An Exact Solution of Axi-symmetric Conductive Heat Transfer in Cylindrical Composite Laminate under the General Boundary Condition
This study presents an exact general solution for
steady-state conductive heat transfer in cylindrical composite
laminates. Appropriate Fourier transformation has been obtained
using Sturm-Liouville theorem. Series coefficients are achieved by
solving a set of equations that related to thermal boundary conditions
at inner and outer of the cylinder, also related to temperature
continuity and heat flux continuity between each layer. The solution
of this set of equations are obtained using Thomas algorithm. In this
paper, the effect of fibers- angle on temperature distribution of
composite laminate is investigated under general boundary
conditions. Here, we show that the temperature distribution for any
composite laminates is between temperature distribution for
laminates with θ = 0° and θ = 90° .
[1] C. K. Chao, F.M. Che, and M.H. Shen, "An exact solution for thermal
stresses in a three-phase composite cylinder under uniform heat flow,
" Int. J. Solids and Structures, vol.44, pp.926-940, 2007.
[2] V. Pradeep, and N. Ganesan, "Thermal buckling and vibration
behavior of multi-layer rectangular viscoelastic sandwich plates,"
Journal of Sound and Vibration, vol. 310, pp.169-183, 2008.
[3] J.Q. Tarn, "state space formalism for anisotropic elasticity. PartII:
cylindrical anisotropy," Int. J. Solids Struct. Vol.39, pp.5157-5172,
2002.
[4] W.A. Wooster, A textbook in crystal physics. Cambridge University
Press, London, 1957, pp.455
[5] J.F. Nye, Physical properties of crystals. Clarendon Press, London,
1957, pp.309.
[6] C.C. Ma and S.S Chang, "Analytical exact solutions of heat conduction
problems for anisotropic multilayered media, " Int. J. Heat and Mass
Transfer vol.47 pp.1643-1655, 2004.
[7] M.R. Kulkarani, and R.P. Brady, "A model of global thermal
conductivity in laminated Carboncarbon composites, " Composites
science and Technology vol.57, pp.277-285, 1997.
[8] B.T. Johansson, and D. Lesnic, " A method of fundamental solutions
for transient heat conduction in layered materials, " Engineering
Analysis with Boundary Elements, vol.33, pp.1362-1367, 2009.
[9] Y. Sun, and I.S. Wichman, "On transient heat conduction in a onedimensional
composite slab, " Int J Heat and Mass Transfer,
vol.47, pp.1555-1559, 2004.
[10] A. Karageorghis, and D. Lesnic, "Steady-state nonlinear heat
conduction in composite materials, ", Comput. Methods Appl .Mech.
Engrg, vol. 197, pp. 3122-3137, 2008.
[11] A. Haji-Sheikh, J.V. Beck, and D. Agonater, "Steady-state heat
conduction in multi-layer bodies, " Int J Heat and Mass Transfer
vol.46 pp.2363-2379, 2003.
[12] Z-S Guo, et al. "Temperature distribution of thick thermo set
composites, " J Model Simul Mater SciEng, vol.12 pp.443-452, 2004.
[13] S. Singh, P.K. Jain, and Rizwan-uddin, "Analytical solution to
transient heat conduction in polar coordinates with multiple layers in
radial direction, " Int. J. Thermal Sciences vol.47 pp.261-273, 2008.
[14] R. Bahadur, A. Bar-Cohen, "Orthotropic thermal conductivity effect on
cylindrical pin fin heat transfer, " Int. J. Heat and Mass Transfer
vol.50 pp.1155-1162, 2007.
[15] O.O. Onyejekwe, "heat conduction in composite media: a boundary
integral approach, " Computers and chemical Engineering vol.26 pp.
1621-1632, 2002.
[16] J.Q. Tarn, Y.M. Wang, "Heat conduction in a cylindrically anisotropic
tube of a functionally graded material, " Chin J. Mech., Vol.19 pp.365-
372, 2003.
[17] J.Q. Tarn, Y.M. Wang, "End effects of heat conduction in circular
cylinders of functionally graded materials and laminated composites, "
Inter. J. Heat Mass Transfer vol.47, pp.5741-5747, 2004.
[18] J. Zhang, M. Tanaka, and T. Matsumoto, "A simplified approach for
heat conduction analysis of CNT-based nano-composites, " Comput.
Methods Appl. Mech. Engrg., vol.193 pp.5597-5609, 2004.
[19] N.A. Roberts, D.G. Walker, D.Y. Li, "Molecular dynamics simulation of
thermal conductivity of nanocrystalline composite films, " Int. J.
Heat and Mass Transfer, Vol.52, pp.2002- 2008, 2008.
[20] Y.S. Cha, W.J. Minkowycz, and S.Y. Seol, "Transverse temperature
distribution and heat generation rate in composite superconductors
subjected to constant thermal disturbance, " Int. Comm. Heat Mass
Transfer, Vol. 22, No.4, pp. 461-474, 1995.
[21] M.H. Kayhani, M. Shariati, M. Nourozi, M., Karimi Demneh, "Exact
solution of conductive heat transfer in cylindrical composite laminate, "
Int. J. Heat and Mass Transfer, Vol 46, pp.83-94, 2009.
[22] T. Myint-U, and L. Debnath, LinearPartial Differential Equations for
Scientists and Engineers, Birkhauser Boston, 2007.
[23] Y.S. Touloukian, C.Y. Ho, Thermophysical properties of matter,
plenumpress, vol.2, Thermal Conductivity of Nonmetallic Solids, New
York, 1972, pp.740, 1972.
[1] C. K. Chao, F.M. Che, and M.H. Shen, "An exact solution for thermal
stresses in a three-phase composite cylinder under uniform heat flow,
" Int. J. Solids and Structures, vol.44, pp.926-940, 2007.
