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A New Exact Analysis for Anisotropic Conductive Heat Transfer in Truncated Composite Spherical Shells

Published online by Cambridge University Press:  14 April 2019

M. Norouzi ,
H. Rahmani  and
A. K Birjandi
M. Norouzi*
Affiliation:
Faculty of Mechanical EngineeringShahrood University of Technology
H. Rahmani
Affiliation:
Faculty of Mechanical EngineeringAmirkabir University of Technology Tehran, Iran
A. K Birjandi
Affiliation:
Faculty of Mechanical EngineeringShahrood University of Technology Shahrood, Iran
*
*Corresponding author ([email protected])
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Abstract

In the present paper, a general analytical solution is proposed for anisotropic heat conduction through truncated composite spherical shells. The solution is so important in designing the spherical vessels which are usually used to store the CNG, LNG, LPG and other petroleum condensates. Herein, it is supposed that the fiber angle of composite laminate is in range of zero to 90 degrees. Heat convection with ambient flow, an external heat radiation, and a possible internal heat generation are modeled within the heat transfer equation. The exact solution is derived using the complex finite Fourier transform method. The particular solution of transferred equation is found based on the Green’s function and Sturm-Liouville theories. Finally, an inverse integral transformation is applied to form the final analytical solution in physical space. Defining four materials differing in the value of conductivity coefficient in fiber direction, the effects of used composite material and fiber angle on temperature distribution of the spherical shell are investigated in detail.

Keywords

Analytical solutionAnisotropic heat conductionTruncated composite spherical shellComposite spherical vessel
Type
Research Article
Information
Journal of Mechanics , Volume 35 , Issue 5 , October 2019 , pp. 677 - 691
Copyright
© The Society of Theoretical and Applied Mechanics 2019 

