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

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

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

In this work, a new mathematical model of magneto-thermoelasticity theory is constructed in the context of a new consideration of heat conduction law with time-fractional order. This model is appli...

Fractional order theory of a perfect conducting thermoelastic medium

Two-temperature theory in magneto-thermoelasticity with fractional order dual-phase-lag heat transfer

State space approach of two-temperature magneto-thermoelasticity with thermal relaxation in a medium of perfect conductivity

A one-dimensional model of the two-temperature generalized magneto-viscoelasticity with two relaxation times in a perfect conducting medium is established. The state space approach is adopted for the solution of one-dimensional problems for any set of boundary conditions. The resulting formulation together with the Laplace transform techniques are applied to a specific problem of a half-space subjected to thermal shock and traction-free surface. The inversion of the Laplace transforms is carried out using a numerical approach. Numerical results are given and illustrated graphically for the problem. Some comparisons have been shown in figures to estimate the effects of the temperature discrepancy and the applied magnetic field.

Two-temperature theory in generalized magneto-thermo-viscoelasticity

We introduce a magnetohydrodynamic model of a boundary-layer equation for a conducting viscous fluid. The state space approach is adopted for one-dimensional problems including heat sources with one relaxation time. The resulting formulation is applied to a problem for the whole space with a plane distribution of heat sources. The reflection method together with the solution obtained for the whole space is applied to a semi-space problem with a plane distribution of heat sources located inside the fluid. Numerical results for the velocity, temperature, and induced-magnetic- and induced-electric-field distributions are given and illustrated graphically for both problems. PACS No.: 47.65+a

Alaa Abd-El Bary

Papers

State space approach of two-temperature magneto-thermoelasticity with thermal relaxation in a medium of perfect conductivity

Two-temperature theory in generalized magneto-thermo-viscoelasticity

State space formulation for boundary-layer magneto-hydrodynamic free convection flow with one relaxation time