[2] V. Pradeep, and N. Ganesan, "Thermal buckling and vibration
behavior of multi-layer rectangular viscoelastic sandwich plates,"
Journal of Sound and Vibration, vol. 310, pp.169-183, 2008.
[3] J.Q. Tarn, "state space formalism for anisotropic elasticity. PartII:
cylindrical anisotropy," Int. J. Solids Struct. Vol.39, pp.5157-5172,
2002.
[4] W.A. Wooster, A textbook in crystal physics. Cambridge University
Press, London, 1957, pp.455
[5] J.F. Nye, Physical properties of crystals. Clarendon Press, London,
1957, pp.309.
[6] C.C. Ma and S.S Chang, "Analytical exact solutions of heat conduction
problems for anisotropic multilayered media, " Int. J. Heat and Mass
Transfer vol.47 pp.1643-1655, 2004.
[7] M.R. Kulkarani, and R.P. Brady, "A model of global thermal
conductivity in laminated Carboncarbon composites, " Composites
science and Technology vol.57, pp.277-285, 1997.
[8] B.T. Johansson, and D. Lesnic, " A method of fundamental solutions
for transient heat conduction in layered materials, " Engineering
Analysis with Boundary Elements, vol.33, pp.1362-1367, 2009.
[9] Y. Sun, and I.S. Wichman, "On transient heat conduction in a onedimensional
composite slab, " Int J Heat and Mass Transfer,
vol.47, pp.1555-1559, 2004.
[10] A. Karageorghis, and D. Lesnic, "Steady-state nonlinear heat
conduction in composite materials, ", Comput. Methods Appl .Mech.
Engrg, vol. 197, pp. 3122-3137, 2008.
[11] A. Haji-Sheikh, J.V. Beck, and D. Agonater, "Steady-state heat
conduction in multi-layer bodies, " Int J Heat and Mass Transfer
vol.46 pp.2363-2379, 2003.
[12] Z-S Guo, et al. "Temperature distribution of thick thermo set
composites, " J Model Simul Mater SciEng, vol.12 pp.443-452, 2004.
[13] S. Singh, P.K. Jain, and Rizwan-uddin, "Analytical solution to
transient heat conduction in polar coordinates with multiple layers in
radial direction, " Int. J. Thermal Sciences vol.47 pp.261-273, 2008.
[14] R. Bahadur, A. Bar-Cohen, "Orthotropic thermal conductivity effect on
cylindrical pin fin heat transfer, " Int. J. Heat and Mass Transfer
vol.50 pp.1155-1162, 2007.
[15] O.O. Onyejekwe, "heat conduction in composite media: a boundary
integral approach, " Computers and chemical Engineering vol.26 pp.
1621-1632, 2002.
[16] J.Q. Tarn, Y.M. Wang, "Heat conduction in a cylindrically anisotropic
tube of a functionally graded material, " Chin J. Mech., Vol.19 pp.365-
372, 2003.
[17] J.Q. Tarn, Y.M. Wang, "End effects of heat conduction in circular
cylinders of functionally graded materials and laminated composites, "
Inter. J. Heat Mass Transfer vol.47, pp.5741-5747, 2004.
[18] J. Zhang, M. Tanaka, and T. Matsumoto, "A simplified approach for
heat conduction analysis of CNT-based nano-composites, " Comput.
Methods Appl. Mech. Engrg., vol.193 pp.5597-5609, 2004.
[19] N.A. Roberts, D.G. Walker, D.Y. Li, "Molecular dynamics simulation of
thermal conductivity of nanocrystalline composite films, " Int. J.
Heat and Mass Transfer, Vol.52, pp.2002- 2008, 2008.
[20] Y.S. Cha, W.J. Minkowycz, and S.Y. Seol, "Transverse temperature
distribution and heat generation rate in composite superconductors
subjected to constant thermal disturbance, " Int. Comm. Heat Mass
Transfer, Vol. 22, No.4, pp. 461-474, 1995.
[21] M.H. Kayhani, M. Shariati, M. Nourozi, M., Karimi Demneh, "Exact
solution of conductive heat transfer in cylindrical composite laminate, "
Int. J. Heat and Mass Transfer, Vol 46, pp.83-94, 2009.
[22] T. Myint-U, and L. Debnath, LinearPartial Differential Equations for
Scientists and Engineers, Birkhauser Boston, 2007.
[23] Y.S. Touloukian, C.Y. Ho, Thermophysical properties of matter,
plenumpress, vol.2, Thermal Conductivity of Nonmetallic Solids, New
York, 1972, pp.740, 1972.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:52513", author = "M.kayhani and M.Nourouzi and A. Amiri Delooei", title = "An Exact Solution of Axi-symmetric Conductive Heat Transfer in Cylindrical Composite Laminate under the General Boundary Condition", abstract = "This study presents an exact general solution for
steady-state conductive heat transfer in cylindrical composite
laminates. Appropriate Fourier transformation has been obtained
using Sturm-Liouville theorem. Series coefficients are achieved by
solving a set of equations that related to thermal boundary conditions
at inner and outer of the cylinder, also related to temperature
continuity and heat flux continuity between each layer. The solution
of this set of equations are obtained using Thomas algorithm. In this
paper, the effect of fibers- angle on temperature distribution of
composite laminate is investigated under general boundary
conditions. Here, we show that the temperature distribution for any
composite laminates is between temperature distribution for
laminates with θ = 0° and θ = 90° .", keywords = "exact solution, composite laminate, heat conduction,cylinder, Fourier transformation.", volume = "4", number = "9", pages = "804-8", }
