We study the Oberbeck-Boussinesq approximation describing the motion of an incompressible, heat-conducting fluid occupying a general unbounded domain in R3. We provide a rigorous justification of the model by means of scale analysis of the full Navier-Stokes-Fourier system in the low Mach and Froude number regime on large domains, the diameter of which is proportional to the speed of sound. Fin...

An analytical solution of the Boussinesq equations for the motion of a viscous stably stratified fluid driven by a surface thermal forcing with large horizontal gradients (step changes) is obtained. This analytical solution is one of the few available for wall-bounded buoyancy-driven flows. The solution can be used to verify that computer codes for Boussinesq fluid system simulations are free o...

In turbulent Rayleigh-Bénard convection (a fluid between two parallel horizontal plates and heated from below) a transition was predicted to occur [1,2] with increasing Rayleigh number Ra from a ‘‘classical’’ state with laminar boundary layers (BLs) to an ‘‘ultimate’’ state with turbulent BLs. Recently, this transition was found in measurements of the Nusselt number Nu and Reynolds number Re as...

We demonstrate the specific non-Boussinesq roles played by various fluid properties in thermal convection by allowing each of them to possess, one at a time, a temperature dependence that could be either positive or negative. The negative temperature dependence of the coefficient of thermal expansion hinders effective thermal convection and reduces the Nusselt number, whereas the negative depen...

this work presents a numerical analysis of entropy generation in γ-shaped enclosure that was submitted to the natural convection process using a simple thermal lattice boltzmann method (tlbm) with the boussinesq approximation.  a 2d thermal lattice boltzmann method with 9 velocities, d2q9, is used to solve the thermal flow problem. the simulations are performed at a constant prandtl number (pr ...

Abstract Boussinesq theory can model quite accurately viscous flows that involve multiple fluids with interfaces between them, so long as there is not much difference the densities of various fluids. However, approximation generally poor when density ratio large. Here, we propose an Extended approximate equation, allows for large ratios, while still remaining straightforward to implement. Examp...

This paper is concerned with the local well-posedness of Oberbeck Boussinesq approximation for unsteady motion a drop in another fluid separated by closed interface surface tension. We are devoted to obtaining linearized Oberbeck-Boussinesq fixed domain using Hanzawa transformation, and maximal $ L^{p} $-$ L^{q} regularities two-phase system obtained authors [10] establish existence uniqueness ...

This paper studies solutions of the two-dimensional incompressible Boussinesq equations with fractional dissipation. The spatial domain is a periodic box. The Boussinesq equations concerned here govern the coupled evolution of the fluid velocity and the temperature and have applications in fluid mechanics and geophysics. When the dissipation is in the supercritical regime (the sum of the fracti...

This work presents a numerical analysis of entropy generation in Γ-Shaped enclosure that was submitted to the natural convection process using a simple thermal lattice Boltzmann method (TLBM) with the Boussinesq approximation.  A 2D thermal lattice Boltzmann method with 9 velocities, D2Q9, is used to solve the thermal flow problem. The simulations are performed at a constant Prandtl number (Pr ...