Exact Thermal Analysis of Functionally Graded Cylindrical and Spherical Vessels

Yıl 2017, Cilt: 9 Sayı: 2, 112 - 126, 04.07.2017

Vebil Yıldırım

https://doi.org/10.24107/ijeas.318459

Cited By: 4

Öz

Thermal
analyses of radially functionally graded (FG) thick-walled a spherical vessel and
an infinite cylindrical vessel or a circular annulus are conducted analytically
by the steady-state 1-D Fourier heat conduction theory under Dirichlet’s
boundary conditions. By employing simple-power material grading pattern the
differential equations are obtained in the form of Euler-Cauchy types.
Analytical solution of the differential equations gives the temperature field
and the heat flux distribution in the radial direction in a closed form. Three
different physical metal-ceramic pairs first considered to study the effect of
the aspect ratio, which is defined as the inner radius to the outer radius of
the structure, on the temperature and heat flux variation along the radial coordinate.
Then a parametric study is performed with hypothetic inhomogeneity indexes for
varying aspect ratios.     

Anahtar Kelimeler

Thermal analysis; functionally graded; exact solution; axisymmetric; cylindrical vessel, spherical vessel, inhomogeneity index, aspect ratio, thick-walled

Kaynakça

• Chang, Y.P., Tsou, R.C.H., Heat conduction in an anisotropic medium homogeneous in cylindrical regions—steady state. ASME J. Heat Transfer, 99(1), 132–134. 1977.
• Chang, Y. P., Tsou, R.C.H., Heat conduction in an anisotropic medium homogeneous in cylindrical coordinates-unsteady state. ASME J. Heat Transfer, 99(1), 41–46, 1977.
• Ootao, Y., Tanigawa, Y., Fukuda T., Axisymmetric transient thermal stress analysis of a multilayered composite hollow cylinder. Journal of Thermal Stresses, 14(2), 201-213, 1991.
• Obata, Y., Noda, N., Steady thermal stresses in a hollow circular cylinder and a hollow sphere of a functionally gradient material. Journal of Thermal Stresses, 17(3), 471–487, 1994.
• Zimmerman, R.W., Lutz, M.P., Thermal stresses and thermal expansion in a uniformly heated functionally graded cylinder. J. Therm. Stresses, 22 (2), 177–188, 1999.
• Tarn, J.Q., Exact solutions for functionally graded anisotropic cylinders subjected to thermal and mechanical loads. Int. J. Solids Struct., 38, 8189–8206, 2001.
• Awaji, H., Sivakuman, R., Temperature and stress distributions in a hollow cylinder of functionally graded material: the case of temperature-dependent material properties. Journal of American Ceramic Society, 1059-1065, 2001.
• Jabbari, M., Sohrabpor, S., Eslami, M.R., Mechanical and thermal stresses in a functionally graded hollow cylinder due to radially symmetric loads. Int. J. Pressure Vessels Piping, 79, 493–497, 2002.
• Jabbari, M., Sohrabpour, S., Eslami, M.R., General solution for mechanical and thermal stresses in a functionally graded hollow cylinder due to nonaxisymmetric steady-state loads. ASME J. Appl. Mech., 70 , 111–118, 2003.
• Jabbari, M., Bahtui, A., Eslami, M.R., Axisymmetric mechanical and thermal stresses in thick long FGM cylinders. J. Therm. Stresses, 29 (7), 643–663, 2006.
• Liew, K.M., Kitipornchai, S., Zhang, X.Z., Lim, C.W., Analysis of the thermal stress behaviour of functionally graded hollow circular cylinders. Int. J. Solids Struct., 40, 2355–2380, 2003.
• Tarn, J.Q., Wang, Y.M., End effects of heat conduction in circular cylinders of functionally graded materials and laminated composites. Int. J. Heat Mass Transfer, 47, 5741–5747, 2004.
• Ruhi, M., Angoshtari, A., Naghdabadi, R., Thermoelastic analysis of thick-walled finite-length cylinders of functionally graded materials. Journal of Thermal Stresses, 28 (4), 391-408, 2005.
• Oral, A., Anlas, G., Effects of radially varying moduli on stress distribution of nonhomogeneous anisotropic cylindrical bodies. International Journal of Solids and Structures, 5568–5588, 2005.
• Eslami, M.R., Babai, M.H., Poultangari, R., Thermal and mechanical stresses in a functionally graded thick sphere. Int. J. Pressure Vessels Piping, 82 (7), 522–527, 2005.
• Ootao, Y., Tanigawa, Y., Transient thermoelastic analysis for a functionally graded hollow cylinder. Journal of Thermal Stresses, 29(11), 1031–1046, 2006.
• Pelletier, J.L., Vel, S.S., An exact solution for the steady-state thermoelastic response of functionally graded orthotropic cylindrical shells. Int. J. Solids Struct., 43, 1131–1158, 2006.
• Birman, V., Byrd., L.W., Modeling and analysis of functionally graded materials and structures. Applied Mechanics Reviews, 60, 195-216, 2007.
• Kayhani, M.H., Shariati, M., Nourozi, M., Demneh, M.K., Exact solution of conductive heat transfer in cylindrical composite laminate. Heat Mass Transfer, 46, 83–94, 2009.
• Kayhani, M.H., Norouzi, M., Delouei, A.A., A general analytical solution for heat conduction in cylindrical multilayer composite laminates. Int. J. Therm. Sci., 52, 73–82, 2012.
• Hosseini, S.M., Abolbashari, M.H., A unified formulation for the analysis of temperature field in a thick hollow cylinder made of functionally graded materials with various grading patterns. Heat Transfer Eng., 33, 261–271, 2012.
• Bayat, Y., Ghannad, M., Torabi, H., Analytical and numerical analysis for the FGM thick sphere under combined pressure and temperature loading. Archive of Applied Mechanics, 229-242, 2012.
• Lee, S.Y., Huang, C.C., Analytic solutions for heat conduction in functionally graded circular hollow cylinders with time-dependent boundary conditions. Mathematical Problems in Engineering, Article ID 816385, 1-8. 2013.
• Wang, H.M., An effective approach for transient thermal analysis in a functionally graded hollow cylinder. International Journal of Heat and Mass Transfer, 67, 499-505, 2013.
• Li, H., Liu, Y., Functionally graded hollow cylinders with arbitrary varying material properties under non-axisymmetric loads. Mechanics Research Communications, 55, 1-9, 2014.
• Delouei, A.A., Norouzi, M., Exact analytical solution for unsteady heat conduction in fiber-reinforced spherical composites under the general boundary conditions. Journal of Heat Transfer, 137, 1-8. 2015.
• Arefi, M., Nonlinear thermal analysis of a hollow functionally graded cylinder with temperature-variable material properties. Journal of Applied Mechanics and Technical Physics, 56(2), 267-273, 2015.
• Chen, A., Jian, S., Lumped models for transient thermal analysis of multilayered composite pipeline with active heating. Applied Thermal Engineering, 87, 749–759, 2015.
• Daneshjou, K., Bakhtiari, M., Parsania H., Fakoor, M., Non-Fourier heat conduction analysis of infinite 2D orthotropic FG hollow cylinders subjected to time-dependent heat source. Applied Thermal Engineering, 98, 582–590, 2016.
• Hetnarski, B., Eslami, M.R., Thermal Stresses-Advanced Theory and Applications, Springer. Chap. 4-ISBN: 978-1-4020-9246-62009.