Viscoelastic initially stressed microbeam heated by an intense pulse laser via photo-thermoelasticity with two-phase lag

This work aims to assess the response of viscoelastic Kelvin–Voigt microscale beams under initial stress. The microbeam is photostimulated by the light emitted by an intense picosecond pulsed laser. The photothermal elasticity model with dual-phase lags, the plasma wave equation and Euler–Bernoulli beam theory are utilized to construct the system equations governing the thermoelastic vibrations of microbeams. Using the Laplace transform technique, the problem is solved analytically and expressions are provided for the distributions of photothermal fields. Taking aluminum as a numerical example, the effect of the pulsed laser duration coefficient, viscoelasticity constants and initial stress on photothermal vibrations has been studied. In addition, a comparison has been made between different models of photo-thermoelasticity to validate the results of the current model. Photo-microdynamic systems might be monolithically integrated on aluminum microbeams using microsurface processing technology as a result of this research.

2D PROBLEM FOR A SPHERE IN THE FRACTIONAL ORDER THEORY THERMOELASTICITY TO AXISYMMETRIC TEMPERATURE DISTRIBUTION

In the present article, we implement the fractional thermoelasticity theory to a 2D issue for a sphere whose surface is free from traction, subject to a provided axisymmetric temperature distribution of heat. The medium is supposed to be quiescent initially. A direct method is used to get a solution and the Laplace transform technique is used. Mathematical models for copper material are designed as a particular instance. Numerical results are computed with help of Mathcad software and graphically represented and the fractional-order parameter effect has been explained.

Hydrodynamic behaviour of velocity of applied magnetic field on unsteady MHD Couette flow of dusty fluid in an annulus

This research work inspects mass transport phenomenon of Saffman’s dusty fluid model for transient magnetohydrodynamics fluid flow of a binary mixture passing through an annular duct. Particularly, effort has been devoted to theoretically explore the role of velocity of applied magnetic field. Here, our treatment of the governing momentum equations accountable for the flow is done using the classical Laplace transform technique and Riemann-Sum Approximation. The effects of the physical parameters such as time, relaxation time parameter, radii ratio, Hartmann number, variable mass parameter and velocity of applied magnetic field on the fluid phase velocity, dust phase velocity and skin friction have been illustrated pictorially. It is concluded that contrary to the known classical effect of boosting Hartmann number on velocity, both components of flow (fluid and dust phase) and skin friction are seen to be heightened with an overwhelming presence of velocity of applied magnetic field. For large time, it is anticipated that higher profiles for velocity and skin friction are seen with fluid phase and an accelerated moving wall.

Influence of Radiative Heat Energy on the MHD Flow of Cu-kerosene Nanofluid Over a Vertical Plate: Laplace Transform Technique

The present study reveals the heat transfer phenomena of magnetohydrodynamic (MHD) nanofluid over a moving vertical plate due to the interaction of thermal radiation. Due to enhancing thermal properties, instead of water, kerosene is treated as the base fluid with the inclusion of Cu (Copper) nanoparticles. In addition to that, for the nanofluid viscosity and thermal conductivity the Einstein’s model and Mintsa’s model, respectively. The transformed models for the governing equations proposed here are handled analytically employing Laplace Transform Technique. However, the variations of various parameters are obtained because the constructed flow phenomena are presented via graph. In the particular case, the consequence obtained is compared with the earlier study to get the validation which provides a road map for further investigation.

Convergence of the uniaxial PML method for time-domain electromagnetic scattering problems

In this paper, we propose and study the uniaxial perfectly matched layer (PML) method for three-dimensional time-domain electromagnetic scattering problems, which has a great advantage over the spherical one in dealing with problems involving anisotropic scatterers. The truncated uniaxial PML problem is proved to be well-posed and stable, based on the Laplace transform technique and the energy method. Moreover, the $L^2$-norm and $L^{\infty}$-norm error estimates in time are given between the solutions of the original scattering problem and the truncated PML problem, leading to the exponential convergence of the time-domain uniaxial PML method in terms of the thickness and absorbing parameters of the PML layer. The proof depends on the error analysis between the EtM operators for the original scattering problem and the truncated PML problem, which is different from our previous work (SIAM J. Numer. Anal. 58(3) (2020), 1918-1940).

The Solutions of Some Riemann–Liouville Fractional Integral Equations

In this paper, we propose the solutions of nonhomogeneous fractional integral equations of the form I0+3σy(t)+a·I0+2σy(t)+b·I0+σy(t)+c·y(t)=f(t), where I0+σ is the Riemann–Liouville fractional integral of order σ=1/3,1,f(t)=tn,tnet,n∈N∪{0},t∈R+, and a,b,c are constants, by using the Laplace transform technique. We obtain solutions in the form of Mellin–Ross function and of exponential function. To illustrate our findings, some examples are exhibited.

Application of water based drilling clay-nanoparticles in heat transfer of fractional Maxwell fluid over an infinite flat surface

In the present paper, unsteady free convection flow of Maxwell fluid containing clay-nanoparticles is investigated. These particles are hanging in water, engine oil and kerosene. The values for nanofluids based on the Maxwell-Garnett and Brinkman models for effective thermal conductivity and viscosity are calculated numerically. The integer order governing equations are being extended to the novel non-integer order fractional derivative. Analytical solutions of temperature and velocity for Maxwell fluid are build using Laplace transform technique and expressed in such a way that they clearly satisfied the boundary conditions. To see the impact of different flow parameters on the velocity, we have drawn some graphs. As a result, we have seen that the fractional model is superior in narrate the decay property of field variables. Some limiting solutions are obtained and compared with the latest existing literature. Moreover, significant results can be observed for clay nanoparticles with different base fluids.

A competing risks cure frailty model: An application to relapse-free survival of breast cancer patients

In competing risks cure models, if there is unobserved heterogeneity among susceptible patients, application of the methods that do not consider this heterogeneity, may lead to invalid results. Therefore, this study aimed to introduce a model to cover the above properties of survival studies. We introduced a unified model by combining a parametric mixture cure gamma frailty model and vertical modeling of competing risks. We obtained estimates of parameters by an iterative method and Laplace transform technique. Then, we calculated the cumulative incidence functions (CIFs) and related confidence bounds by using a bootstrap approach. We conducted an extensive simulation study to evaluate the performance of the proposed model. The results of the simulation study showed the superior performance of our proposed competing risks cure frailty model. Finally, we applied the proposed method to analyze a real dataset of breast cancer patients.