Mondal Sudip, Mallik Sadek Hossain, Kanoria M
Bhatkunda High School, Burdwan 713153, India.
Department of Mathematics, Aliah University, Kolkata 700091, India.
Int Sch Res Notices. 2014 Oct 28;2014:646049. doi: 10.1155/2014/646049. eCollection 2014.
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.
在对具有分数阶的双相滞后热传导进行新的考量的背景下，构建了一种双温度广义热弹性新理论。然后采用该理论研究热导率可变的各向同性均匀半无限广义热弹性固体中的热弹性相互作用，其边界受到热载荷和机械载荷作用。该问题的基本方程已写成拉普拉斯变换域中的向量矩阵微分方程形式，然后使用状态空间方法求解。利用傅里叶级数展开技术通过数值计算拉普拉斯变换的逆变换。获得了感兴趣的物理量的数值估计并以图形方式进行了描绘。在图中展示了一些热物理量的比较，以研究可变热导率、温度差异和分数阶参数的影响。
