Abstract The present work considers a two-dimensional (2D) heat conduction problem in the semi-infinite domain based on the classical Fourier model and other non-Fourier models, e.g., the Maxwell–Cattaneo–Vernotte (MCV) equation, parabolic, hyperbolic, and modified hyperbolic dual-phase-lag (DPL) equations. Using the integral transform technique, Laplace, and Fourier transforms, we provide a solution of the problem (Green’s function) in Laplace domain. The thermal double-strip problem, allowing the wave interference within the heat conductor, is considered. A numerical technique, based on the Durbin series for inverting Laplace transform and the trapezoidal rule for calculating an integral form of the solution in the double-strip case, is adopted to recover the solution in the physical domain. Finally, discussions for different non-Fourier heat transfer situations are presented. We compare among the speeds of hyperbolic heat transfer models and shed light on the concepts of flux-precedence and temperature-gradient-precedence, hallmarks of the lagging response idea. Otherwise, we emphasize the existence of a relationship between the waves speed and the time instant of interference onset, underlying the five employed heat transfer models.

Two-sided Laplace transform

Heat equation

10.1140/epjp/s13360-022-03488-8

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Citations (7)

On the plane strain problem of dynamical flexoelectric effect in dielectrics subject to Sinc-shaped surface loading

Mathematics and Mechanics of Solids (2023)

Mohsen A. Fayik A. R. El-Dhaba Emad Awad

Flexoelectricity is a nanoscale phenomenon in dielectric crystals, where the mechanical loads resulting from the first strain gradient shares producing electricity. In this work, we present a numerical investigation for the plane strain problem of the dynamical flexoelectric effect in isotropic dielectrics. A surface loading based on the Sinc function, that is, sinc π (x), with a temporal exponentially decay, is applied to the upper surface of a semi-infinite dielectric crystal. Two cases for the electric potential are considered: (1) Open circuit, in which there is zero charge on the terminals; and (2) Short-circuit, where there is a given value for the potential of the terminals. This type of surface loading is often used in applications such as seismic analysis and electrical engineering, especially signal processing and digital signal processing. Also, it can be used to model other types of dynamic loads, such as wind or wave loads. Furthermore, this setting generates a two-dimensional formulation, known as the plane strain problem. Laplace and Fourier transform techniques are employed for solving the field equations. Suitable numerical techniques are implemented to present the solution to the physical domain. We choose the Strontium Titanate material (SrTiO 3 ) for the two-dimensional simulation. Discussion for the behavior of the dynamical polarization, electric field, electric potential, and stresses is provided in the two-dimensional setting. Effects of the model parameters on electricity generation and behavior are studied.

Flexoelectricity

Sinc function

10.1177/10812865231173343

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Citations (5)

On the time-fractional Cattaneo equation of distributed order

Physica A Statistical Mechanics and its Applications (2018)

Emad Awad

10.1016/j.physa.2018.12.005

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Citations (29)

Crossover Dynamics from Superdiffusion to Subdiffusion: Models and Solutions

Fractional Calculus and Applied Analysis (2020)

Emad Awad Ralf Metzler

Mean squared displacement

Continuous-time random walk

10.1515/fca-2020-0003

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Citations (31)

Intertextuality in Friday Khutba

Journal of Islamic Studies and Culture (2017)

Emad Awad

Intertextuality in Friday Khutba Emad S. Awad Abstract The present study aims at providing a linguistic analysis of the khutba in its socio-political arena. The underlying assumption that facilitates this type of analysis is that, for Muslims, Islam is not only a religion but also a way of life. Consequently, the khutba represents the nexus of the religious and the civic discourse. It accommodates the luminal, in-between position of the khatibs as culture brokers in the sense that they contextualize and mediate the religious/Islamic texts like the Quran and the Hadith. The theoretical framework that is employed to account for the data of the study is intertextuality. Intertextuality capitalizes on the interaction across texts, so it fares well with the religious discourse. Coupled with the theory of six degrees of separation, the components of the communicative event and the attributes in object-oriented programming are incorporated in a model that is developed to account for the khutbas. Full Text: PDF DOI: 10.15640/jisc.v5n1a7

Intertextuality

10.15640/jisc.v5n1a7

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Citations (2)

A closed-form solution for thermally induced affine deformation in unbounded domains with a temporally accelerated anomalous thermal conductivity

Journal of Physics A Mathematical and Theoretical (2024)

