scholarly journals Solution of Lord-Shulmans and dual-phase-lag theories problem on a photothermal rotational semiconductor medium with voids and initial stress

2020 ◽  
Vol 24 (Suppl. 1) ◽  
pp. 59-68
Author(s):  
Hammad Alotaibi
Keyword(s):  
Boundary Conditions ◽  
Initial Stress ◽  
Carrier Density ◽  
Equations Of Motion ◽  
Phase Lag ◽  
Dual Phase ◽  
Stress Components ◽  
Differential Equa ◽  
Generalized Thermoelastic ◽  
Thermoelastic Theory

This paper discusses a photo-thermal rotational semiconductor medium with ini?tial stress, and voids by considering two thermoelastic theories: Lord-Shulman and Dual-Phase-Lag models. The equations of motion, temperature, voids, and photothermal have been investigated under two generalized thermoelastic theory. The technique of normal mode has been applied to solve the differential equa?tions system with appropriate boundary conditions. Quantities of physical interest such as displacement, stress components, concentration, temperature, and carrier density are calculated and displayed graphically to demonstrate the effect of the external parameters. The obtained results, by using the two theories, show that the dual-phase-lag theory gives an origin results comparing with obtained results by Lord-Shulman theory. By neglecting the initial stress and voids, and considering the only dual-phase-lag theory, then the results obtained in this paper are deduced to the results of Abbas et al. [1].

scholarly journals Solution of Lord-Shulmans and dual-phase-lag theories problem on a photothermal rotational semiconductor medium with voids and initial stress

2020 ◽  
Vol 24 (Suppl. 1) ◽  
pp. 59-68
Author(s):  
Hammad Alotaibi
Keyword(s):  
Boundary Conditions ◽  
Initial Stress ◽  
Carrier Density ◽  
Equations Of Motion ◽  
Phase Lag ◽  
Dual Phase ◽  
Stress Components ◽  
Differential Equa ◽  
Generalized Thermoelastic ◽  
Thermoelastic Theory

This paper discusses a photo-thermal rotational semiconductor medium with ini?tial stress, and voids by considering two thermoelastic theories: Lord-Shulman and Dual-Phase-Lag models. The equations of motion, temperature, voids, and photothermal have been investigated under two generalized thermoelastic theory. The technique of normal mode has been applied to solve the differential equa?tions system with appropriate boundary conditions. Quantities of physical interest such as displacement, stress components, concentration, temperature, and carrier density are calculated and displayed graphically to demonstrate the effect of the external parameters. The obtained results, by using the two theories, show that the dual-phase-lag theory gives an origin results comparing with obtained results by Lord-Shulman theory. By neglecting the initial stress and voids, and considering the only dual-phase-lag theory, then the results obtained in this paper are deduced to the results of Abbas et al. [1].

The initial stress effect on a thermoelastic micro-elongated solid under the dual-phase-lag model

2021 ◽  
Vol 127 (9) ◽  
Author(s):  
Mohamed I. A. Othman ◽  
Sarhan Y. Atwa ◽  
Ebtesam E. M. Eraki ◽  
Mohamed F. Ismail
Keyword(s):  
Initial Stress ◽  
Stress Effect ◽  
Phase Lag ◽  
Dual Phase ◽  
Lag Model

Thermomechanical response in a two-dimension porous medium subjected to thermal loading

2019 ◽  
Vol 30 (8) ◽  
pp. 4103-4117
Author(s):  
Tareq Saeed ◽  
Ibrahim Abbas
Keyword(s):  
Porous Medium ◽  
Design Methodology ◽  
Thermal Loading ◽  
Volume Fraction ◽  
Eigenvalue Approach ◽  
Content Type ◽  
Stress Components ◽  
Generalized Thermoelastic ◽  
Physical Quantities ◽  
Thermoelastic Theory

Purpose The purposes of this study, a mathematical model of generalized thermoelastic theory subjected to thermal loading is presented to study the wave propagation in a two-dimensional porous medium. Design/methodology/approach By using Fourier–Laplace transforms with the eigenvalue approach, the physical quantities are analytically obtained. Findings The derived method is evaluated with numerical results, which are applied to the porous medium in simplified geometry. Originality/value Numerical outcomes for all the physical quantities considered are implemented and represented graphically. The variations of temperature, the changes in volume fraction field, the displacement components and the stress components have been depicted graphically.

A Closed Form Solution of Dual-Phase Lag Heat Conduction Problem With Time Periodic Boundary Conditions

2019 ◽  
Vol 141 (3) ◽  
Author(s):  
Pranay Biswas ◽  
Suneet Singh ◽  
Hitesh Bindra
Keyword(s):  
Heat Conduction ◽  
Boundary Conditions ◽  
Closed Form ◽  
Computational Cost ◽  
Closed Form Solution ◽  
Form Solution ◽  
Fourier Series Expansion ◽  
Phase Lag ◽  
Dual Phase ◽  
Time Periodic

The Laplace transform (LT) is a widely used methodology for analytical solutions of dual phase lag (DPL) heat conduction problems with consistent DPL boundary conditions (BCs). However, the inversion of LT requires a series summation with large number of terms for reasonably converged solution, thereby, increasing computational cost. In this work, an alternative approach is proposed for this inversion which is valid only for time-periodic BCs. In this approach, an approximate convolution integral is used to get an analytical closed-form solution for sinusoidal BCs (which is obviously free of numerical inversion or series summation). The ease of implementation and simplicity of the proposed alternative LT approach is demonstrated through illustrative examples for different kind of sinusoidal BCs. It is noted that the solution has very small error only during the very short initial transient and is (almost) exact for longer time. Moreover, it is seen from the illustrative examples that for high frequency periodic BCs the Fourier and DPL model give quite different results; however, for low frequency BCs the results are almost identical. For nonsinusoidal periodic function as BCs, Fourier series expansion of the function in time can be obtained and then present approach can be used for each term of the series. An illustrative example with a triangular periodic wave as one of the BC is solved and the error with different number of terms in the expansion is shown. It is observed that quite accurate solutions can be obtained with a fewer number of terms.

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