The equations of motion and the constitutive relations are derived for the theory of micropolar generalized two-temperature thermoelasticity. An equation of energy balance, including the strain energy function, is deduced and the uniqueness theorem for the case of anisotropic solid is proved by the aid of the energy equation. The formulation is applied to a thermal shock half-space problem, to study the effect of two-temperature influence on the distribution of relevant variables.

Thermal shock

10.1080/01495730903542829

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Citations (72)

From continuous-time random walks to the fractional Jeffreys equation: Solution and properties

International Journal of Heat and Mass Transfer (2021)

Emad Awad Trifce Sandev Ralf Metzler Aleksei V. Chechkin

Continuous-time random walk

Anomalous Diffusion

Mean squared displacement

Heat equation

Fourier number

10.1016/j.ijheatmasstransfer.2021.121839

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Citations (21)

Thermal oscillations and resonance in electron–phonon interaction process

Zeitschrift für angewandte Mathematik und Physik (2024)

Emad Awad Weizhong Dai С. Л. Соболев

10.1007/s00033-024-02277-w

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Citations (2)

Thermal oscillations and resonance in electron-phonon interaction process

arXiv (Cornell University) (2024)

Emad Awad Weizhong Dai С. Л. Соболев

Thermal resonance, in which the temperature amplitude attains a maximum value (peak) in response to an external exciting frequency source, is a phenomenon pertinent to the presence of underdamped thermal oscillations and explicit finite-speed for the thermal wave propagation. The present work investigates the occurrence condition for thermal resonance phenomenon during the electron-phonon interaction process in metals based on the hyperbolic two-temperature model. First, a sufficient condition for underdamped electron and lattice temperature oscillations is discussed by deriving a critical frequency (a material characteristic). It is shown that the critical frequency of thermal waves near room temperature, during electron-phonon interactions, may be on the order of terahertz ($10-20$ THz for Cu and Au, i.e., lying within the terahertz gap). It is found that whenever the natural frequency of metal temperature exceeds this frequency threshold, the temperature oscillations are of underdamped type. However, this condition is not necessary, since there is a small frequency domain, below this threshold, in which the underdamped thermal wave solution is available but not effective. Otherwise, the critical damping and the overdamping conditions of the temperature waves are determined numerically for a sample of pure metals. The thermal resonance conditions in both electron and lattice temperatures are investigated. The occurrence of resonance in both electron and lattice temperature is conditional on violating two distinct critical values of frequencies. When the natural frequency of the system becomes larger than these two critical values, an applied frequency equal to such a natural frequency can drive both electron and lattice temperatures to resonate together with different amplitudes and behaviors. However, the electron temperature resonates earlier than the lattice temperature.

10.1007/s00033-024-02277-w

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Citations (3)

Transient Finite-Speed Heat Transfer Influence on Deformation of a Nanoplate with Ultrafast Circular Ring Heating

Mathematics (2023)

Mohsen A. Fayik Sharifah E. Alhazmi M. A. Abdou Emad Awad

The present study provides a theoretical estimate for the thermal stress distribution and the displacement vector inside a nano-thick infinite plate due to an exponentially temporal decaying boundary heating on the front surface of the elastic plate. The surface heating is in the form of a circular ring; therefore, the axisymmetric formulation is adopted. Three different hyperbolic models of thermal transport are considered: the Maxwell-Cattaneo-Vernotte (MCV), hyperbolic Dual-Phase-Lag (HDPL) and modified hyperbolic Dual-Phase-Lag (MHDPL), which coincides with the two-step model under certain constraints. A focus is directed to the main features of the corresponding hyperbolic thermoelastic models, e.g., finite-speed thermal waves, singular surfaces (wave fronts) and wave reflection on the rear surface of the plate. Explicit expressions for the thermal and mechanical wave speeds are derived and discussed. Exact solution for the temperature in the short-time domain is derived when the thermalization time on the front surface is very long. The temperature, hydrostatic stress and displacement vector are represented in the space-time domain, with concentrating attention on the thermal reflection phenomenon on the thermally insulated rear surface. We find that the mechanical wave speeds are approximately equal for the considered models, while the thermal wave speeds are entirely different such that the modified hyperbolic dual-phase-lag thermoelasticity has the faster thermal wave speed and the Lord-Shulman thermoelasticity has the slower thermal wave speed.

