Subject of this study is the free boundary problem of a liquid layer that is dried by evaporation. Using a Stefan type problem, we model the diffusion driven drying of a layer of liquid paint consisting of resin and solvent. The effect of a small perturbation of the flat boundary is considered. We include the discussion of evaporation constant as a free parameter. For both small and big wavenum...

in the age of technology, it is vital to cool down different parts of a device to use it more beneficially. using nanofluids is one of the most common methods which has shown very effective results. in this paper, we have rephrased a classic equation in fluid mechanics, i.e. the falkner-skan boundary layer equation, in order to be used for nanofluid. this nonlinear equation, which was presented...

In this paper we construct numerical schemes to approximate linear transport equations with slab geometry by one-dimensional diffusion equations. We treat both the case of pure diffusive scaling and the case where kinetic and diffusive scalings coexist. The diffusion equations and their data are derived from asymptotic and layer analysis which allows general scattering kernels and general data....

Heisenberg spin equation equivalence to nonlinear Schrödinger equation recently demonstrated by Rogers and Schief , is applied to the investigation of vortex filaments in magnetohydrodynamics (MHD) dynamos. The use of Gauss-Mainard-Codazzi equations allows us to investigate in detail the influence of curvature and torsion of vortex filaments in the MHD dynamos. This application follows closely ...

An integral approach is employed to investigate the effects of blockage on fluid flow and heat transfer from a circular cylinder confined between parallel planes. The integral form of the boundary-layer momentum equation is solved using the modified von Kármán–Pohlhausen method, which uses a fourth-order velocity profile inside the hydrodynamic boundary layer. The potential flow velocity, outsi...