0
Research Papers: Thermal Systems

# A New Approach to Thermal Analysis of a Multilayered Cylindrical Structure With Imperfect Bonds and Internal Heat Source

[+] Author and Article Information
M. Bakhtiari

Department of Mechanical Engineering,
Iran University of Science and Technology,
Narmak, Tehran 16844, Iran
e-mail: m.bakhtiari@isme.ir

K. Daneshjou

Department of Mechanical Engineering,
Iran University of Science and Technology,
Narmak, Tehran 16844, Iran
e-mail: kjoo@iust.ac.ir

R. Alibakhshi

Department of Mechanical Engineering,
Iran University of Science and Technology,
Narmak, Tehran 16844, Iran
e-mail: r_alibakhshi@cmps2.iust.ac.ir

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received November 16, 2015; final manuscript received June 13, 2016; published online August 2, 2016. Assoc. Editor: Alan McGaughey.

J. Heat Transfer 138(12), 122801 (Aug 02, 2016) (8 pages) Paper No: HT-15-1734; doi: 10.1115/1.4034038 History: Received November 16, 2015; Revised June 13, 2016

## Abstract

In the present research, a new and straightforward mathematical model, named augmented state-space method, is introduced to solve the heat conduction equation for a multilayered orthotropic hollow cylinder with bonding imperfection in the presence of heat source. Since such problems including heat source are inherently inhomogeneous and complex, augmented state-space method converts these inhomogeneous equations into homogeneous ones. The transient solution will be achieved by present method based on laminate approximation theory in the Laplace domain, and then the solutions obtained are retrieved into the time domain by applying the numerical Laplace transform inversion. All material properties can be considered to vary continuously within the cylinder along the radial direction with arbitrary grading pattern. Based on the proposed method, the solution of heat conduction problem can be also obtained for general boundary conditions which may be included various combinations of arbitrary temperature, flux, or convection. Due to lack of any data on the transient thermal analysis corresponding to problems with imperfect bonds in the cylindrical coordinate system $(r,θ),$ comparison is carried out with the available results for the three-layer semi-circular annular region with perfect bonds in the literature. Finally, the influence of orthotropy and interface imperfection on the distribution of the temperature field for three-layer hollow cylinder, in which the second layer is made of orthotropic functionally graded material (FGM), will be visualized.

