Application of Differential Transform Method to Thermoelastic Problem for Annular Disks of Variable Thickness with Temperature-Dependent Parameters

This article analyzes the one-dimensional steady temperature field and related thermal stresses in an annular disk of variable thickness that has a temperature-dependent heat transfer coefficient and is capable of temperature-dependent internal heat generation. The temperature dependencies of the thermal conductivity, Young’s modulus, and the coefficient of linear thermal expansion of the disk are considered, whereas Poisson’s ratio is assumed to be constant. The differential transform method (DTM) is employed to analyze not only the nonlinear heat conduction but also the resulting thermal stresses. Analytical solutions are developed for the temperature and thermal stresses in the form of simple power series. Numerical calculations are performed for an annular cooling/heating fin of variable thickness. Numerical results show that the sufficiently converged analytical solutions are in good agreement with the solutions obtained by the Adomian decomposition method and give the effects of the temperature-dependent parameters on the temperature and thermal stress profiles in the disk. The DTM is useful as a new analytical method for solving thermoelastic problems for a body with temperature-dependent parameters including material properties.

[1]  Rong-Hua Yeh,et al.  Fins with temperature dependent surface heat flux. I: Single heat transfer mode , 1994 .

[2]  Tasawar Hayat,et al.  Some exact solutions of the fin problem with a power law temperature-dependent thermal conductivity , 2010 .

[3]  A. Campo,et al.  Approximate analytic temperature solution for uniform annular fins by adapting the power series method , 1998 .

[4]  M. Kartal,et al.  Stress Distributions In Cooling Fins Of Variable Thickness With And Without Rotation , 2005 .

[5]  Cha'o-Kuang Chen,et al.  Optimization of circular fins with variable thermal parameters , 1999 .

[6]  C. Lo,et al.  Application of Hybrid Differential Transform/Control-Volume Method to Hyperbolic Heat Conduction Problems , 2009 .

[7]  I. Hashim,et al.  Analytical solutions to heat transfer equations by homotopy-perturbation method revisited , 2008 .

[8]  M. Bouaziz,et al.  A least squares method for a longitudinal fin with temperature dependent internal heat generation and thermal conductivity , 2011 .

[9]  Naotake Noda,et al.  Thermal Stresses in Materials with Temperature-Dependent Properties , 1991 .

[10]  Ming-Jyi Jang,et al.  Differential transformation approach to thermal conductive problems with discontinuous boundary condition , 2010, Appl. Math. Comput..

[11]  Cha'o-Kuang Chen,et al.  Application of differential transformation to eigenvalue problems , 1996 .

[12]  C. Chiu,et al.  THERMAL STRESSES IN ANNULAR FINS WITH TEMPERATURE-DEPENDENT CONDUCTIVITY UNDER PERIODIC BOUNDARY CONDITION , 2002 .

[13]  C. Bert.  Application of Differential Transform Method to Heat Conduction in Tapered Fins , 2002 .

[14]  H. Ünal.  Determination of the temperature distribution in an extended surface with a non-uniform heat transfer coefficient , 1985 .

[15]  D. Ganji,et al.  Differential Transformation Method to determine fin efficiency of convective straight fins with temperature dependent thermal conductivity , 2009 .

[16]  N. Noda,et al.  THERMAL-STRESS PROBLEMS IN INDUSTRY. 3: TEMPERATURE DEPENDENCY OF ELASTIC MODULI FOR SEVERAL METALS AT TEMPERATURES FROM -196 TO 1000° C , 1979 .

[17]  Daniel Lesnic,et al.  A decomposition method for power-law fin-type problems , 2004 .

[18]  Mohsen Torabi,et al.  THE APPLICATION OF DIFFERENTIAL TRANSFORMATION METHOD TO NONLINEAR EQUATIONS ARISING IN HEAT TRANSFER , 2011 .

[19]  Saeid Abbasbandy,et al.  Exact analytical solution of a nonlinear equation arising in heat transfer , 2010 .

[20]  Mohammad Mehdi Rashidi,et al.  New analytical method for solving Burgers' and nonlinear heat transfer equations and comparison with HAM , 2009, Comput. Phys. Commun..

[21]  Takahiro Endo,et al.  Studies of Liquid Film Flow in Two-Phase Annular and Annular-Mist Flow Regions : Part 1, Downflow in a Vertical Tube , 1973 .

[22]  Cha'o-Kuang Chen,et al.  Application of the decomposition method to thermal stresses in isotropic circular fins with temperature-dependent thermal conductivity , 2002 .

[23]  Song-Ping Zhu,et al.  An efficient computational method for modelling transient heat conduction with nonlinear source terms , 1996 .

[24]  Cha’o-Kuang Chen,et al.  APPLICATION OF TAYLOR TRANSFORMATION TO THE THERMAL STRESSES IN ISOTROPIC ANNULAR FINS , 1998 .

[25]  Chieh-Li Chen,et al.  Hybrid differential transform and finite difference method to solve the nonlinear heat conduction problem , 2008 .

[26]  H. Ahmadikia,et al.  Analytical Solution for Different Profiles of Fin with Temperature-Dependent Thermal Conductivity , 2010 .

[27]  Huan-Sen Peng,et al.  Hybrid differential transformation and finite difference method to annular fin with temperature-dependent thermal conductivity , 2011 .

[28]  J. Nowinski.  Transient Thermoelastic Problem for an Infinite Medium With a Spherical Cavity Exhibiting Temperature-Dependent Properties , 1962 .

[29]  H. Ünal.  Temperature distributions in fins with uniform and non-uniform heat generation and non-uniform heat transfer coefficient , 1987 .

[30]  R. J. Moitsheki,et al.  Steady Heat Transfer through a Two-Dimensional Rectangular Straight Fin , 2011 .