The unsteady natural convection flow of an incompressible viscous fluid near a vertical plate that applies an arbitrary shear stress to the fluid is studied using the Laplace transform technique. The fluid flow is due to both the shear and the heating of the plate. Closed-form expressions for velocity and temperature are established under the usual Boussinesq approximation. For illustration pur...

Dual Scattering Channel schemes generalise Johns’ TLM algorithm and replace the latter in situations where the transmission line picture of wave propagation fails. This is notoriously the case in applications to fluid dynamics, for instance. In this paper, a DSC numerical solution of the Oberbeck-Boussinesq equations is presented, which approximate the Navier-Stokes equations for viscous quasi ...

We justify the global-in-time diffusive limit of the Boltzmann equation inside a periodic domain T. We only assume that in the initial expansion (1.2) at t = 0, the kinetic parts are well-prepared, but the fluid parts could be general, i.e. the fluids parts are not required to satisfy the incompressibility and Boussinesq relations. For this case, the fluid initial layers are created and preserv...

While non-Boussinesq hexagonal convection patterns are well known to be stable close to threshold (i.e. for Rayleigh numbers R ≈ Rc), it has often been assumed that they are always unstable to rolls already for slightly higher Rayleigh numbers. Using the incompressible Navier-Stokes equations for parameters corresponding to water as a working fluid, we perform full numerical stability analyses ...

The figures on the left show effect of Prandtl number (Pr) Rayleigh-B\'enard problem with Boussinesq conditions, for same Grashof ${10}^{9}$. Top: Pr = 12.73; bottom, ${10}^{\ensuremath{-}4}$. plot right shows that low molecular yields an inversely varying turbulent number; is, flow behaves effectively as a high fluid. data are non-Boussinesq conditions. qualitative is case well, but dependence...

The stationary problem for the heat convection of compressible fluid is considered around the equilibrium solution with the external forces in the horizontal strip domain z0 < z < z0 + 1 and it is proved that the solution exists uniformly with respect to z0 ≥ Z0 . The limit system as z0 → +∞ is the Oberbeck-Boussinesq equations. Mathematics Subject Classification (2010). Primary 35Q35; Secondar...

the problem of combined heat and mass transfer of an electrically conducting fluid in mhdnatural convection adjacent to a vertical surface is analyzed, taking into account the effects of ohmic heatingin the presence of suction or injection. an approximate numerical solution for the steady laminar boundarylayerflow over a wall of the wedge in the presence of species concentration and mass diffus...

We compute the full set of second-order inertial corrections to instantaneous force and torque acting on a small spherical rigid particle moving unsteadily in general steady linear flow. This is achieved by using matched asymptotic expansions formulating problem coordinate system co-moving with background Effects unsteadiness fluid-velocity gradients are assumed be small, but dominate far field...

This paper presents a parametric finite-difference scheme concerning the numerical solution of theone-dimensional Boussinesq-type set of equations, as they were introduced byPeregrine, in the case of wavesrelatively long with small amplitudes in water of constant depth. The method which is used can be considered asa generalization of the Crank-Nickolson method and it has been ap...