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This study aims to attempt to construct a new mathematical model of the generalized thermoelasiticity theory based on the memory-dependent derivative (MDD) considering three-phase-lag effects. The governing equations of the problem associated with kernel function and time delay are illustrated in the form of vector matrix differential equations. Implementing Laplace and Fourier transform tools, the problem is sorted out analytically by an eigenvalue approach method. The inversion of Laplace and Fourier transforms are executed, incorporating series expansion procedures. Displacement component, temperature and stress distributions are obtained numerically and illustrated graphically and compared with the existing literature.

This study is to analyze the influence of MDD of three-phase-lag heat conduction interaction in an isotropic semi-infinite medium. The current model has been connected to generalize two-dimensional (2D) thermoelasticity problem. The governing equations are shown in vector matrix form of differential equation concerning Laplace-transformed domain and solved by using the eigenvalue technique. The combined Laplace Fourier transform is applied to find the analytical interpretations of temperature, stresses, displacement for silicon material in a non-dimensional form. Inverse Laplace transform has been found by applying Fourier series expansion techniques introduced by Honig and Hirdes (1984) after performing the inverse Fourier transform.

The main conclusion of this current study is to demonstrate an innovative generalized concept for heat conducting Fourier’s law associated with moderation of time parameter, time delay variable and kernel function by applying the MDDs. However, an important role is played by the time delay parameter to characterize the behavioral patterns of the physical field variables. Further, a new categorization for materials may be created rendering to this new idea along MDD for the time delay variables to develop a new measure of its potential to regulate heat in the medium.

Generalized thermoelasticity is hastily undergoing modification day-by-day from basic thermoelasticity. It has been progressed to get over from the limitations of fundamental thermoelasticity, for instance, infinite velocity components of thermoelasticity interference, in the adequate thermoelastic response of a solid to short laser pulses and deprived illustrations of thermoelastic performance at low temperature. In the past few decades, the fractional calculus is used to change numerous existing models of physical procedure, and its applications are used in various fields of physics, continuum mechanics, fluid mechanics, biology, viscoelasticity, biophysics, signal and image processing, control theory, engineering fields, etc.

The spectral boundary element method for solving two‐dimensional transient heat conduction problems is developed. This method is combined with the fast Fourier transform (FFT) to convert the solution between the time and frequency domains. The fundamental solutions in the frequency domain, required for the present method, are discussed. The resulting line integrations in the frequency domain are discretized using constant boundary elements and used in a Fortran boundary element program. Three examples are used to illustrate the accuracy and effectiveness of the method in both the frequency and time domains. First, the frequency domain solution procedure is verified using the steady‐state example of a semi‐infinite half space with a heat flux applied to a patch of the surface. This spectral boundary element method is then applied to the problem of a circular hole in an infinite solid subjected to a time‐varying heat flux, and solutions in both the frequency and time domains are presented. Finally, the method is used to solve the circular hole problem with a convection boundary condition. The accurary of these results leads to the conclusion that the spectral boundary element method in conjunction with the FFT is a viable option for transient problems. In addition, this spectral approach naturally produces frequence domain information which is itself of interest.

The present investigation is concerned with a two‐dimensional problem in electromagnetic micropolar elasticity for a half‐space whose surface is subjected to mechanical or thermal source in the presence of a transverse magnetic field. Laplace and Fourier transform technique is used to solve the problem. As an application of the approach concentrated/continuous mechanical or thermal source has been taken. The integral transforms have been inverted by using a numerical technique to obtain the components of normal strain, temperature distribution, normal force stress and tangential couple stress in the physical domain. The expressions of these quantities have been given and illustrated graphically to depict the magnetic effect for two different theories of generalized thermoelasticity, Lord and Shulman (L‐S theory) and Green and Lindsay (G‐L theory). Some special cases of interest are also deduced from the present investigation.

The system of equations for fractional thermo-viscoelasticity is used to investigate two-dimensional bioheat transfer and heat-induced mechanical response in human skin tissue with rheological properties.

Laplace and Fourier’s transformations are used. The resulting formulation is applied to human skin tissue subjected to regional hyperthermia therapy for cancer treatment. The inversion process for Fourier and Laplace transforms is carried out using a numerical method based on Fourier series expansions.

Comparisons are made with the results anticipated through the coupled and generalized theories. The influences of volume materials properties and fractional order parameters for all the regarded fields are examined. The results indicate that volume relaxation parameters, as well as fractional order parameters, play a major role in all considered distributions.

