Analysis to Thermoelastic Interactions under a Heat Conduction Model with a Delay Term

# International Journal of Science and Research (IJSR)www.ijsr.net | Open Access | Fully Refereed | Peer Reviewed International Journal

Research Paper | Mathematics | India | Volume 4 Issue 11, November 2015

### Analysis to Thermoelastic Interactions under a Heat Conduction Model with a Delay Term

The present work is concerned with a heat conduction model an exact heat conduction model with a delay term. A generalized thermoelasticity theory was proposed by Roychoudhuri (2007) based on the heat conduction law with three -phase-lag effects for the purpose of considering the delayed response in times due to the microstructural interactions in the heat transport mechanism. However, the model define ill-posed problem. Hence, Recently, Quintanilla (2011) has proposed to reformulate this constitutive equation as a heat conduction theory with a single deley term and has investigated the spatial behavior of the solutions for this theory. A Phragmen- Lindelof type alternative is obtained and it has been shown that the solutions either decay in an exponential way or blow-up at infinity in an exponential way. The obtained results are extended to a thermoelasticity theory by considering the Taylor series approximation of the equation of heat conduction to the delay term and Phragmen-Lindelof type alternative is obtained for the forward and backward in time equations. The formulation is then is applied to solve a boundary value problem of an isotropic elastic half space with its plane boundary subjected to exponential decrease in temperature and zero stress. The homotopy analysis method is applied to obtain the solution of the problem. . The problem is discussed with different graphs of numerical values of the field variables.

Keywords: Thermoelasticity, Relaxation Parameter, Homotopy, Half Space

Edition: Volume 4 Issue 11, November 2015

Pages: 1398 - 1402

Sudhakar Yadav, "Analysis to Thermoelastic Interactions under a Heat Conduction Model with a Delay Term", International Journal of Science and Research (IJSR), https://www.ijsr.net/search_index_results_paperid.php?id=NOV151489, Volume 4 Issue 11, November 2015, 1398 - 1402

#### Similar Articles with Keyword 'Homotopy'

Research Paper, Mathematics, India, Volume 4 Issue 11, November 2015

Pages: 1398 - 1402

### Analysis to Thermoelastic Interactions under a Heat Conduction Model with a Delay Term

Research Paper, Mathematics, India, Volume 4 Issue 10, October 2015

Pages: 2126 - 2129

### A Homotopy Analysis Approach to a Thermoelastic Interactions under the Boundary Condition: Heat Source Varying Exponentially with Time and Zero Stress

Research Paper, Mathematics, India, Volume 3 Issue 10, October 2014

Pages: 504 - 507

### A Space Having the Homotopy Type with Fuzzy Modules

Dr. Pravanjan Kumar Rana

Research Paper, Mathematics, India, Volume 5 Issue 6, June 2016

Pages: 574 - 577

### A Study of Function Spaces through a Functor

Dr. Pravanjan Kumar Rana

Research Paper, Mathematics, Iraq, Volume 6 Issue 6, June 2017

Pages: 529 - 538

### Efficient Iterative Method for Initial and Boundary Value Problems Appear in Engineering and Applied Sciences

Majeed Ahmed AL-Jawary, Mustafa Mahmood Azeez