Abstract

In this study, an analytical solution is proposed for the problem of transient anisotropic conductive heat transfer in composite cylindrical shells. The composite shells are considered to have directional heat transfer properties, which is due to the existence of fibers which can be winded in any direction. The composite shells usually show high conductivity in the direction parallel to fiber direction and low conductivity in other two orthogonal directions. To solve the heat transfer partial differential equation, finite Fourier transform and separation of variables method are used. The present solution is used to find the temperature distribution in a composite cylindrical vessel for which the composite material is graphite/epoxy and the vessel is prone to an external heat flux and also ambient flow. The analytical solution is verified perfectly by the data obtained from a second-order finite difference solution. The solution is used to investigate the effects of values of fiber angle and material conductivity coefficients on temperature distribution of the composite cylindrical vessel. The results show the important role of fiber angle values on the temperature distribution of vessel.

References

References
1.
Antonucci
,
V.
,
Giordano
,
M.
,
Hsiao
,
K.-T.
, and
Advani
,
S. G.
,
2002
, “
A Methodology to Reduce Thermal Gradients Due to the Exothermic Reactions in Composites Processing
,”
Int. J. Heat Mass Transfer
,
45
(
8
), pp.
1675
1684
.10.1016/S0017-9310(01)00266-6
2.
Guo
,
Z.-S.
,
Du
,
S.
, and
Zhang
,
B.
,
2005
, “
Temperature Field of Thick Thermoset Composite Laminates During Cure Process
,”
Compos. Sci. Technol.
,
65
(
3–4
), pp.
517
523
.10.1016/j.compscitech.2004.07.015
3.
Behzad
,
T.
, and
Sain
,
M.
,
2007
, “
Finite Element Modeling of Polymer Curing in Natural Fiber Reinforced Composites
,”
Compos. Sci. Technol.
,
67
(
7–8
), pp.
1666
1673
.10.1016/j.compscitech.2006.06.021
4.
Dlouhy
,
I.
,
Chlup
,
Z.
,
Boccaccini
,
D.
,
Atiq
,
S.
, and
Boccaccini
,
A.
,
2003
, “
Fracture Behaviour of Hybrid Glass Matrix Composites: Thermal Ageing Effects
,”
Composites, Part A
,
34
(
12
), pp.
1177
1185
.10.1016/j.compositesa.2003.08.004
5.
Gilbert
,
A.
,
Kokini
,
K.
, and
Sankarasubramanian
,
S.
,
2008
, “
Thermal Fracture of Zirconia–Mullite Composite Thermal Barrier Coatings Under Thermal Shock: An Experimental Study
,”
Surf. Coat. Technol.
,
202
(
10
), pp.
2152
2161
.10.1016/j.surfcoat.2007.09.001
6.
Gilbert
,
A.
,
Kokini
,
K.
, and
Sankarasubramanian
,
S.
,
2008
, “
Thermal Fracture of Zirconia–Mullite Composite Thermal Barrier Coatings Under Thermal Shock: A Numerical Study
,”
Surf. Coat. Technol.
,
203
(
1–2
), pp.
91
98
.10.1016/j.surfcoat.2008.08.003
7.
Norouzi
,
M.
,
Rahmani
,
H.
,
Birjandi
,
A. K.
, and
Joneidi
,
A. A.
,
2016
, “
A General Exact Analytical Solution for Anisotropic Non-Axisymmetric Heat Conduction in Composite Cylindrical Shells
,”
Int. J. Heat Mass Transfer
,
93
, pp.
41
56
.10.1016/j.ijheatmasstransfer.2015.09.072
8.
Norouzi
,
M.
, and
Rahmani
,
H.
,
2015
, “
On Exact Solutions for Anisotropic Heat Conduction in Composite Conical Shells
,”
Int. J. Therm. Sci.
,
94
, pp.
110
125
.10.1016/j.ijthermalsci.2015.02.018
9.
Huang
,
S.
, and
Chang
,
Y.
,
1980
, “
Heat Conduction in Unsteady, Periodic, and Steady States in Laminated Composites
,”
ASME J. Heat Transfer
,
102
(
4
), pp.
742
748
.10.1115/1.3244383
10.
Chang
,
Y.
,
Kang
,
C.
, and
Chen
,
D. J.
,
1973
, “
The Use of Fundamental Green's Functions for the Solution of Problems of Heat Conduction in Anisotropic Media
,”
Int. J. Heat Mass Transfer
,
16
(
10
), pp.
1905
1918
.10.1016/0017-9310(73)90208-1
11.
Sarkar
,
D.
,
Shah
,
K.
,
Haji-Sheikh
,
A.
, and
Jain
,
A.
,
2014
, “
Analytical Modeling of Temperature Distribution in an Anisotropic Cylinder With Circumferentially-Varying Convective Heat Transfer
