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In this paper, we validate the boundary layer expansion for a family of plane‐parallel flows to nonhomogeneous incompressible magnetohydrodynamic equations with no‐slip boundary conditions imposed on velocity field and perfectly conducting conditions on magnetic field. The convergence rate is established in Sobolev sense. We extend the result of Navier–Stokes system to the case of MHD equations and also investigate the stabilizing effect of the magnetic field by considering the uniform magnetic field. [ABSTRACT FROM AUTHOR]

This paper is concerned with the Rayleigh–Taylor instability for the nonhomogeneous incompressible Navier–Stokes equations with Navier‐slip boundary conditions around a steady state in an infinite slab, where the Navier‐slip coefficients do not have defined sign and the slab is horizontally periodic. Motivated by Jiang et al. (Sci. China Math., 2013), we extend the result from Dirichlet boundary condition to Navier‐slip boundary conditions. Our results indicate the factor that "heavier density with increasing height" still plays a key role in the instability under Navier‐slip boundary conditions. [ABSTRACT FROM AUTHOR]

For a 230t large steel ingot which is firstly manufactured in one industrial plant, both of the analytical calculation and the numerical simulation methods were adopted to predict the total solidification time based on their own physical and mathematical models. The results showed that the total solidification time calculated by the analytical method was 46.0 h, and that was 40.2 h by the numerical method. Comparing with the actual stripping time of 45.8 h for the 230t large steel ingot, both of the estimated values agreed reasonably well with the actual one. For the purpose of practical utilization, the analytical method tends to be more convenient rather than the numerical one. This study can provide a kind of reference for the prediction on the total solidification time of large steel ingots. [ABSTRACT FROM AUTHOR]