Assuming exponential-varying properties in the radial direction and based on the elasticity theory, an exact closed-form analytical solution is obtained to elastic analysis of FGM thick-walled cylindrical pressure vessels in the plane strain condition. Following this, radial distribution of radial displacement, radial stress, and circumferential stress are plotted for different values of material inhomogeneity constant. The displacements and stresses distributions are compared with the solutions of the finite element method (FEM).
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An exact solution of an unsteady flow past an exponentially accelerated infinite vertical plate with variable temperature and mass diffusion is presented in the presence of a magnetic field. The plate temperature and species concentration level near the plate is made to rise linearly with time. The dimensionless governing equations are solved using the Laplace-transform technique. Velocity, temperature and concentration profiles are studied for different physical parameters such as the magnetic field parameter, thermal Grashof number, mass Grashof number, Schmidt number, time and parameter a. It is observed that velocity decreases with increasing the magnetic field parameter. It is also observed that the velocity increases with increasing values of a.
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W artykule przedstawiono realizację splotową wzoru zespolonego de Moivre’a-Eulera w dziedzinie czasu dyskretnego. Podano przykłady zastosowań do rozkładu fizycznego prądu w teorii mocy.
EN
In the article is presented the convolution realization of de Moivre-Euler formula in discrete time domain. It was shown that this approach makes identification of power phenomena in electrical circuit in the time domain and current decomposition into physical components in special case.
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W artykule przedstawiono aspekty obliczeniowe, splotowej realizacji wzoru zespolonego de Moivre’a-Eulera w dziedzinie czasu dyskretnego. Wzór ten znajduje zastosowanie do rozkładu fizycznego praw teorii mocy.
EN
In the article the numerical aspects of the convolution realization of the Moivre-Euler formula In discrete-time domain is presented.
Effects of transfer of mass and free convection on the flow field of an incompressible viscous fluid past an exponentially accelerated vertical plate with variable surface temperature and mass diffusion are studied. Results for velocity, concentration, temperature are obtained by solving governing equations using the Laplace transform technique. It is observed that the velocity increases with decreasing values of the chemical reaction parameter or radiation parameter. But the trend is just reversed with respect to the time parameter. The skin friction is also studied.
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