In this work, we study the thermoelastic interactions in an unbounded medium with a spherical cavity in the context of a very recently proposed heat conduction model established by Quintanilla (2011). This model is a reformulation of three-phase-lag conduction model and is an alternative heat conduction theory with a single delay term. We make an attempt to study the thermoelastic interactions in an isotropic elastic medium with a spherical cavity subjected to three types of thermal and mechanical loads in the contexts of two versions of this new model. Analytical solutions for the distributions of the field variables are found out with the help of the integral transform technique. A detailed analysis of analytical results is provided by short-time approximation concept. Further, the numerical solutions of the problems are obtained by applying numerical inversion of Laplace transform.We observe significant variations in the analytical results predicted by different heat conduction models. Numerical values of field variables are also observed to show significantly different results for a particular material. Several important points related to the prediction of the new model are highlighted.
Kumari, Bharti; Kumar, Anil; Gupta, Manushi; and Mukhopadhyay, Santwana
Analysis of a recent heat conduction model with a delay for thermoelastic interactions in an unbounded medium with a spherical cavity,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 13,
2, Article 17.
Available at: https://digitalcommons.pvamu.edu/aam/vol13/iss2/17