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References

REFERENCES

Barrett, D.J., “The mechanics of z-fiber reinforcement,” Composite Structures, 312, pp. 23–32 (1996).CrossRefGoogle Scholar
Mair, R.I., “Advanced composite structures research in Australia,” Composite Structures, 57, pp. 3–10 (2002).CrossRefGoogle Scholar
Chao, C., Chen, F. and Shen, M., “An exact solution for thermal stresses in a three-phase composite cylinder under uniform heat flow,” International journal of solids and structures, 44, pp. 926–940 (2007).CrossRefGoogle Scholar
Xiao, J., Gilhooley, D., Batra, R., Gillespie, J. and McCarthy, M., “Analysis of thick composite laminates using a higher-order shear and normal deformable plate theory (HOSNDPT) and a meshless method,” Composites Part B: Engineering, 39, pp. 414–427 (2008).CrossRefGoogle Scholar
Pradeep, V. and Ganesan, N., “Thermal buckling and vibration behavior of multi-layer rectangular viscoelastic sandwich plates,” Journal of Sound and Vibration, 310, pp. 169–183 (2008).CrossRefGoogle Scholar
Papargyris, D., Day, R., Nesbitt, A. and Bakavos, D., “Comparison of the mechanical and physical properties of a carbon fibre epoxy composite manufactured by resin transfer moulding using conventional and microwave heating,” Composites Science and Technology, 68, pp. 1854–1861 (2008).CrossRefGoogle Scholar
Topal, U. and Uzman, U., “Thermal buckling load optimization of laminated composite plates,” Thin-Walled Structures, 46, pp. 667–675 (2008).CrossRefGoogle Scholar
Antonucci, V., Giordano, M., Hsiao, K.T. and Advani, S.G., “A methodology to reduce thermal gradients due to the exothermic reactions in composites processing,” International journal of heat and mass transfer, 45, pp. 1675–1684 (2002).CrossRefGoogle Scholar
Guo, Z.S., Du, S. and Zhang, B., “Temperature field of thick thermoset composite laminates during cure process,” Composites science and technology, 65, pp. 517–523 (2005).CrossRefGoogle Scholar
Behzad, T. and Sain, M., “Finite element modeling of polymer curing in natural fiber reinforced composites,” Composites Science and Technology, 67, pp. 1666–1673 (2007).CrossRefGoogle Scholar
Dlouhy, I., Chlup, Z., Boccaccini, D., Atiq, S. and Boccaccini, A., “Fracture behaviour of hybrid glass matrix composites: thermal ageing effects,” Composites Part A: Applied Science and Manufacturing, 34, pp. 1177–1185 (2003).CrossRefGoogle Scholar
Gilbert, A., Kokini, K. and Sankarasubramanian, S., “Thermal fracture of zirconia-mullite composite thermal barrier coatings under thermal shock: An experimental study,” Surface and Coatings Technology, 202, pp. 2152–2161 (2008).CrossRefGoogle Scholar
Gilbert, A., Kokini, K. and Sankarasubramanian, S., “Thermal fracture of zirconia-mullite composite thermal barrier coatings under thermal shock: A numerical study,” Surface and Coatings Technology, 203, pp. 91–98 (2008).CrossRefGoogle Scholar
Wang, F., Hua, Q. and Liu, C.S., “Boundary function method for inverse geometry problem in two-dimensional anisotropic heat conduction equation,” Applied Mathematics Letters, 84, pp. 130–136 (2018).CrossRefGoogle Scholar
Gu, Y., He, X., Chen, W. and Zhang, C., “Analysis of three-dimensional anisotropic heat conduction problems on thin domains using an advanced boundary element method,” Computers & Mathematics with Applications, 75(1), pp. 33–44 (2018).CrossRefGoogle Scholar
Wang, F., Chen, W., Qu, W. and Gu, Y., “A BEM formulation in conjunction with parametric equation approach for three-dimensional Cauchy problems of steady heat conduction,” Engineering Analysis with Boundary Elements, 63, pp. 1–14 (2016).CrossRefGoogle Scholar
Dulk, I. and Kovacshazy, T., “Steady-state heat conduction in multilayer bodies: An analytical solution and simplification of the eigenvalue problem,” International Journal of Heat and Mass Transfer, 67, pp. 784–797 (2013).CrossRefGoogle Scholar
De Monte, F., “Transient heat conduction in one-dimensional composite slab. A ‘natural’analytic approach,” International Journal of Heat and Mass Transfer, 43, pp. 3607–3619 (2000).CrossRefGoogle Scholar
De Monte, F., “An analytic approach to the unsteady heat conduction processes in one-dimensional composite media,” International Journal of Heat and Mass Transfer, 45, pp. 1333–1343 (2002).CrossRefGoogle Scholar
De Monte, F., “Unsteady heat conduction in two-dimensional two slab-shaped regions. Exact closed-form solution and results,” International Journal of Heat and Mass Transfer, 46, pp. 1455–1469 (2003).CrossRefGoogle Scholar
De Monte, F., “Multi-layer transient heat conduction using transition time scales,” International journal of thermal sciences, 45, pp. 882–892 (2006).CrossRefGoogle Scholar
Salt, H., “Transient conduction in a two-dimensional composite slab—I. Theoretical development of temperature modes,” International Journal of Heat and Mass Transfer, 26, pp. 1611–1616 (1983).CrossRefGoogle Scholar
Salt, H., “Transient conduction in a two-dimensional composite slab—II. Physical interpretation of temperature modes” International Journal of Heat and Mass Transfer, 26, pp. 1617–1623 (1983).CrossRefGoogle Scholar
