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Research Papers: Design and Analysis

General Solution for Equation of Transient Heat Conduction in Functionally Graded Material Hollow Cylinder With Piezoelectric Internal and External Layers

[+] Author and Article Information
M. Jabbari

Mechanical Engineering Department,
Islamic Azad University,
South Tehran Branch,
Tehran 145 781 5751, Iran

M. A. Kiani

Mechanical Engineering Department,
Islamic Azad University,
South Tehran Branch,
Tehran 615 563 5893, Iran

Contributed by the Pressure Vessel and Piping Division of ASME for publication in the JOURNAL OF PRESSURE VESSEL TECHNOLOGY. Manuscript received February 3, 2015; final manuscript received June 24, 2017; published online August 8, 2017. Assoc. Editor: Albert E. Segall.

J. Pressure Vessel Technol 139(5), 051206 (Aug 08, 2017) (6 pages) Paper No: PVT-15-1022; doi: 10.1115/1.4037195 History: Received February 03, 2015; Revised June 24, 2017

In this paper, the exact solution of the equation of transient heat conduction in two dimensions for a hollow cylinder made of functionally graded material (FGM) and piezoelectric layers is developed. Temperature distribution, as function of radial and circumferential directions and time, is analytically obtained for different layers, using the method of separation of variables and generalized Bessel function. The FGM properties are assumed to depend on the variable r, and they are expressed as power functions of r.

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References

Yang, Y.-C. , Wang, T.-S. , and Chen, C.-K. , 1986, “ Thermoelastic Transient Response of an Infinitely Long Annular Cylinder,” J. Therm. Stresses, 9(1), pp. 19–30. [CrossRef]
Awaji, H. , and Sivakumar, R. , 2001, “ Temperature and Stress Distributions in a Hollow Cylinder of Functionally Graded Material: The Case of Temperature-Independent Material Properties,” J. Am. Ceram. Soc., 84(5), pp. 1059–1065. [CrossRef]
Awaji, H. , and Sivakumar, R. , 2002, “ Analysis of Transient Temperature and Stress Distributions in an Functionally Graded Material Hollow Cylinder,” Trans. Jpn. Soc. Mech. Eng., 68(666), pp. 293–299. [CrossRef]
Jabbari, M. , Vaghari, A. R. , Bahtui, A. , and Eslami, M. R. , 2008, “ Exact Solution for Asymmetric Transient Thermal and Mechanical Stresses in FGM Hollow Cylinders With Heat Source,” Struct. Mech. Eng., 29(5), pp. 551–565. [CrossRef]
Jabbari, M. , Sohrabpour, S. , and Eslami, M. R. , 2002, “ Mechanical and Thermal Stresses in a Functionally Graded Hollow Cylinder Due to Radially Symmetric Loads,” Int. J. Pressure Vessels Piping, 79(7), pp. 493–497. [CrossRef]
Jabbari, M. , Sohrabpour, S. , and Eslami, M. R. , 2003, “ General Solution for Mechanical and Thermal Stresses in a Functionally Graded Hollow Cylinder Due to Nonaxisymmetric Steady-State Loads,” ASME J. Appl. Mech., 70(1), pp. 111–118. [CrossRef]
Jabbari, M. , Bahtui, A. , and Eslami, M. R. , 2006, “ Axisymmetric Mechanical and Thermal Stresses in Thick Long FGM Cylinders,” J. Therm. Stresses, 29(7), pp. 643–663. [CrossRef]
Jabbari, M. , Mohazzab, A. H. , and Bahtui, A. , 2009, “ One-Dimensional Moving Heat Source in a Hollow FGM Cylinder,” ASME J. Appl. Mech., 131(2), p. 021202.
Kayhani, M. H. , Shariati, M. , Nourozi, M. , and Demneh, M. K. , 2009, “ Exact Solution of Conductive Heat Transfer in Cylindrical Composite Laminate,” Heat Mass Transfer, 46(1), pp. 83–94. [CrossRef]
Eslami, M. R. , Babai, M. H. , and Poultangari, R. , 2005, “ Thermal and Mechanical Stresses in a Functionally Graded Thick Sphere,” Int. J. Pressure Vessels Piping, 82(7), pp. 522–527. [CrossRef]
Asgari, M. , and Akhlaghi, M. , 2009, “ Transient Heat Conduction in Two-Dimensional Functionally Graded Hollow Cylinder With Finite Length,” Heat Mass Transfer, 45(11), pp. 1383–1392. [CrossRef]
Singh, S. , Jain, P. K. , and Rizwan-Uddin , 2008, “ Analytical Solution to Transient Heat Conduction in Polar Coordinates With Multiple Layers in Radial Direction,” Int. J. Therm. Sci., 47(3), pp. 261–273. [CrossRef]
Hosseini, S. M. , Akhlaghi, M. , and Shakeri, M. , 2007, “ Transient Heat Conduction in Functionally Graded Thick Hollow Cylinders by Analytical Method,” Heat Mass Transfer, 43(7), pp. 669–675. [CrossRef]
Chu, H. S. , and Chen, L. S. , 1989, “ Transient Thermal Stresses of a Composite Hollow Cylinder Heated by a Moving Line Source,” Comput. Struct., 33(5), pp. 1205–1214. [CrossRef]

Figures

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Fig. 1

Geometry of the laminated shell

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Fig. 2

Transient temperature distribution in the outer piezo layer hollow cylinder

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Fig. 3

Transient temperature distribution in FGM hollow cylinder

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Fig. 4

Transient temperature distribution in the inner piezo layer

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Fig. 5

Transient temperature with various power law indices

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Fig. 6

Temperature distribution in the outer piezo layer at θ=π/3

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Fig. 7

Temperature distribution in FGM layer at θ=π/3

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Fig. 8

Temperature distribution in the inner piezo layer at θ=π/3

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Fig. 9

The comparison of present results and method in Ref. [4]

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