Emad Awad Noha Samir

Abstract One of the successful mathematical tools in the 21st century is the distributed-order fractional derivative, particularly, the bi-fractional diffusion equation of natural form (Chechkin et al 2002 Phys. Rev. E 66 046129) and the bi-fractional diffusion equation of the modified form (Sokolov 2004 Acta Phys. Pol. B 35 ). The present study adopts the bi-fractional diffusion heat equation of the modified form that uses two Riemann–Liouville time-fractional derivatives with different fractional orders and the Riesz space-fractional derivative, and bears the property of variable thermal conductivity with temporal acceleration; i.e. the material thermal conduction transits from a low value at the small values of time ( t → 0) to a larger value at the long-time domain ( t → ∞ ). The corresponding fractional thermoelasticity theory, that uses the bi-fractional diffusion heat equation of the modified form, is exclusively considered in this work. For a quasi-static unbounded Hookean domain, exact solutions for the temperature, hydrostatic stress, and the displacement fields are derived in both short-time and long-time domains, in terms of the Fox H -function.The exact solutions for the linearized problem are derived using the inversion of problem variables from the Laplace-Fourier space. Adding a zero initial condition on the normal stress of the unbounded space transforms the conventional Cauchy problem to a mixed initial-boundary value problem in order to derive a generalized form of the displacement. Additionally, thermal energy is not conserved in the presence of space fractality. The effect of such an accelerating transition in the thermal conduction on the displacement component is focused on, and it is found that the displacement inherits a similar transition behavior.

10.1088/1751-8121/ad878f

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Citations (0)

Dual-phase-lag in the balance: Sufficiency bounds for the class of Jeffreys’ equations to furnish physical solutions

International Journal of Heat and Mass Transfer (2020)

Emad Awad

Lattice (music)

10.1016/j.ijheatmasstransfer.2020.119742

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Citations (19)

Modeling of anomalous thermal conduction in thermoelectric magnetohydrodynamics: Couette formulation with a multiphase pressure gradient

Physics of Fluids (2024)

Emad Awad

A metal/liquid-metal junction is a practical thermoelectric cell causing heat absorption or release according to the direction of electric current and temperature gradient. During thermoelectric processes, the possibility of activating the anomalous heat transfer is considered in this work based on adopting a fractional version of Jeffreys equation with three fractional parameters. Because of the connection between the mean-squared displacement of diffusive hot particles and the thermal conductivity, the fractional Jeffreys law is employed to simulate the low thermal conductivity with crossovers; accelerated or retarded transition, and the transition from high (superconductivity—above the Fourier heat conduction) to low (subconductivity—below the Fourier heat conduction) thermal conductivity. The Couette formulation describing a pressure-driven flow of a viscous thick liquid-metal layer bounded by two similar metallic plates, in the presence of a constant transverse magnetic field, is investigated. A triple-phase pressure gradient, consisting of the phases: (i) ramp-up, (ii) dwell, and (iii) exponential decay, is applied as a real-life flow cause and compared with the classical constant pressure gradient and the impulsive pressure gradient case. The velocity and temperature are obtained in the Laplace domain, and then a suitable numerical technique based on the Fourier series approximation is used to recover the solutions in the real domain. It is found that the retarded crossover of low thermal conduction shows “ultraslow” temperature propagation within the thick layer, which indicates to a case of ultralow heat conduction. As well as the strong correlation between the pressure gradient type (constant, impulsive, or three-phase) and direction (favorable or adverse) and its induced velocity, the temperature gradient between the two plates plays a key role in the determination of the velocity direction and magnitude.

Pressure gradient

Temperature Gradient

Heat current

10.1063/5.0190970

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Citations (2)

Diffusion-induced stresses due to an impulsive mass source under non-Fickian mass transfer models

Research Square (Research Square) (2022)

Mohsen A. Fayik Amr El Dhaba Emad Awad

Abstract The description of the mass transfer mechanisms in various physical and engineering fields, e.g., Li-ion battery, is of a significant importance for optimizing their performance. The present work introduces a comparative study describing the different responses of a perfectly elastic material when different non-Fickian diffusion situations are considered. The uncoupled theory of elastic diffusion, in which the diffusion process is described by non-Fickian laws, such as Cattaneo, Jeffreys-type and Burgers-type constitutive laws, is employed in this modeling. Diffusion of lithium ions inside the silicon anode is one of the physical situations in which diffusion-induced stresses may be significant. An impulsive initial value problem, consisting of an initial lithium ions amount starts impulsively to diffuse over the entire space of a silicon material, is considered. Direct approach together with Laplace and exponential Fourier transforms techniques are employed to obtain the solution in the Laplace transformed domain. Inverse Laplace transform is computed numerically to obtain the solution in the physical domain. Comparisons among the material responses to different diffusion regimes are presented.

Constant (computer programming)

10.21203/rs.3.rs-2022488/v1

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Citations (1)