Abstract
The present investigation is intended to demonstrate the magnetic field, relaxation time, hydrostatic initial stress, and two temperature on the thermal shock problem. The governing equations are formulated in the context of Lord-Shulman theory with the presence of bodily force, two temperatures, thermal shock, and hydrostatic initial stress. We obtained the exact solution using the normal mode technique with appropriate boundary conditions. The field quantities are calculated analytically and displayed graphically under thermal shock problem with effect of external parameters respect to space coordinates. The results obtained are agreeing with the previous results obtained by others when the new parameters vanish. The results indicate that the effect of magnetic field and initial stress on the conductor temperature, thermodynamic temperature, displacement and stress are quite pronounced. In order to illustrate and verify the analytical development, the numerical results of temperature, displacement and stress are carried out and computer simulated results are presented graphically. This study helpful in the development of piezoelectric devices.
Highlights
More attentions have been considered by researchers and engineers to the thermoelasticity theory to release the confliction of infinite speed due to the thermal signals, because of the importance in diverse fields as geophysics, acoustics, engineers, plasma physics, and industries
The results indicate that the effect of magnetic field and initial stress on the conductor temperature, thermodynamic temperature, displacement and stress are quite pronounced
The thermodynamic temperature increases with increasing of time and longitudinal wave velocity, while it decreases with increasing of wave number and relaxation time, as well, there is no effect of magnetic field and initial stress on the thermodynamic temperature
Summary
More attentions have been considered by researchers and engineers to the thermoelasticity theory to release the confliction of infinite speed due to the thermal signals, because of the importance in diverse fields as geophysics, acoustics, engineers, plasma physics, and industries. Bahar et al [17] introduced the formulation of state space in thermoelastic problems which developed in Sherief [18] including the heat sources effectively. Othman et al [25] studied the reflection waves in a generalized thermoelastic medium from a free surface under hydrostatic initial stress under different thermoelastic theories. Youssef [26] studied the problem of generalized thermoelastic infinite medium with a cylindrical cavity subjected to a ramp-type heating and loads. The main purpose of the present investigation is intended to demonstrate the magnetic field, relaxation time, hydrostatic initial stress, and two temperature on the thermal shock problem. The governing equations are formulated in the context of Lord-Shulman theory with the presence of body force, two temperatures, thermal shock, and hydrostatic initial stress. The field quantities are calculated analytically and displayed graphically under thermal shock problem with effect of external parameters respect to space coordinates
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