This paper presents an exact analytical solution for two-dimensional conductive heat transfer in spherical composite pressure vessels .The vessels are in spherical shape and fibers are winded in circumferential direction. The analytical solution is obtained under the general boundary conditions which consist of convection, conduction and radiation inside/outside of vessel. The heat transfer equ...

The discretization of the two-dimensional convection-diffusion equation usually leads to a linear system whose matrix coefficient is block two-cyclic consistently ordered. For the solution of the resulting linear system, several efficient stationary iterative methods were proposed, among others, by Chin and Manteuffel (1988), Elman and Golub (1990), de Pillis (1991) and Eiermann, Niethammer and...

In this paper, we are interested in the mathematical analysis of a non-classical conservation law. The model describes stratigraphic processes of the geology, taking into account a limited weathering condition. Firstly, we present the physical topic and the mathematical formulation, which lead to an original conservation law. Then, the definition of a solution and some mathematical tools in ord...

where f = f(x), g = g(x), h = h(x), A = A(u) and B = B(u) are arbitrary smooth functions of their variables, f(x)g(x)A(u) 6=0. Our aim is not to give a physical interpretation of the solution of diffusion equations (that is too huge and cannot be reached in the scope of a short paper), but to list the already known exact solutions of equations from the class under consideration. However, in som...

We study the speed of propagating fronts of the convection reaction diffusion equation ut + μuux = uxx + f(u) for reaction terms f(u) such that in the non convective case fronts joining two equilibrium states exist. A variational principle for the wave speed is constructed from which upper and lower bounds are obtained. We find that, in general, there is a transition value μc below which advect...

The effect of ergodisation (either by additional coils like in TEXTOR-DED or by intrinsic plasma effects like in W7-X) defines the need for transport models being able to describe this properly. A prerequisite for this is the concept of local magnetic coordinates allowing a correct discretization with minimized numerical errors [1]. For these coordinates the full respective metric tensor has to...

A set of travelling wave solutions to a hyperbolic generalization of the convectionreaction-diffusion is studied by the methods of local nonlinear alnalysis and numerical simulation. Special attention is paid to displaying appearance of the compactly supported soloutions, shock fronts, soliton-like solutions and peakons PACS codes: 02.30.Jr; 47.50.Cd; 83.10.Gr

We present an explicit fourth-order compact nite diierence scheme for approximating the three dimensional convection-diiusion equation with variable coeecients. This 19-point formula is deened on a uniform cubic grid. Fourier smoothing analysis is performed to show that the smoothing factor of certain relaxation techniques used with the scheme is smaller than 1. We design a parallelization-orie...

to diffusion, a convection term is present. Our overall aim is to look at the effect of convection on the existence and What is the long-time effect of adding convention to a discretised reaction-diffusion equation? For linear problems, it is well known stability of the true and spurious fixed points. that convection may denormalise the process, and, in particular, The potential denormalising e...