Bio-thermo-mechanics includes bioheat transfer, biomechanics, burn injury and physiology. In clinical applications, knowledge of bio-thermo-mechanics in living tissues is very important. One can infer from the numerical results that, with a finite distance, the thermo-mechanical waves spread to skin tissue, removing the unrealistic predictions of the Pennes’ model.

To provide a new method and methodology for researches and academic members which can help them to develop scientific work.

The paper presents closed‐form expressions for the harmonic components of the space‐vector pulsewidth modulated (PWM) waveforms under inverter fault‐mode operations. The main method that is used is the Laplace transform and Fourier series expansion theorem.

Provides information about harmonic sources and its influence on the behavior of the induction machine.

The calculated harmonics show a very close agreement with measured harmonics from an experimental digital signal processor (DSP) based modulator. It provides a very useful source of theoretical and practical information for scientific and research area.

The method is original and has not been published before. The new and original approach is given by the use of the Laplace transform of space‐vectors in the complex plane. This will help to understand harmonics which are formed in four‐switch voltage source inverter.

The Laplace and Fourier transforms have been employed to find the general solution to the fields equations in porous generalized thermoelastic medium subjected to thermomechanical boundary conditions permeated with various heat sources; in the transformed form. On the boundary surface, the distributed sources have been taken. To get the solution in the physical form, a numerical inversion technique has been used. The effect of continuous and moving heat sources with the thermomechanical boundary conditions; and the response of boundary sources (concentrated and continuous) with heat source varying with depth; on the normal stress component, change in volume fraction field and temperature distribution have been depicted graphically for a particular model. A particular case is also deduced from the present formulation.

This paper aims to investigate the transient disturbances created by an internal line heat source that suddenly starts moving uniformly inside a visco‐elastic half‐space.

Generalised theory of thermo‐elasticity with relaxation time proposed by Lord‐Shulman is applied. The material of the semi‐infinite medium is an isotropic visco‐elastic solid of Kelvin‐Voight type. Fourier and Laplace transform techniques are used.

Applying the Fourier and Laplace transform techniques, expressions for displacement components in the transformed domain are found. These expressions prove the existence of three waves – a modified thermal wave, a visco‐elastic wave of defused nature and a transverse visco‐elastic wave.

Surface displacement components were evaluated on the boundary for only a short time.

The paper provides numerical results that are illustrated graphically to highlight the variations of surface displacement components with distance for different values of time, source depth and velocity of the source.

This paper presents analytical and experimental results that quantify the performance of an induction motor fed by a space‐vector pulse width modulated four‐switch (B4) voltage source inverter. First, as voltage vectors in the inverter form unsymmetrical sequences, the discrete Fourier transform is used to express the voltage vectors in symmetrical form. Second, by using a mixed p‐z approach for every voltage vector sequence, we can derive a closed‐form solution, including steady‐state and transient components of the motor currents. From the motor currents, we can derive an analytical equation for the electromagnetic torque. Both the steady‐state and transient components of the motor currents are determined in a simple and lucid analytical form, which avoids involved matrix inversion as well as exponentiation. The theoretical considerations are verified on an experimental unit.

This paper aims to examine the unsteady flow of an incompressible, viscous, conducting couple stress fluid flow through a porous medium over an infinite plate that is started into motion in its own plane by an impulse. The presence of a uniform magnetic field in a direction perpendicular to the plate is assumed.

Casting the governing equations into matrix form, the authors use state space approach and Laplace transform technique to obtain the field variables. The inversion of Laplace transform is carried through the adoption of a numerical technique.

Two specific problems related to a heated plate and a plate under uniform heating are examined and the variation of temperature and velocity with respect to the couple stress parameter numerically is studied. Numerical results concerning velocity and temperature distribution are presented graphically.

The authors have attempted the problem in fluid dynamics through state space approach which is exploited with tremendous success in modern control theory but not enough in fluid dynamics.

The purpose of this paper is to deal with a new generalized model of thermoelasticity theory with memory-dependent derivatives (MDD).

The two-dimensional equations of generalized thermoelasticity with MDD are solved using a state-space approach. The numerical inversion method is employed for the inversion of Laplace and Fourier transforms.

The solutions are presented graphically for different values of time delay and kernel function.

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 two-dimensional problem of an isotropic plate.