Analytical Solution of Heat Transfer in a Cone Made of Functionally Graded Material

Document Type : Research Article

Authors

1 Shahrood University of Technology

2 بجنورد-فنی و مهندسی- گروه مهندسی مکانیک

Abstract

In the current study, the problem of two-dimensional steady-state heat conduction in a truncated hollow cone made of functionally graded materials is referred and an exact analytical solution is presented. In the present study, the properties of a material are modified in accordance with a power function. The thermal boundary conditions are also assumed to be non-homogeneous. The separation of variable method is implemented to acquire the exact steady-state temperature distribution. The obtained solution is adequately verified using numerical data. To further demonstrate the ability of the solution, an illustrative case that is exposed to a combination of boundary conditions is studied. In particular, the influences of effective parameters on the temperature distribution are investigated for the current geometry. The outcome of this study would be helpful to shed light on the process of designing and optimizing relatively complex geometries. Also, considering the analyticity of the present solution, the results of this study can be useful for a better understanding of the heat transfer mechanisms of functionally graded materials. In the present case, increasing the amount of m and κ, the thermal conductivity increased by about 8 and 2 percent respectively, which would increase the distribution of cone temperature.

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Main Subjects

References

[1] B. Yildirim, S. Dag, F. Erdogan, Three dimensional fracture analysis of FGM coatings under thermomechanical loading, International journal of Fracture, 132(4) (2005) 371-397.
[2] V. Birman, T. Keil, S. Hosder, Functionally graded materials in engineering, in:  Structural interfaces and attachments in biology, Springer, 2013, pp. 19-41.
[3] F. Watari, A. Yokoyama, M. Omori, T. Hirai, H. Kondo, M. Uo, T. Kawasaki, Biocompatibility of materials and development to functionally graded implant for bio-medical application, Composites Science and Technology, 64(6) (2004) 893-908.
[4] W. Pompe, H. Worch, M. Epple, W. Friess, M. Gelinsky, P. Greil, U. Hempel, D. Scharnweber, K. Schulte, Functionally graded materials for biomedical applications, Materials Science and Engineering: A, 362(1-2) (2003) 40-60.
[5] Y. Miyamoto, W. Kaysser, B. Rabin, A. Kawasaki, R.G. Ford, Functionally graded materials: design, processing and applications, Springer Science & Business Media, 2013.
[6] R.M. Mahamood, E.T. Akinlabi, Functionally graded materials, Springer, 2017.
[7] S. Karimnejad, A.A. Delouei, M. Nazari, M. Shahmardan, M. Rashidi, S. Wongwises, Immersed boundary—thermal lattice Boltzmann method for the moving simulation of non-isothermal elliptical particles, Journal of Thermal Analysis and Calorimetry,   1-15.
[8] W. Ge, C. Zhao, B. Wang, Thermal radiation and conduction in functionally graded thermal barrier coatings. Part II: Experimental thermal conductivities and heat transfer modeling, International Journal of Heat and Mass Transfer, 134 (2019) 166-174.
[9] S. Karimnejad, A.A. Delouei, M. Nazari, M. Shahmardan, A. Mohamad, Sedimentation of elliptical particles using Immersed Boundary–Lattice Boltzmann Method: A complementary repulsive force model, Journal of Molecular Liquids, 262 (2018) 180-193.
[10] K. Torabi, H. Afshari, Thermo-Mechanical Stress Analysis in a Rotating Radially Graded FG-Disc with Non-Uniform Thickness.
[11] C. Nie, B. Yu, Inversing heat flux boundary conditions based on precise integration FEM without iteration and estimation of thermal stress in FGMs, International Journal of Thermal Sciences, 140 (2019) 201-224.
[12] A.A. Delouei, A. Emamian, S. Karimnejad, H. Sajjadi, A. Tarokh, On 2D asymmetric heat conduction in functionally graded cylindrical segments: A general exact solution, International Journal of Heat and Mass Transfer, 143 (2019) 118515.