<>

## References

Lu, X. , Tervola, P. , and Viljanen, M. , 2006, “ Transient Analytical Solution to Heat Conduction in Composite Circular Cylinder,” Int. J. Heat Mass Transfer, 49(1–2), pp. 341–348.
Norouzi, M. , Rezaei Niya, S. M. , Kayhani, M. H. , Karimi Demneh, M. , and Naghavi, M. S. , 2012, “ Exact Solution of Unsteady Conductive Heat Transfer in Cylindrical Composite Laminates,” ASME J. Heat Transfer, 134(10), p. 101301.
Cossali, G. E. , 2009, “ Periodic Heat Conduction in a Solid Homogeneous Finite Cylinder,” Int. J. Therm. Sci., 48(4), pp. 722–732.
Hahn, D. W. , and Özisik, M. N. , 2012, Heat Conduction, 3rd ed., Wiley, Hoboken, NJ. [PubMed] [PubMed]
Zukauskas, A. , and Ziugzda, J. , 1985, Heat Transfer of a Cylinder in Crossflow, Academy of Sciences of the Lithuanian SSR, Hemisphere Publishing, Washington, DC.
Timoshenko, M. V. , 1996, “ Numerical Simulation of Heat Transfer in Multilayer Structures With Generalized Nonideal Contact,” J. Eng. Phys. Thermophys., 69(5), pp. 590–595.
Cheng, Z. Q. , and Batra, R. C. , 2001, “ Thermal Effects on Laminated Composite Shells Containing Interfacial Imperfections,” Compos. Struct., 52(1), pp. 3–11.
Liu, Y. , Mioduchowski, A. , and Ru, C. Q. , 2002, “ Effect of Imperfect Interface on Thermal Stresses-Assisted Matrix Cracking in Fiber Composites,” J. Therm. Stresses, 25(6), pp. 585–599.
Duschlbauer, D. , Pettermann, H. E. , and Bohm, H. J. , 2003, “ Heat Conduction of Spheroidal Inhomogeneity With Imperfectly Bonded Interface,” J. Appl. Phys., 94(3), pp. 1539–1549.
Cai, J. B. , Chen, W. Q. , and Ye, G. R. , 2004, “ Effect of Interlaminar Bonding Imperfections on the Behavior of Angle-Ply Laminated Cylindrical Panels,” Compos. Sci. Technol., 64(12), pp. 1753–1762.
Chen, W. Q. , Jung, J. P. , Kim, G. W. , and Lee, K. Y. , 2005, “ Cross-Ply Laminated Cylindrical Panels With Viscous Interfaces Subjected to Static Loading,” Eur. J. Mech. A/Solids, 24(5), pp. 728–739.
Chen, W. Q. , Zhou, Y. Y. , Lü, C. F. , and Ding, H. J. , 2009, “ Bending of Multiferroic Laminated Rectangular Plates With Imperfect Interlaminar Bonding,” Eur. J. Mech. A/Solids, 28(4), pp. 720–727.
Salti, B. , and Laraqi, N. , 1999, “ 3-D Numerical Modeling of Heat Transfer Between Two Sliding Bodies: Temperature and Thermal Contact Resistance,” Int. J. Heat Mass Transfer, 42(13), pp. 2363–2374.
Bauzin, J. G. , and Laraqi, N. , 2004, “ Simultaneous Estimation of Frictional Heat Flux and Two Thermal Contact Parameters for Sliding Solids,” Numer. Heat Transfer, 45(4), pp. 313–328.
Salazar, A. , and Celorrio, R. , 2006, “ Application of the Thermal Quadrupole Method to the Propagation of Thermal Waves in Multilayered Cylinders,” J. Appl. Phys., 100(11), p. 113535.
Santos, H. , Soares, C. M. M. , Soares, C. A. M. , and Reddy, J. N. , 2008, “ A Semi-Analytical Finite Element Model for the Analysis of Cylindrical Shells Made of Functionally Graded Materials Under Thermal Shock,” Compos. Struct., 86(1–3), pp. 10–21.
Delouei, A. A. , and Norouzi, M. , 2015, “ Exact Analytical Solution for Unsteady Heat Conduction in Fiber-Reinforced Spherical Composites Under the General Boundary Conditions,” ASME J. Heat Transfer, 137(10), pp. 101701–101708.
Keles, I. , and Conker, C. , 2011, “ Transient Hyperbolic Heat Conduction in Thick-Walled FGM Cylinders and Spheres With Exponentially-Varying Properties,” Eur. J. Mech. A/Solids, 30(3), pp. 449–455.
Ramadan, K. , and Al-Nimr, M. A. , 2009, “ Analysis of Transient Heat Transfer in Multilayer Thin Films With Nonlinear Thermal Boundary Resistance,” Int. J. Therm. Sci., 48(9), pp. 1718–1727.
Lu, X. , Tervola, P. , and Viljanen, M. , 2005, “ A New Analytical Method to Solve Heat Equation for Multi-Dimensional Composite Slab,” J. Phys. A: Math. Gen., 38(13), pp. 2873–2890.
Chen, T.-M. , 2013, “ A Hybrid Transform Technique for the Hyperbolic Heat Conduction Problems,” Int. J. Heat Mass Transfer, 65, pp. 274–279.
Tarn, J. Q. , and Wang, Y. M. , 2004, “ End Effects of Heat Conduction in Circular Cylinders of Functionally Graded Materials and Laminated Composites,” Int. J. Heat Mass Transfer, 47(26), pp. 5741–5747.
Asgari, M. , and Akhlaghi, M. , “ Transient Heat Conduction in Two-Dimensional Functionally Graded Hollow Cylinder With Finite Length,” Heat Mass Transfer, 45(11), pp. 1383–1392.
Tonini, S. , and Cossali, G. E. , 2012, “ A Novel Analytical Solution of the Non-Uniform Convective Boundary Conditions Problem for Heat Conduction in Cylinders,” Int. Commun. Heat Mass Transfer, 39(8), pp. 1059–1065.
Wang, H. M. , 2013, “ An Effective Approach for Transient Thermal Analysis in a Functionally Graded Hollow Cylinder,” Int. J. Heat Mass Transfer, 67, pp. 499–505.
Daneshjou, K. , Bakhtiari, M. , Alibakhshi, R. , and Fakoor, M. , 2015, “ Transient Thermal Analysis in 2D Orthotropic FG Hollow Cylinder With Heat Source,” Int. J. Heat Mass Transfer, 89, pp. 977–984.
Singh, S. , Jain, P. K. , and Uddin, R. , 2011, “ Finite Integral Transform Method to Solve Asymmetric Heat Conduction in A Multilayer Annulus With Time-Dependent Boundary Conditions,” J. Nucl. Eng. Des., 241(1), pp. 144–154.
Singh, S. , Jain, P. K. , and Uddin, R. , 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.
Chen, W. Q. , Bian, Z. G. , Lv, C. F. , and Ding, H. J. , 2004, “ 3D Free Vibration Analysis of a Functionally Graded Piezoelectric Hollow Cylinder Filled With Compressible Fluid,” Int. J. Solids Struct., 41(3–4), pp. 947–964.
Hasheminejad, S. M. , and Rajabi, M. , 2007, “ Acoustic Scattering Characteristics of a Thick-Walled Orthotropic Cylindrical Shell at Oblique Incidence,” Ultrasonics, 47(1–4), pp. 32–48. [PubMed]
Powers, J. M. , 2004, “ On the Necessity of Positive Semi-Definite Conductivity and Onsager Reciprocity in Modelling Heat Conduction in Anisotropic Media,” ASME J. Heat Transfer, 126(5), pp. 670–675.
Rajabi, M. , and Hasheminejad, S. M. , 2009, “ Acoustic Resonance Scattering From a Multilayered Cylindrical Shell With Imperfect Bonding,” Ultrasonics, 49(8), pp. 682–695. [PubMed]

## Figures

Fig. 1

Mechanical model of jth layer of cylindrical structure

Fig. 2

Transient temperature distribution in radial direction at θ=π/2

Fig. 3

Hollow three-layer annular region example problem

Fig. 4

Contours of temperature distribution in r and θ directions: (a) η=0.4, (b) η=1, (c) η=2

Fig. 5

Temperature distribution in radial direction for different values of contact resistance: (a) R = 0.3 × 10−4, (b) R = 0.8 × 10−4, (c) R = 2 × 10−4, (d) R = 5 × 10−4

Fig. 6

Transient temperature distribution for different values of θ and η at r = 0.8

## Errata

Some tools below are only available to our subscribers or users with an online account.

### Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related Proceedings Articles
Related eBook Content
Topic Collections