The Governing Equations of Electrodynamics

2013 ◽  
Vol 60 (2) ◽  
pp. 231-246 ◽  
Author(s):  
Prashant Saxena

In this paper, we present the general governing equations of electrodynamics and continuum mechanics that need to be considered while mathematically modelling the behaviour of electromagnetic acoustic transducers (EMATs). We consider the existence of finite deformations for soft materials and the possibility of electric currents, temperature gradients, and internal heat generation due to dissipation. Starting with Maxwell’s equations of electromagnetism and balance laws of nonlinear elasticity, we present the governing equations and boundary conditions in incremental form in order to solve wave propagation problems of boundary value type.


Author(s):  
J. Buggaramulu ◽  
M. Venkatakrishna ◽  
Y. Harikrishna

The objective of this paper is to analyze an unsteady MHD free convective heat and mass transfer boundary flow past a semi-infinite vertical porous plate immersed in a porous medium with radiation and chemical reaction. The governing equations of the flow field are solved numerical a two term perturbation method. The effects of the various parameters on the velocity, temperature and concentration profiles are presented graphically and values of skin-frication coefficient, Nusselt number and Sherwood number for various values of physical parameters are presented through tables.


2020 ◽  
Vol 22 (4) ◽  
pp. 939-958
Author(s):  
Indrajit Roy ◽  
D. P. Acharya ◽  
Sourav Acharya

AbstractThe present paper investigates the propagation of quasi longitudinal (qLD) and quasi transverse (qTD) waves in a magneto elastic fibre-reinforced rotating semi-infinite medium. Reflections of waves from the flat boundary with surface stress have been studied in details. The governing equations have been used to obtain the polynomial characteristic equation from which qLD and qTD wave velocities are found. It is observed that both the wave velocities depend upon the incident angle. After imposing the appropriate boundary conditions including surface stress the resultant amplitude ratios for the total displacements have been obtained. Numerically simulated results have been depicted graphically by displaying two and three dimensional graphs to highlight the influence of magnetic field, rotation, surface stress and fibre-reinforcing nature of the material medium on the propagation and reflection of plane waves.


2020 ◽  
Vol 10 (7) ◽  
pp. 2600
Author(s):  
Tho Hung Vu ◽  
Hoai Nam Vu ◽  
Thuy Dong Dang ◽  
Ngoc Ly Le ◽  
Thi Thanh Xuan Nguyen ◽  
...  

The present paper deals with a new analytical approach of nonlinear global buckling of spiral corrugated functionally graded carbon nanotube reinforced composite (FG-CNTRC) cylindrical shells subjected to radial loads. The equilibrium equation system is formulated by using the Donnell shell theory with the von Karman’s nonlinearity and an improved homogenization model for spiral corrugated structure. The obtained governing equations can be used to research the nonlinear postbuckling of mentioned above structures. By using the Galerkin method and a three term solution of deflection, an approximated analytical solution for the nonlinear stability problem of cylindrical shells is performed. The linear critical buckling loads and postbuckling strength of shells under radial loads are numerically investigated. Effectiveness of spiral corrugation in enhancing the global stability of spiral corrugated FG-CNTRC cylindrical shells is investigated.


2021 ◽  
Vol 13 (5) ◽  
pp. 2590
Author(s):  
S. A. M. Mehryan ◽  
Kaamran Raahemifar ◽  
Leila Sasani Gargari ◽  
Ahmad Hajjar ◽  
Mohamad El Kadri ◽  
...  

A Nano-Encapsulated Phase-Change Material (NEPCM) suspension is made of nanoparticles containing a Phase Change Material in their core and dispersed in a fluid. These particles can contribute to thermal energy storage and heat transfer by their latent heat of phase change as moving with the host fluid. Thus, such novel nanoliquids are promising for applications in waste heat recovery and thermal energy storage systems. In the present research, the mixed convection of NEPCM suspensions was addressed in a wavy wall cavity containing a rotating solid cylinder. As the nanoparticles move with the liquid, they undergo a phase change and transfer the latent heat. The phase change of nanoparticles was considered as temperature-dependent heat capacity. The governing equations of mass, momentum, and energy conservation were presented as partial differential equations. Then, the governing equations were converted to a non-dimensional form to generalize the solution, and solved by the finite element method. The influence of control parameters such as volume concentration of nanoparticles, fusion temperature of nanoparticles, Stefan number, wall undulations number, and as well as the cylinder size, angular rotation, and thermal conductivities was addressed on the heat transfer in the enclosure. The wall undulation number induces a remarkable change in the Nusselt number. There are optimum fusion temperatures for nanoparticles, which could maximize the heat transfer rate. The increase of the latent heat of nanoparticles (a decline of Stefan number) boosts the heat transfer advantage of employing the phase change particles.


2021 ◽  
pp. 107754632110004
Author(s):  
Hassan Afshari ◽  
Hossein Amirabadi

In this article, a comprehensive study is conducted on the free vibration analysis of rotating truncated conical shells reinforced with functionally graded agglomerated carbon nanotubes The shell is modeled based on the first-order shear deformation theory, and effective mechanical properties are calculated based on the Eshelby–Mori–Tanaka scheme along with the rule of mixture. By considering centrifugal and Coriolis accelerations and initial hoop tension, the set of governing equations is derived using Hamilton’s principle and is solved numerically using the differential quadrature method Convergence and accuracy of the presented model are confirmed and the effects of different parameters on the forward and backward frequencies of the rotating carbon nanotube-reinforced truncated conical shells are investigated.


Sign in / Sign up

Export Citation Format

Share Document