Miller, J. and Weaver, P., “Temperature profiles in composite plates subject to time-dependent complex boundary conditions,” Composite Structures, 59, pp. 267–278 (2003).CrossRefGoogle Scholar
Blanc, M. and Touratier, M., “An efficient and simple refined model for temperature analysis in thin laminated composites,” Composite Structures, 77, pp. 193–205 (2007).CrossRefGoogle Scholar
Hsieh, M.H. and Ma, C.C., “Analytical investigations for heat conduction problems in anisotropic thin-layer media with embedded heat sources,” International Journal of Heat and Mass Transfer, 45, pp. 4117–4132 (2002).CrossRefGoogle Scholar
Ma, C.C. and Chang, S.W., “Analytical exact solutions of heat conduction problems for anisotropic multi-layered media,” International Journal of Heat and Mass Transfer, 47, pp. 1643–1655 (2004).CrossRefGoogle Scholar
Norouzi, M., Rahmani, H., Birjandi, A.K. and Joneidi, A.A., “A general exact analytical solution for anisotropic non-axisymmetric heat conduction in composite cylindrical shells,” International Journal of Heat and Mass Transfer, 93, pp. 41–56 (2016).CrossRefGoogle Scholar
Kayhani, M., Norouzi, M. and Delouei, A.A., “A general analytical solution for heat conduction in cylindrical multilayer composite laminates,” International Journal of Thermal Sciences, 52, pp. 73–82 (2012).CrossRefGoogle Scholar
Kayhani, M., Norouzi, M. and Delouei, A.A., “An exact solution of axi-symmetric conductive heat transfer in cylindrical composite laminate under the general boundary condition,” International Journal of Mechanical andMechatronics Engineering, 4, pp. 776–783 (2010).Google Scholar
Kayhani, M., Norouzi, M. and Delouei, A. A., “On heat conduction problem in multi-layer composite pin fins,” 3th International Conference of Advanced Composite Materials Engineering, Brasov, Romani, pp. 89–94 (2010).Google Scholar
Delouei, A.A., Kayhani, M. and Norouzi, M., “Exact analytical solution of unsteady axi-symmetric conductive heat transfer in cylindrical orthotropic composite laminates,” International Journal of Heat and Mass Transfer, 55, pp. 4427–4436 (2012).CrossRefGoogle Scholar
Tarn, J.Q., “Exact solutions for functionally graded anisotropic cylinders subjected to thermal and mechanical loads,” International Journal of Solids and Structures, 38, pp. 8189–8206 (2001).CrossRefGoogle Scholar
Tarn, J.Q. and Wang, Y.M., “End effects of heat conduction in circular cylinders of functionally graded materials and laminated composites,” International Journal of Heat and Mass Transfer, 47, pp. 5741–5747 (2004).CrossRefGoogle Scholar
Singh, S. and Jain, P.K., “Analytical solution to transient heat conduction in polar coordinates with multiple layers in radial direction,” International journal of thermal Sciences, 47, pp. 261–273 (2008).CrossRefGoogle Scholar
Jain, P.K. and Singh, S., “An exact analytical solution for two-dimensional, unsteady, multilayer heat conduction in spherical coordinates,” International Journal of Heat and Mass Transfer, 53, pp. 2133–2142 (2010).CrossRefGoogle Scholar
Kayhani, M., Shariati, M., Norouzi, M. and Demneh, M.K., “Exact solution of conductive heat transfer in cylindrical composite laminate,” Heat and mass transfer, 46, pp. 83 (2009).CrossRefGoogle Scholar
Norouzi, M., Niya, S.R., Kayhani, M.H., Shariati, M., Demneh, M.K. and Naghavi, M.S., “Exact solution of unsteady conductive heat transfer in cylindrical composite laminates,” Journal of Heat Transfer, 134, pp. 101301 (2012).CrossRefGoogle Scholar
Noruozi, M., Delouei, A.A. and Seilsepour, M., “general exact solution for heat conduction in multilayer spherical composite laminates,” Composite Structures, 106, pp. 288–295 (2013).CrossRefGoogle Scholar
Norouzi, M. and Rahmani, H., “On exact solutions for anisotropic heat conduction in composite conical shells,” International Journal of Thermal Sciences, 94, pp. 110–125 (2015).CrossRefGoogle Scholar
Norouzi, M. and Rahmani, H., “An exact analysis for transient anisotropic heat conduction in truncated composite conical shells,” Applied Thermal Engineering, 124, pp. 422–431 (2017).CrossRefGoogle Scholar
Ozisik, M.N., Heat conduction, 2nd edition, John Wiley & Sons, Canada (1993).Google Scholar
Myint-U, T. and Debnath, L., “Linear partial differential equations for scientists and engineers,” Springer Science & Business Media, (2007).Google Scholar
Abramowitz, M. and Stegun, I.A., Handbook of mathematical functions: with formulas, graphs, and mathematical tables, Vol. 9, Dover, New York, (1972).Google Scholar
Chattopadhyay, S., Pressure vessels: design and practice, 1st edition, CRCpress, Boca Raton (2004).CrossRefGoogle Scholar
Aleck, B.J., Filament wound spherical pressure vessel, in, Google Patents, (1972).Google Scholar
Howell, J.R., Menguc, M.P. and Siegel, R., Thermal radiation heat transfer, 5th edition, CRC press, Boca Raton (2010).CrossRefGoogle Scholar
Windhorst, T. and Blount, G., “Carbon-carbon composites: a summary of recent developments and applications,” Materials & Design, 18, pp. 11–15 (1997).CrossRefGoogle Scholar
Touloukian, Y.S., Powell, R., Ho, C. and Klemens, P., Thermophysical Properties of Matter-The TPRC Data Series, Volume 2. Thermal Conductivity-Nonmetallic Solids, in, Thermophysical and Electronic Properties Information Analysis Center Lafayette In, (1971).Google Scholar