A novel generalized thermoelasticity model based on memory-dependent derivative

In this work, a new model of the magneto-thermoelasticity theory has been constructed in the context of a new consideration of heat conduction with fractional derivative. A one-dimensional application for a conducting half-space of thermoelectric elastic material, which is thermally shocked in the presence of a magnetic field, has been solved using Laplace transform and state-space techniques (Ezzat, 2008 [1]). According to the numerical results and its graphs, a conclusion about the new theory of magneto-thermoelasticity has been constructed. The theories of coupled magneto-thermoelasticity and of generalized magneto-thermoelasticity with one relaxation time follow as limited cases. The result provides a motivation to investigate conducting thermoelectric materials as a new class of applicable materials.

Magneto-thermoelasticity with thermoelectric properties and fractional derivative heat transfer

Generalized thermo-viscoelasticity with memory-dependent derivatives

A new nonlocal theory of generalized thermoelastic materials with voids based on Eringen’s nonlocal elasticity and Caputo fractional derivative is established. The one-dimensional form of the above...

Nonlocal theory of thermoelastic materials with voids and fractional derivative heat transfer

A new generalized model of two-temperature thermoelasticity theory with time-delay and Kernel function is constructed. Taylor theorem in terms of memory-dependent derivatives is proved. The governing coupled equations of the new generalized thermoelasticity with time-delay and Kernel function, which can be chosen freely according to the necessity of applications, are applied to a one-dimensional problem of a half-space. The bounding surface is taken to be traction free and subjected to a time-dependent thermal shock. Laplace transforms technique will be used to obtain the general solution in a closed form. A numerical method is employed for the inversion of the Laplace transforms. According to the numerical results and its graphs, conclusions about the new theory have been constructed. Some comparisons are shown in the figures to estimate the effects of the temperature discrepancy and time-delay parameter on all of the studied fields.

Generalized thermoelasticity with memory-dependent derivatives involving two temperatures

A new mathematical model of electro-thermoelasticity has been constructed in the context of a new consideration of heat conduction with fractional order. The state space approach developed in Ezzat (2008) is adopted for the solution of one-dimensional problem in the presence of heat sources. The Laplace transform technique is used. A numerical method is employed for the inversion of the Laplace transforms. According to the numerical results and its graphs, conclusion about the new theory has been constructed. Some comparisons have been shown in figures to estimate the effects of the fractional order parameter on all the studied fields.

Theory of fractional order in electro-thermoelasticity

In this work, the field equations of the linear theory of thermoelasticity have been constructed in the context of a new consideration of Fourier law of heat conduction with time-fractional order and three-phase lag. A uniqueness and reciprocity theorems are proved. One-dimensional application for a half-space of elastic material in the presence of heat sources has been solved using Laplace transform and state space techniques Ezzat (Canad J Phys Rev 86:1241–1250, 2008). According to the numerical results and its graphs, conclusion about the new theory has been established.

https://link.springer.com/content/pdf/10.1007%2Fs00419-011-0572-6.pdf

Fractional order theory in thermoelastic solid with three-phase lag heat transfer

A new mathematical model of two-temperature magneto-thermoelasticity is constructed where the fractional order heat conduction law is considered. The state space approach is adopted for the solution of one-dimensional application for a perfect conducting half-space of elastic material with heat sources distribution in the presence of a transverse magnetic field. The Laplace-transform technique is used. A numerical method is employed for the inversion of the Laplace transforms. According to the numerical results and its graphs, conclusions about the new theory are given. Some comparisons are shown in figures to estimate the effects of the temperature discrepancy and the fractional order parameter on all the studied fields.

Fractional order heat conduction law in magneto-thermoelasticity involving two temperatures

Electro-thermoelasticity theory with memory-dependent derivative heat transfer

A mathematical model of electro-thermoelasticity has been constructed in the context of a new consideration of heat conduction with memory-dependent derivative. The governing coupled equations with time-delay and kernel function, which can be chosen freely according to the necessity of applications, are applied to several concrete problems. The exact solutions for all fields are obtained in the Laplace transform domain for each problem. According to the numerical results and its graphs, conclusion about the proposed model has been constructed. The predictions of the theory are discussed and compared with dynamic classical coupled theory. The result provides a motivation to investigate conducting thermoelectric viscoelastic materials as a new class of applicable materials.

Ahmed S. El Karamany

Papers

Theory of fractional order in electro-thermoelasticity

Fractional order theory in thermoelastic solid with three-phase lag heat transfer

Fractional order heat conduction law in magneto-thermoelasticity involving two temperatures

Electro-thermoelasticity theory with memory-dependent derivative heat transfer

Thermoelectric viscoelastic materials with memory-dependent derivative