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In this work, an exact analytical solution to the axisymmetric heat conduction equation for hollow spherical objects with temperature-dependent thermal conductivity is presented. The nonlinear differential equation is first transformed into a linear one by means of an integral transform method. Then, the separation of variables method is employed to solve the transformed linear equation. Ultimately, we use the inverse transform to obtain the physical temperature field. Furthermore, two examples are worked out, i.e., the one-dimensional heat conduction in the radial direction and the two-dimensional case with axial symmetry. The solution is presented as an infinite series in terms of Legendre functions. The problem with spherical symmetry is also solved by using perturbation methods up to the third-order approximation, and the results are compared with the exact solution.
Czasopismo
Rocznik
Tom
Strony
405--422
Opis fizyczny
Bibliogr. 9 poz.
Twórcy
autor
- Department of Mechanical Engineering Yasouj University 75914-353 Yasouj, Iran, aminmoosaie@gmail.com
Bibliografia
- 1. R. Trostel, Instationäre Wärmespannungen in einer Hohlkugel, Ingenieur-Archiv, 24, 373–391, 1956.
- 2. R. Shirmohammadi, A. Moosaie, Non-Fourier heat conduction in a hollow sphere with periodic surface heat flux, Int. Commun. Heat Mass Transf., 36, 827–833, 2009.
- 3. A. Moosaie, Axisymmetric non-Fourier temperature field in a hollow sphere, Arch. Appl. Mech., 79, 679–694, 2009.
- 4. R. Trostel, Stationäre Wärmespannungen mit temperaturabhängigen Stoffwerten, Ingenieur-Archiv, 26, 416–434, 1958.
- 5. R. Trostel, Wärmespannungen in Hohlzylindern mit temperaturabhängigen Stoffwerten, Ingenieur-Archiv, 26, 134–142, 1958.
- 6. A. Aziz, T.Y. Na, Periodic heat transfer in fins with variable thermal parameters, Int. J. Heat Mass Transf., 24, 1397–1404, 1981.
- 7. F. Khani, A. Aziz, Thermal analysis of a longitudinal trapezoidal fin with temperaturedependent thermal conductivity and heat transfer coefficient, Commun. Nonlinear Sci. Numer. Simul., 15, 590–601, 2010.
- 8. O.D. Makinde, R.J. Moitsheki, On solutions of nonlinear heat diffusion model for thermal energy storage problem, Int. J. Physical Sciences, 5, 246–250, 2010.
- 9. VDI-Gesellschaft Verfahrenstechnik und Chemieingenieurwesen, Wärmeatlas, Springer, Berlin 2006.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT4-0012-0053