On the Temperature-Rate Dependent Two-Temperature Thermoelasticity Theory

Abstract

This work aims to formulate the temperature-rate dependent two-temperature (TRDTT) theory of thermoelasticity. The two-temperature thermoelasticity theory and the temperature-rate dependent thermoelasticity theory are two well-established thermoelasticity theories, which are developed from the generalized thermodynamic principles independently. Although the constitutive equations for TRDTT theory have been introduced, the formulation for the theory from the thermodynamical principles is not yet derived. Therefore, this work is an attempt to establish the theory from the generalized laws of thermodynamics and derive all the governing equations and constitutive relations for the theory. We derive a new and more general two-temperature relation that involves the temperature-rate terms of conductive and thermodynamic temperatures. We observe that this relation is different from the two-temperature relation reported in the literature. Further, we prove the uniqueness of solution for a general mixed initial boundary value problem in the context of linear modified TRDTT thermoelasticity theory for anisotropic medium. To investigate the effect of the present modified TRDTT theory, we solve a one-dimensional half-space problem and highlight the significance of the present theory.

Photomechanical and Thermal Wave Responses of a Two-Temperature Semiconductor Model with Moisture Diffusivity Process

“…Within the Dual Phase Lag (DPL) model framework, Ezzat et al [12] built a two-temperature magneto thermoelastic fractional order model. The temperature rate dependent two temperature thermoelastic theory was developed by Shivay and Mukhopahyay [13]. (TRDTT).…”

Two-Temperature Semiconductor Model Photomechanical and Thermal Wave Responses with Moisture Diffusivity Process

“…Within the Dual Phase Lag (DPL) model framework, Ezzat et al [12] created a two-temperature magneto thermoelastic fractional order model. The two-temperature thermoelastic theory with temperature rate dependence was developed by Shivay and Mukhopahyay [13] (TRDTT). The conductive and thermodynamic temperature dependency on temperature rate is a foundational element of this theory.…”

On the existence and decay in a new thermoelastic theory with two temperatures

“…This was extended later by Quintanilla [34,35] in the case of the dual phase-lag theories and we note that these theories have deserved much attention in the last twenty years (see, for instance, [2,[26][27][28][30][31][32][33]). Shivay and Mukhopadhyay [37] suggested a new two-temperatures theory for the Green and Lindsay proposition assuming that there is a temperature-rate dependence for the two temperatures. In this case, the relation between the temperatures is modified leading to new mathematical problems.…”