Phase change materials are substances that absorb and release thermal energy during the process of melting and freezing. This characteristic makes phase change material (PCM)  a favourite choice to integrate it in buildings. Stephan problem including melting and solidification in PMC materials is an practical problem in many engineering processes. The position of the moving boundary, its veloci...

An analytic solution is presented describing ̄ow to a drain in a semi-in®nite domain bounded by a leaky layer of constant thickness. The solution is developed by applying the method of images to two parallel boundaries: an inhomogeneity boundary and an equipotential boundary. It is then demonstrated that the solution for the problem with the leaky layer approximated by a leaky boundary (a mixed...

The initialand boundary-value problem for the Benjamin-Bona-Mahony (BBM) equation is studied in this paper. The goal is to understand the periodic behavior (termed as eventual periodicity) of its solutions corresponding to periodic boundary condition or periodic forcing. To this aim, we derive a new formula representing solutions of this initialand boundary-value problem by inverting the operat...

Aquasi-three-dimensional multigrid Navier–Stokes solver on singleandmultiple-passage domains is presented for solving unsteady  ows around oscillating turbine and compressor blades. The conventional direct store method is used for applying the phase-shifted periodic boundary condition over a single blade passage. A parallel version of the solver using the message passing interface standard is ...

We show that there is no blowup solutions, for positive viscosity constant , to the equation f xxt f xxxx +ff xxx f x f xx = 0; x 2 (0; 1); t > 0 with (i) periodic boundary condition, or (ii) Dirichlet boundary condition f = f x = 0 or (iii) Neumann boundary condition f = f xx = 0 on the boundary x = 0; 1. Furthermore we show that every solution decays to the trivial steady state as t goes to i...

We study the time-periodic solutions to systems of conservation laws with ellipticity. It is shown that under time-periodic boundary condition, the system admits at least one global time-periodic solution bounded uniformly with the same period.