An Exact Solution of Axi-symmetric Conductive Heat Transfer in Cylindrical Composite Laminate under the General Boundary Condition

Authors: M.kayhani, M.Nourouzi, A. Amiri Delooei

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.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1330243

References:

[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.