What is Boussinesq approximation in natural convection?

The Boussinesq approximation is a way to solve nonisothermal flow, such as natural convection problems, without having to solve for the full compressible formulation of the Navier-Stokes equations. It assumes that variations in density have no effect on the flow field, except that they give rise to buoyancy forces.

What is Boussinesq model?

In fluid dynamics, the Boussinesq approximation (pronounced [businɛsk], named for Joseph Valentin Boussinesq) is used in the field of buoyancy-driven flow (also known as natural convection). It ignores density differences except where they appear in terms multiplied by g, the acceleration due to gravity.

What is boussinesq hypothesis in turbulence modeling?

Boussinesq’s hypothesis is that the turbulent stresses are related to the mean velocity gradients in almost the same way that the viscous stresses are related to the complete velocity gradients.

How does the Rayleigh number differ from the Grashof number?

The Rayleigh number is defined as the product of the Grashof number, which describes the relationship between buoyancy and viscosity within a fluid, and the Prandtl number, which describes the relationship between momentum diffusivity and thermal diffusivity.

How is natural convection different from forced convection?

In natural convection, any fluid motion is caused by natural means such as the buoyancy effect, i.e. the rise of warmer fluid and fall the cooler fluid. Whereas in forced convection, the fluid is forced to flow over a surface or in a tube by external means such as a pump or fan.

What is the resulting equation in the Boussinesq approximation?

The resulting equation is is the thermal conductivity. The three numbered equations are the basic convection equations in the Boussinesq approximation.

What is Boussinesq in fluid dynamics?

Boussinesq approximation (buoyancy) Jump to navigation Jump to search. In fluid dynamics, the Boussinesq approximation (pronounced [businɛsk], named for Joseph Valentin Boussinesq) is used in the field of buoyancy-driven flow (also known as natural convection).

What are Boussinesq inversions?

Inversions. One feature of Boussinesq flows is that they look the same when viewed upside-down, provided that the identities of the fluids are reversed. The Boussinesq approximation is inaccurate when the dimensionless density difference Δ ρρ is of order unity. For example, consider an open window in a warm room.

Does the Boussinesq approximation ignore gravity?

It ignores density differences except where they appear in terms multiplied by g, the acceleration due to gravity. The essence of the Boussinesq approximation is that the difference in inertia is negligible but gravity is sufficiently strong to make the specific weight appreciably different between the two fluids.