[13] A.A. Delouei, A. Emamian, S. Karimnejad, H. Sajjadi, A closed-form solution for axisymmetric conduction in a finite functionally graded cylinder, International Communications in Heat and Mass Transfer, 108 (2019) 104280.
[14] H. Awaji, Temperature and stress distributions in a plate of functionally graded materials, in:  Fourth international congress on thermal stresses, 2001, pp. 8-11.
[15] M. Kayhani, M. Shariati, M. Nourozi, M.K. Demneh, Exact solution of conductive heat transfer in cylindrical composite laminate, Heat and mass transfer, 46(1) (2009) 83.
[16] M. Li, A.C. Lai, Analytical solution to heat conduction in finite hollow composite cylinders with a general boundary condition, International Journal of Heat and Mass Transfer, 60 (2013) 549-556.
[17] R. Bahadur, A. Bar-Cohen, Orthotropic thermal conductivity effect on cylindrical pin fin heat transfer, in:  ASME 2005 Pacific Rim Technical Conference and Exhibition on Integration and Packaging of MEMS, NEMS, and Electronic Systems collocated with the ASME 2005 Heat Transfer Summer Conference, American Society of Mechanical Engineers, 2005, pp. 245-252.
[18] S.M. Hosseini, M. Akhlaghi, M. Shakeri, Transient heat conduction in functionally graded thick hollow cylinders by analytical method, Heat and Mass Transfer, 43(7) (2007) 669-675.
[19] M. Kayhani, M. Norouzi, A.A. Delouei, A general analytical solution for heat conduction in cylindrical multilayer composite laminates, International Journal of Thermal Sciences, 52 (2012) 73-82.
[20] A.A. Delouei, M. Kayhani, M. Norouzi, Exact analytical solution of unsteady axi-symmetric conductive heat transfer in cylindrical orthotropic composite laminates, International Journal of Heat and Mass Transfer, 55(15-16) (2012) 4427-4436.
[21] M. Norouzi, H. Rahmani, A.K. Birjandi, A.A. Joneidi, A general exact analytical solution for anisotropic non-axisymmetric heat conduction in composite cylindrical shells, International Journal of Heat and Mass Transfer, 93 (2016) 41-56.
[22] H. Wang, C. Liu, Analytical solution of two-dimensional transient heat conduction in fiber-reinforced cylindrical composites, International Journal of Thermal Sciences, 69 (2013) 43-52.
[23] H. Ding, H. Wang, W. Chen, Dynamic responses of a functionally graded pyroelectric hollow sphere for spherically symmetric problems, International journal of mechanical sciences, 45(6-7) (2003) 1029-1051.
[24] A.A. Delouei, M. Norouzi, Exact analytical solution for unsteady heat conduction in fiber-reinforced spherical composites under the general boundary conditions, Journal of Heat Transfer, 137(10) (2015) 101701.
[25] A.H. Mohazzab, M. Jabbari, Two-dimensional stresses in a hollow FG Sphere with heat source, in:  Advanced Materials Research, Trans Tech Publ, 2011, pp. 700-705.
[26] M. Norouzi, A. Emamian, M. Davoodi, An analytical and experimental study on dynamics of a circulating Boger drop translating through Newtonian fluids at inertia regime, Journal of Non-Newtonian Fluid Mechanics, 267 (2019) 1-13.
[27] M. Davoodi, S. Lerouge, M. Norouzi, R. Poole, Secondary flows due to finite aspect ratio in inertialess viscoelastic Taylor–Couette flow, Journal of Fluid Mechanics, 857 (2018) 823-850.
[28] J. Torabi, Y. Kiani, M. Eslami, Linear thermal buckling analysis of truncated hybrid FGM conical shells, Composites Part B: Engineering, 50 (2013) 265-272.
[29] M. Akbari, Y. Kiani, M. Eslami, Thermal buckling of temperature-dependent FGM conical shells with arbitrary edge supports, Acta Mechanica, 226(3) (2015) 897-915.
[30] M. Norouzi, H. Rahmani, On exact solutions for anisotropic heat conduction in composite conical shells, International Journal of Thermal Sciences, 94 (2015) 110-125.
[31] O. Mn, Heat conduction, in, Wiley, New York, 1993.
[32] J.C. Halpin, Primer on Composite Materials Analysis, (Revised), Routledge, 2017.
Amirkabir Journal of Mechanical Engineering
Volume 53, Issue 1 (Special Issue)
April 2021
Pages 539-552

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