Numerical investigations have been carried out to predict the near-wall dynamics in indirect natural convection for air (Pr = 0.7) and water (Pr = 5.2). Near-wall flow structures appear to be line plumes. Three-dimensional laminar, steady-state model was used to model the problem. Density was formulated using the Boussinesq approximation. Flux scaling, plume spacing and plume lengths obtained numerically are found to have the same trend with the results available in the literature. Plume length and Nusselt number, Nu exhibits an increasing trend with an increase in Rayleigh number, RaH for both Pr fluids. The plume spacing is found to have an inverse relationship with RaH. The cube root of Rayleigh number based on plume spacing, Raλ1/3 is found to have a slight dependence on the dimensionless plume spacing, λ/H. Nu scales as NuCRaHn, n =0.26 for air and n =0.3 for water. Heat transfer is thus found to be dominated by near-wall phenomenon. Nu shows a nonlinear relationship with LpH/A and is found to be an accurate representation of heat transfer.

References

References
1.
Schuh
,
H.
,
1950
, “
The Solution of Laminar Boundary Layer Over a Flat Plate for Velocity and Temperature Fields for Variable Physical Properties and for Diffusion Field at High Concentration
,”
NACA, Technical Memorandum No. 1275
.
2.
Stewartson
,
K.
,
1958
, “
On Free Convection From Horizontal Plate
,”
Z. Angew. Math. Phys.
,
9
(
3
), pp.
276
282
.
3.
Townsend
,
A.
,
1959
, “
Temperature Fluctuations Over a Heated Horizontal Surface
,”
J. Fluid Mech.
,
5
(
02
), pp.
209
241
.
4.
Deardorff
,
J.
,
1970
, “
Convective Velocity and Temperature Scales for the Unstable Planetary Boundary Layer and for Rayleigh Convection
,”
J. Atmos. Sci.
,
27
(
8
), pp.
1211
1213
.
5.
Spalding
,
D.
, and
Cruddace
,
R. G.
,
1960
, “
Theory of Steady Laminar Buoyant Flow Above a Line Heat Source in a Fluid of Large Pr and Temperature Dependent Viscosity
,”
Int. J. Heat Mass Transfer
,
3
(
1
), pp.
55
59
.
6.
Fujii
,
T.
,
1963
, “
Theory of Steady Laminar Natural Convection Above a Horizontal Line and Point Heat Source
,”
Int. J. Heat Mass Transfer
,
6
(
7
), pp.
597
606
.
7.
Rotem
,
Z.
, and
Claassen
,
L.
,
1969
, “
Natural Convection Above Unconfined Horizontal Surfaces
,”
J. Fluid Mech.
,
39
(
1
), pp.
173
192
.
8.
Pera
,
L.
, and
Gebhart
,
B.
,
1973
, “
On Stability of Natural Convection Boundary Layer Flow Over Horizontal and Slightly Inclined Surfaces
,”
Int. J. Heat Mass Transfer
,
16
(
6
), pp.
1147
1163
.
9.
Tamai
,
N.
, and
Asaeda
,
T.
,
1984
, “
Sheet Like Plumes Near a Heated Bottom Plate at Large Rayleigh Number
,”
J. Geophys. Res.
,
89
(
C1
), pp.
727
734
.
10.
Nield
,
D.
,
1987
, “
Throughflow Effects in the Rayleigh-Bénard Convective Instability Problem
,”
J. Fluid Mech.
,
185
(
1
), pp.
353
360
.
11.
Castaing
,
B.
,
Gunaratne
,
G.
,
Heslot
,
F.
,
Kadanoff
,
L.
,
Libchaber
,
A.
,
Thomae
,
S.
,
Wu
,
X.
,
Zaleski
,
S.
, and
Zanetti
,
G.
,
1989
, “
Scaling of Hard Thermal Turbulence in Rayleigh-Bénard Convection
,”
J. Fluid Mech.
,
204
(
1
), pp.