,”
Int. J. Heat Mass Transfer
,
79
, pp.
1027
1033
.10.1016/j.ijheatmasstransfer.2014.08.060
12.
Singh
,
S.
, and
Jain
,
P. K.
,
2008
, “
Analytical Solution to Transient Heat Conduction in Polar Coordinates With Multiple Layers in Radial Direction
,”
Int. J. Thermal Sci.
,
47
(
3
), pp.
261
273
.10.1016/j.ijthermalsci.2007.01.031
13.
Miller
,
J.
, and
Weaver
,
P.
,
2003
, “
Temperature Profiles in Composite Plates Subject to Time-Dependent Complex Boundary Conditions
,”
Compos. Struct.
,
59
(
2
), pp.
267
278
.10.1016/S0263-8223(02)00054-5
14.
Blanc
,
M.
, and
Touratier
,
M.
,
2007
, “
An Efficient and Simple Refined Model for Temperature Analysis in Thin Laminated Composites
,”
Compos. Struct.
,
77
(
2
), pp.
193
205
.10.1016/j.compstruct.2005.07.001
15.
Jain
,
P. K.
,
Singh
,
S.
, and
Uddin
,
R.
,
2010
, “
An Exact Analytical Solution for Two-Dimensional, Unsteady, Multilayer Heat Conduction in Spherical Coordinates
,”
Int. J. Heat Mass Transfer
,
53
(
9–10
), pp.
2133
2142
.10.1016/j.ijheatmasstransfer.2009.12.035
16.
Haji-Sheikh
,
A.
,
Beck
,
J.
, and
Agonafer
,
D.
,
2003
, “
Steady-State Heat Conduction in Multi-Layer Bodies
,”
Int. J. Heat Mass Transfer
,
46
(
13
), pp.
2363
2379
.10.1016/S0017-9310(02)00542-2
17.
Kaisare
,
A.
,
Agonafer
,
D.
,
Haji-Sheikh
,
A.
,
Chrysler
,
G.
, and
Mahajan
,
R.
,
2009
, “
Development of Analytical Model to a Temperature Distribution of a First Level Package With a Nonuniformly Powered Die
,”
ASME J. Electron. Packag.
,
131
(
1
), p.
011005
.10.1115/1.3068303
18.
Singh
,
S.
, and
Jain
,
P. K.
,
2011
, “
Finite Integral Transform Method to Solve Asymmetric Heat Conduction in a Multilayer Annulus With Time-Dependent Boundary Conditions
,”
Nucl. Eng. Des.
,
241
(
1
), pp.
144
154
.10.1016/j.nucengdes.2010.10.010
19.
Lu
,
X.
,
Tervola
,
P.
, and
Viljanen
,
M.
,
2006
, “
Transient Analytical Solution to Heat Conduction in Composite Circular Cylinder
,”
Int. J. Heat Mass Transfer
,
49
(
1–2
), pp.
341
348
.10.1016/j.ijheatmasstransfer.2005.06.019
20.
Lu
,
X.
,
Tervola
,
P.
, and
Viljanen
,
M.
,
2005
, “
An Efficient Analytical Solution to Transient Heat Conduction in a One-Dimensional Hollow Composite Cylinder
,”
J. Phys. A: Math. Gen.
,
38
(
47
), p.
10145
.10.1088/0305-4470/38/47/007
21.
Delouei
,
A. A.
,
Kayhani
,
M.
, and
Norouzi
,
M.
,
2012
, “
Exact Analytical Solution of Unsteady Axi-Symmetric Conductive Heat Transfer in Cylindrical Orthotropic Composite Laminates
,”
Int. J. Heat Mass Transfer
,
55
(
15
), pp.
4427
4436
.10.1016/j.ijheatmasstransfer.2012.04.012
22.
Norouzi
,
M.
,
Niya
,
S. R.
,
Kayhani
,
M.
,
Shariati
,
M.
,
Demneh
,
M. K.
, and
Naghavi
,
M.
,
2012
, “
Exact Solution of Unsteady Conductive Heat Transfer in Cylindrical Composite Laminates
,”
ASME J. Heat Transfer
,
134
(
10
), p.
101301
.10.1115/1.4006009
23.
Delouei
,
A. A.
, and
Norouzi
,
M.
,
2015
, “
Exact Analytical Solution for Unsteady Heat Conduction in Fiber-Reinforced Spherical Composites Under the General Boundary Conditions
,”
ASME J. Heat Transfer
,
137
(
10
), p.
101701
.10.1115/1.4030348
24.
Norouzi
,
M.
, and
Rahmani
,
H.
,
2017
, “
An Exact Analysis for Transient Anisotropic Heat Conduction in Truncated Composite Conical Shells
,”
Appl. Therm. Eng.
,
124
, pp.
422
431
.10.1016/j.applthermaleng.2017.06.039
25.
Griffis
,
C. A.
,
Masumura
,
R.
A., and
Chang
,
C. I.
,
1981
, “
Thermal Response of Graphite Epoxy Composite Subjected to Rapid Heating
,”
J. Compos. Mater.
,
15
(
5
), pp.
427
442
.10.1177/002199838101500503
26.
Cole
,
K. D.
,
Beck
,
J. V.
,
Woodbury
,
K. A.
, and
De Monte
,
F.
,
2014
, “
Intrinsic Verification and a Heat Conduction Database
,”
Int. J. Therm. Sci.
,
78
, pp.
36
47
.10.1016/j.ijthermalsci.2013.11.002
You do not currently have access to this content.