zbMATH — the first resource for mathematics

Transient hyperbolic heat conduction in thick-walled FGM cylinders and spheres with exponentially-varying properties. (English) Zbl 1278.80002
Summary: This paper focuses on non-Fourier hyperbolic heat conduction analysis for heterogeneous hollow cylinders and spheres made of functionally graded material (FGM). All the material properties vary exponentially across the thickness, except for the thermal relaxation parameter which is taken to be constant. The cylinder and sphere are considered to be cylindrically and spherically symmetric, respectively, leading to one-dimensional heat conduction problems. The problems are solved analytically in the Laplace domain, and the results obtained are transformed to the real-time space using the modified Durbin’s numerical inversion method. The transient responses of temperature and heat flux are investigated for different inhomogeneity parameters and relative temperature change values. The comparisons of temperature distribution and heat flux between various time and material properties are presented in the form of graphs.

80A20 Heat and mass transfer, heat flow (MSC2010)
PDF BibTeX Cite
Full Text: DOI
[1] Al-Nimr, M.A.; Naji, M., The hyperbolic heat conduction equation in an anisotropic material, Int. J. thermophys., 21, 281-287, (2000)
[2] Babaei, M.H.; Chen, Z.T., Hyperbolic heat conduction in a functionally graded hollow sphere, Int. J. thermophys., 29, 1457-1469, (2008)
[3] Babaei, M.H.; Chen, Z.T., Transient hyperbolic heat conduction in a functionally graded hollow cylinder, Int. J. thermophys., 24, 325-330, (2010)
[4] Calım, F.F., Dynamic analysis of beams on viscoelastic foundation, Eur. J. mech. A solid, 28, 469-476, (2009) · Zbl 1158.74400
[5] Chen, H.T.; Peng, S.Y.; Yang, P.C., Numerical method for hyperbolic inverse heat conduction problems, Int. commun. heat mass, 28, 847-856, (2001)
[6] Chen, T.M., Numerical solution of hyperbolic heat conduction problems in the cylindrical coordinate system by the hybrid green’s function method, Int. J. heat mass transfer, 53, 1319-1325, (2010) · Zbl 1183.80018
[7] Durbin, F., Numerical inversion of Laplace transforms: an efficient improvement to dubner and abate’s method, Comput. J., 17, 371-376, (1974) · Zbl 0288.65072
[8] Hosseini, S.M.; Akhlaghi, M.; Shakeri, M., Transient heat conduction in functionally graded thick hollow cylinders by analytical method, Heat mass transfer, 43, 669-675, (2007)
[9] Jabbari, M.; Mohazzab, A.H.; Bahtui, A., One-dimensional moving heat source in a hollow FGM cylinder, J. press. vess-T asme, 131, 021202.1-021202.7, (2009)
[10] Jiang, F., Solution and analysis of hyperbolic heat propagation in hollow spherical objects, Heat mass transfer, 42, 1083-1091, (2006)
[11] Jiang, F.M.; Sousa, A.C.M., Analytical solution for hyperbolic heat conduction in a hollow sphere, J. thermophys. heat transfer, 19, 595-598, (2005)
[12] Liu, K.C.; Chen, H.T., Numerical analysis for the hyperbolic heat conduction problem under a pulsed surface disturbance, Appl. math. comput., 159, 887-901, (2004) · Zbl 1063.65109
[13] Liu, K.-C.; Lin, C.-N.; Wang, J.-S., Numerical solutions for the hyperbolic heat conduction problems in a layered solid cylinder with radiation surface, Appl. math. comput., 164, 805-820, (2005) · Zbl 1070.65103
[14] Lu, X.; Tervola, P.; Viljanen, M., Transient analytical solution to heat conduction in composite circular cylinder, Int. J. heat mass transfer, 49, 341-348, (2006) · Zbl 1189.74029
[15] Moosaie, A., Axisymmetric non-Fourier temperature field in a hollow sphere, Arch. appl. mech., 79, 679-694, (2009) · Zbl 1264.80014
[16] Shirmohammadi, R.; Moosaie, A., Non-Fourier heat conduction in a hollow sphere with periodic surface heat flux, Int. commun. heat mass, 36, 827-833, (2009)
[17] Sutradhar, A.; Paulino, G.H.; Gray, L.J., Transient heat conduction in homogeneous and non-homogeneous materials by the Laplace transform Galerkin boundary element method, Eng. anal. bound. elem., 26, 119-132, (2002) · Zbl 0995.80010
[18] Tsai, C.S.; Lin, Y.C.; Hung, C.I., A study on the non-Fourier effects in spherical media due to sudden temperature changes on the surfaces, Heat mass transfer, 41, 709-716, (2005)
[19] Wang, H.; Qin, Q.-H.; Kang, Y.-L., A meshless model for transient heat conduction in functionally graded materials, Comput. mech., 38, 51-60, (2006) · Zbl 1097.80001
[20] Zanchini, E.; Pulvirenti, B., Periodic heat conduction with relaxation time in cylindrical geometry, Heat mass transfer, 33, 319-326, (1998)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.