1
30
.
12.
Zocchi
,
G.
,
Moses
,
E.
, and
Libchaber
,
A.
,
1990
, “
Coherent Structures in Turbulent Convection
,”
Phys. A: Stat. Mech. Appl.
,
166
(
3
), pp.
387
407
.
13.
Iwase
,
Y.
, and
Honda
,
S.
,
1997
, “
An Interpretation to the Nu- Ra Relationship for Convection in a Spherical Shell
,”
Geophys. J. Int.
,
130
(
3
), pp.
801
804
.
14.
Theerthan
,
S.
, and
Arakeri
,
J.
,
1998
, “
A Model for Near-Wall Dynamics in Turbulent Rayleigh-Bénard Convection
,”
J. Fluid Mech.
,
373
, pp.
221
254
.
15.
Theerthan
,
S.
, and
Arakeri
,
J.
,
2000
, “
Planform Structure and Heat Transfer in Turbulent Free Convection Over Horizontal Surfaces
,”
Phys. Fluids
,
12
(
4
), pp.
884
894
.
16.
Niemela
,
J.
,
Skrbek
,
L.
,
Sreenivasan
,
K.
, and
Donnelly
,
R.
,
2001
, “
The Wind in Confined Thermal Convection
,”
J. Fluid Mech.
,
449
, pp.
169
178
.
17.
Kenjereš
,
S.
, and
Hanjalić
,
K.
,
2002
, “
Numerical Insight Into Flow Structure in Ultraturbulent Thermal Convection
,”
Phys. Rev. E
,
66
(
3
), p.
036307
.
18.
Puthenveetil
,
B. A.
,
Ananthakrishna
,
G.
, and
Arakeri
,
J. H.
,
2005
, “
Multifractal Nature of Plume Structure in High-Rayleigh-Number Convection
,”
J. Fluid Mech.
,
526
, pp.
245
256
.
19.
Puthenveettil
,
B. A.
, and
Arakeri
,
J. H.
,
2005
, “
Plume Structure in High-Rayleigh-Number Convection
,”
J. Fluid Mech.
,
542
(
1
), pp.
217
249
.
20.
Puthenveettil
,
B. A.
, and
Arakeri
,
J. H.
,
2008
, “
Convection Due to an Unstable Density Difference Across a Permeable Membrane
,”
J. Fluid Mech.
,
609
, pp.
139
170
.
21.
Puthenveettil
,
B.
,
Gunasegarane
,
G.
,
Agrawal
,
Y.
,
Schmeling
,
D.
,
Bosbach
,
J.
, and
Arakeri
,
J.
,
2011
, “
Length of Near Wall Plumes in Turbulent Convection
,”
J. Fluid Mech.
,
685
, pp.
335
364
.
22.
Rama Reddy
,
G.
, and
Puthenveettil
,
B.
,
2011
, “
The Pe ∼ 1 Regime of Convection Across a Horizontal Permeable Membrane
,”
J. Fluid Mech.
,
679
, pp.
476
504
.
23.
Gunasegarane
,
G.
, and
Puthenveetil
,
B.
,
2014
, “
Dynamics of Line Plumes on Horizontal Surfaces in Turbulent Convection
,”
J. Fluid Mech.
,
749
, pp.
37
78
.
24.
Prakash
,
V.
,
Sreenivas
,
K.
, and
Arakeri
,
J.
,
2017
, “
The Role of Viscosity Contrast on Plume Structure in Laboratory Modelling of Mantle Convection
,”
Chem. Eng. Sci.
,
58
, pp.
245
256
.
25.
Dropkin
,
D.
, and
Somerscales
,
E.
,
1965
, “
Heat Transfer by Natural Convection in Liquids Confined by Two Parallel Plates Which Are Inclined at Various Angles With Respect to the Horizontal
,”
ASME J. Heat Transfer
,
87
(
1
), pp.
77
82
.
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