling Simulation and Applied Optimization (ICMSAO)
, Bahrain
, 2019
.26.
M.
Loukili
and S.
Mordane
, Computation of Nonlinear Free-Surface Flows Using the Method of Fundamental Solutions
, Advances In Intelligent Sys. Comp.
763
, 420
–430
(2019
).
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