Table of Contents
International Scholarly Research Notices
Volume 2014 (2014), Article ID 646049, 13 pages
http://dx.doi.org/10.1155/2014/646049
Research Article

Fractional Order Two-Temperature Dual-Phase-Lag Thermoelasticity with Variable Thermal Conductivity

1Bhatkunda High School, Burdwan 713153, India
2Department of Mathematics, Aliah University, Kolkata 700091, India
3Department of Applied Mathematics, University of Calcutta, Kolkata 700009, India

Received 10 May 2014; Revised 4 August 2014; Accepted 4 August 2014; Published 29 October 2014

Academic Editor: Abdelouahed Tounsi

Copyright © 2014 Sudip Mondal et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A new theory of two-temperature generalized thermoelasticity is constructed in the context of a new consideration of dual-phase-lag heat conduction with fractional orders. The theory is then adopted to study thermoelastic interaction in an isotropic homogenous semi-infinite generalized thermoelastic solids with variable thermal conductivity whose boundary is subjected to thermal and mechanical loading. The basic equations of the problem have been written in the form of a vector-matrix differential equation in the Laplace transform domain, which is then solved by using a state space approach. The inversion of Laplace transforms is computed numerically using the method of Fourier series expansion technique. The numerical estimates of the quantities of physical interest are obtained and depicted graphically. Some comparisons of the thermophysical quantities are shown in figures to study the effects of the variable thermal conductivity, temperature discrepancy, and the fractional order parameter.