Thermoelastic damping

Reflection

10.3390/math11051099

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Citations (5)

Generalized Lagging Response of Thermoelastic Beams

Mathematical Problems in Engineering (2014)

Ibrahim H. El‐Sirafy M.A. Abdou Emad Awad

The vibrations of Euler‐Bernoulli metal beam are accommodated in the present study by taking into account the possibility of activating the microstructural effects, captured by the temperature gradient phase lag, in the fast transient process captured by the heat flux phase lag. The thermal moment is approximated as the difference between the top and the bottom surface temperatures (Massalas and Kalpakidis 1983). Three generalizations of the Biot model of thermomechanics are considered: Lord‐Shulman, dual‐phase‐lag (Tzou 1997), and modified dual‐phase‐lag (Awad 2012). It is found that when the response time is shortened, the material dimensions are small, or when the method of heating is changed, the dual‐phase‐lag model records a significant decrease in the lattice variables. The spurious serrations of the classical thermoelastic wave are smoothed in the dual‐phase‐lag wave. The dual‐phase‐lag thermoelasticity is the closest macroscopic approach to the ultrafast model (Chen et al. 2002).

Thermoelastic damping

Phase lag

Spurious relationship

Homogenization

10.1155/2014/780679

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Citations (6)

Analytical Aspects in the Theory of Thermoelastic Bodies with Microstructure and Two Temperatures

Journal of Thermal Stresses (2010)

Magdy A. Ezzat Emad Awad

Abstract In the present work, some essential theorems on the linear coupled theory of micropolar thermoelasticity with two temperatures are established. The uniqueness theorem is proved in two distinct approaches without the positive definiteness assumptions on the thermoelastic modulus. The reciprocity theorem is established by the aid of an integral identity that involves two admissible processes at two different instants. The continuous dependence results on the external data are studied. The variational principle of Gurtin type is established. Finally, we solve the problems of concentrated heat source and body force to study the effect of two-temperature influence on the relevant variables. Keywords: Concentrated loadsContinuous dependence theoremMicropolar elasticityReciprocity theoremTwo-temperature thermoelasticityUniqueness theoremVariational principle

Thermoelastic damping

Positive definiteness

Reciprocity

Variational principle

10.1080/01495731003776069

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Citations (6)

Exact solutions for a two-dimensional thermoelectric MHD flow with steady-state heat transfer on a vertical plate with two instantaneous infinite hot suction lines

arXiv (Cornell University) (2022)

Emad Awad S. M. Abo‐Dahab M. A. Abdou

In the present work, the mathematical description of a two-dimensional unsteady magneto-hydrodynamics slow flow with thermoelectric properties (TEMHD) on an infinite vertical partially hot porous plate is presented. The Laplace-Fourier transform technique is employed to simplify the field equations. For the steady-state heat transfer assumption, exact expressions for the temperature and stream function are analytically obtained for TEMHD flow on a wall with two infinite instantaneous hot suction lines. The results obtained are displayed graphically.

10.48550/arxiv.2212.01665

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Citations (1)

On the coupled theory of thermo-piezoelectric/piezomagnetic materials with two temperatures

Canadian Journal of Physics (2010)

Magdy A. Ezzat Ahmed S. El‐Karamany Emad Awad

In the present work, the theory of two-temperature thermoelasticity for a piezoelectric/piezomagnetic materials is formulated. An equation of energy balance is introduced and the uniqueness theorem is proved. An integral identity that involves two admissible processes at two different instants is introduced and the reciprocity theorem is proved without using Laplace transform. The variational principle of Gurtin type is established.

Reciprocity

10.1139/p10-015

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Citations (17)