A semi-analytical solution is developed for the propagation of plane acoustic waves in a varying area duct, sustaining 1-D mean flow with temperature gradient. The can be non-isentropic, such that axial variation and prescribed independently. case an isentropic flow, which are linked, discussed. second order differential equation (ODE) pressure derived from linearised Euler equations frequency ...

The objective of this article is to carry out an approximate analytical solution of the time fractional order Cauchy-reaction diffusion equation by using a semi analytical method referred as the fractional-order reduced differential transform method (FRDTM). The fractional derivative is illustrated in the Caputo sense. The FRDTM is very efficient and effective powerful mathematical tool for sol...

A semi-analytical iterative method as one of the newest analytical methods is used for the elastic analysis of thick-walled spherical pressure vessels made of functionally graded materials subjected to internal pressure. This method is accurate, fast and has a reasonable order of convergence. It is assumed that material properties except Poisson’s ratio are graded through the thickness directio...

Based on a Lie symmetry analysis, we construct a closed form solution to the kinematic part of the (partial differential) Cosserat equations describing the mechanical behavior of elastic rods. The solution depends on two arbitrary analytical vector functions and is analytical everywhere except a certain domain of the independent variables in which one of the arbitrary vector functions satisfies...

Various methods for calculating the capacitance of unloaded rolling elements are compared to improve electric characterization element bearings. Semi-analytical approximations and finite simulations applied a closed-form analytical two-dimensional solution is derived comparison. The results show that most common semi-analytical approximation, which uses effective radii express contact geometry,...

Abstract—This paper presents new semi-analytical expressions to calculate the self-inductance and the electromagnetic force for a ferromagnetic cylinder of finite length placed inside a circular coil of rectangular cross section. The proposed analytical model is based on boundary value problems with Fourier analysis. Laplace’s and Poisson’s equations are solved in each region by using the separ...

Previous studies on tidal dynamics of coastal aquifers have focussed on the inland propagation of oceanic tides in the cross-shore direction, a con®guration that is essentially one-dimensional. Aquifers at natural coasts can also be in ̄uenced by tidal waves in nearby estuaries, resulting in a more complex behaviour of head ̄uctuations in the aquifers. We present an analytical solution to the tw...