Contour integration solution for a thermoelastic problem of a spherical cavity

Abstract We study a 1D problem of a spherical cavity whose surface is traction free and kept at a temperature that depends on the time. Laplace transform techniques are utilized. We use contour integration and the complex inversion formula to get the inverse transforms as definite integrals. Numerical computations are illustrated graphically.

[1]  H. Sherief,et al.  Generalized Theory of Thermoviscoelasticity and a Half-Space Problem , 2011 .

[2]  Magdy A. Ezzat,et al.  The dependence of the modulus of elasticity on reference temperature in generalized thermoelasticity with thermal relaxation , 2004, Appl. Math. Comput..

[3]  F. Hamza,et al.  THEORY OF GENERALIZED MICROPOLAR THERMOELASTICITY AND AN AXISYMMETRIC HALF-SPACE PROBLEM , 2005 .

[4]  H. Sherief,et al.  A problem for an infinite thermoelastic body with a spherical cavity , 1998 .

[5]  M. El-Hagary Generalized Thermoelastic Diffusion Problem for an Infinite Medium with a Spherical Cavity , 2012 .

[6]  D. McClure Nonlinear segmented function approximation and analysis of line patterns , 1975 .

[7]  Santwana Mukhopadhyay,et al.  Solution of a Problem of Generalized Thermoelasticity of an Annular Cylinder with Variable Material Properties by Finite Difference Method , 2009 .

[8]  H. Lord,et al.  A GENERALIZED DYNAMICAL THEORY OF THERMOELASTICITY , 1967 .

[9]  H. Sherief,et al.  A Mathematical Model for Short-Time Filtration in Poroelastic Media with Thermal Relaxation and Two Temperatures , 2011, Transport in Porous Media.

[10]  C. Cattaneo,et al.  Sulla Conduzione Del Calore , 2011 .

[11]  Magdy A. Ezzat,et al.  Magneto-thermoelasticity with thermoelectric properties and fractional derivative heat transfer , 2011 .

[12]  G. Honig,et al.  A method for the numerical inversion of Laplace transforms , 1984 .

[13]  Sherief HanyH.,et al.  GENERALIZED ONE-DIMENSIONAL THERMAL-SHOCK PROBLEM FOR SMALL TIMES , 1981 .

[14]  R. Hetnarski SOLUTION OF THE COUPLED PROBLEM OF THERMOELASTICITY IN THE FORM OF SERIES OF FUNCTIONS , 1964 .

[15]  R. Hetnarski THE FUNDAMENTAL SOLUTION OF THE COUPLED THERMO ELASTIC PROBLEM FOR SMALL TIMES , 1964 .

[16]  H. Sherief,et al.  SOLUTION OF THE GENERALIZED PROBLEM OF THERMOELASTICITY IN THE FORM OF SERIES OF FUNCTIONS , 1994 .

[17]  H. Sherief,et al.  PROBLEM IN GENERALIZED THERMOELASTICITY , 1986 .

[18]  H. Sherief,et al.  Two-dimensional problem for a thick plate with axi-symmetric distribution in the theory of generalized thermoelastic diffusion , 2016 .

[19]  W. E. Raslan Application of Fractional Order Theory of Thermoelasticity in a Thick Plate Under Axisymmetric Temperature Distribution , 2015 .

[20]  Hany H. Sherief,et al.  Application of fractional order theory of thermoelasticity to a 2D problem for a half-space , 2014, Appl. Math. Comput..

[21]  Magdy A. Ezzat,et al.  A thermal-shock problem in magneto-thermoelasticity with thermal relaxation , 1996 .

[22]  Hany H. Sherief,et al.  Generalized thermoelasticity for anisotropic media , 1980 .

[23]  J. Maxwell,et al.  The Dynamical Theory of Gases , 1905, Nature.

[24]  H. Sherief,et al.  A SHORT TIME SOLUTION FOR A PROBLEM IN THERMOELASTICITY OF AN INFINITE MEDIUM WITH A SPHERICAL CAVITY , 1998 .

[25]  H. Sherief,et al.  A MODE-I CRACK PROBLEM FOR AN INFINITE SPACE IN GENERALIZED THERMOELASTICITY , 2005 .

[26]  H. Sherief,et al.  A two-dimensional thermoelasticity problem for a half space subjected to heat sources , 1999 .

[27]  Eman M. Hussein Fractional Order Thermoelastic Problem for an Infinitely Long Solid Circular Cylinder , 2015 .