In the present work, a hybrid of Fourier transform and homotopy perturbation method is developed for solving the non-homogeneous partial differential equations with variable coefficients. The Fourier transform is employed with combination of homotopy perturbation method (HPM), the so called Fourier transform homotopy perturbation method (FTHPM) to solve the partial differential equations. The c...

Abstract The design of thermoelastic damping (TED) affected by the phase-lagging non-Fourier heat conduction effects becomes significant but challenging for enlarging quality factor widely-used microresonators operating in extreme situations, including ultra-high excitation frequency and ultra-low working temperature. However, there does not exist a rational method designing TED framework law. ...

In this work, an analysis of thermoelastic, homogeneous, and isotropic microbeams was conducted in the context non-Fourier heat conduction law. The first end microbeam based on a graphene strip, which connected to electrical voltage source. Under simple boundary conditions maintained by fixed side ratios, Lord–Shulman model generalized thermoelasticity applied. thermally loaded with source due ...

In this paper, we study the magnetohydrodynamics of Darcy flow in a non-Newtonian liquid. The influence thermophoresis on particle deposition is examined Maxwell nanofluid. our model, temperature distribution generated by Fourier law heat conduction with nonlinear thermal radiation and sink/source. We also examine Soret–Dufour effects mass concentration equations. Brownian thermophoretic diffus...

A transient inverse heat conduction problem focused on gas quenching of steel plates and rings is posed and solved, both analytically and numerically. The quenching objective is to calculate the transient convective heat transfer coefficient which would produce an optimized phase transformation cooling curve. The governing nonlinear heat equation is nondimensionalised, and a small parameter, th...

1. Everything is number 2. Ancient Astronomy 3. Optics and statics 4. The middle ages and the renaissance 5. Mechanics of motion 6. Newtonian mechanics 7. Early differential equations 8. The Brachistochrone 9. Early methods of solutionLinear differential equations 10 Newton’s second law as a differential equationThe method of perturbations 11. The vibrating stringPartial differential equations ...

Synopsis Iterative reconstructions of undersampled non-Cartesian data are computationally expensive because non-Cartesian Fourier transforms are much less e cient than Cartesian Fast Fourier Transforms. Here, we introduce an algorithm that does not require non-uniform Fourier transforms during optimization iterations, resulting in large reductions in computation times with no impairment of imag...

Effect of a crystalline-amorphous interface on heat conduction has been studied using atomistic simulations of a silicon system. System with amorphous silicon was created using the bond-switching Monte Carlo simulation method and heat conduction near room temperature was studied by molecular dynamics simulations of this system. INTRODUCTION As the sizes of electronic devices decrease an increas...

In this paper, we study a generalisation of the Caginalp phase field system obtained by considering Fourier law as heat conduction and involving two temperatures. first section, are interested in existence uniqueness solutions. section 2, address question asymptotic behaviour solutions, particular with demonstration global attractor. For this, needed to show that is dissipative know regularity ...