# What does a high Rayleigh number mean?

## What does a high Rayleigh number mean?

In fluid mechanics, the Rayleigh number (Ra) for a fluid is a dimensionless number associated with buoyancy-driven flow, also known as free or natural convection. It characterises the fluid’s flow regime: a value in a certain lower range denotes laminar flow; a value in a higher range, turbulent flow.

How do I find my Rayleigh number?

The Rayleigh number is simply 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.

What is the typical Rayleigh number for the onset of convection?

Hence it may also be viewed as the ratio of buoyancy and viscosity forces multiplied by the ratio of momentum and thermal diffusivities. It is closely related to the Nusselt number. For most engineering purposes, the Rayleigh number is large, somewhere around 106 to 108.

### What is Rayleigh number in heat transfer?

Rayleigh number is a dimensionless number that represents the ratio of buoyancy and thermal diffusivity. Below the critical Rayleigh number, convection does not occur and heat is transferred through thermal conduction. Above the critical Rayleigh number, heat is transferred through convection.

Can you have a negative Rayleigh number?

It can’t. It will be negative if the Ts is lower than Tinf, and simply change the order for them.

What is characteristic length in Rayleigh number?

Restrepo and Glicksman [20] informed that the thermal boundary layer thickness decreases with increasing Rayleigh number. These researchers defined the Rayleigh number taking the characteristic length as one-half of the plate length.

#### What is G in Rayleigh number?

The Rayleigh number is defined for a plane-parallel layer without internal heat sources and heated from below and cooled from above as(18.7)Ra=ρgαΔTb3ηκ,where g is gravity and α is the coefficient of thermal expansion, describing the relative volume change with changing temperature of a material.

What is beta in the Rayleigh number?

Rayleigh number, Ra, is a dimensionless term used in the calculation of natural convection. where g is acceleration due to gravity, β’ is coefficient of thermal expansion of the fluid, ΔT is temperature difference, x is length, ν is kinematic viscosity and κ is thermal diffusivity of the fluid.

How does natural convection occur?

Natural convection arises from temperature differences among air parcels, or heat transfer at surfaces (i.e. surface-to-air temperature difference). In the absence of forced convection, natural convection becomes the only means of air mixing inside enclosed spaces.

## Can the Rayleigh number be negative?

How does forced convection occur?

Convection is a heat transfer mechanism where heat moves from one place to another through fluid currents. Forced convection is simply using this mechanism in a useful way to heat or cool a home efficiently, such as using a fan. This forcing can be done with a ceiling fan, a pump, suction device, or other.

What is critical Reynolds number?

1 Critical Reynolds Number. A critical Reynolds number is determined as a limit where the laminar flow changes to turbulent flow. If the calculated NRe is greater than the critical Reynolds number NRec, the flow regime is turbulent; otherwise the flow regime is laminar.

### What is the Rayleigh number for thermal diffusion across a distance?

The time scale for thermal diffusion across a distance is the thermal diffusivity. Thus the Rayleigh number Ra is . The Rayleigh number can be written as the product of the Grashof number and the Prandtl number: R a = G r P r . {\\displaystyle \\mathrm {Ra} =\\mathrm {Gr} \\mathrm {Pr} .}

What is Rayleigh number in fluid mechanics?

In fluid mechanics, the Rayleigh number (Ra) for a fluid is a dimensionless number associated with buoyancy-driven flow, also known as free or natural convection. [1] [2] [3] It characterises the fluid’s flow regime: [4] a value in a certain lower range denotes laminar flow ; a value in a higher range, turbulent flow .

What is the Rayleigh number for convection?

For free convection near a vertical wall, the Rayleigh number is defined as: β is the thermal expansion coefficient (equals to 1/ T, for ideal gases, where T is absolute temperature). In the above, the fluid properties Pr, ν, α and β are evaluated at the film temperature, which is defined as:

#### What is the Rayleigh number in porous media?

Porous media. The Rayleigh number above is for convection in a bulk fluid such as air or water, but convection can also occur when the fluid is inside and fills a porous medium, such as porous rock saturated with water. Then the Rayleigh number, sometimes called the Rayleigh-Darcy number, is different.