# Convection

The convection is a mode of transfer of Chaleur where this one is advectée ( transported - led , but these terms are in fact unsuitable) by at least a fluid. Thus during the cooking of the pastes, water is put moving spontaneously: the groups of particles of fluid close to the bottom of the Casserole are heated, thus dilate become less dense (cf Density) and go up; those of the surface of the pan are cooled by the contact of surface with a less hot medium, thus contract gain in Densité and plunge. The Chaleur is then transferred in a way much more effective than by the thermal Conduction or the Rayonnement, which are the two other modes of transfer of heat. It is beautiful the pan.

This very common physical phenomenon occurs in many systems (pan, terrestrial coat, star,…) in various forms.

# Phenomena convectifs

## Everyday life

• the movement in a Casserole posed on the Feu is explained by the differences of Densité created by the Chauffage. The fluid is put moving spontaneously when the difference of Température between the top and the bottom of the layer of water reaches a breaking value.
• the chimney or cigarette smoke goes up because combustion creates a very hot and very light zone compared to the environment. This zone of fluid goes up under the action of the Poussée of Archimedes.
• the Chauffage by the ground concerns the same principle. The hot layer at the base of the parts, because of thermal dilation, becomes lighter (relatively) and generates a circulation in the house.

## Technology

• the burner of the Montgolfier reheating the air above him and makes assemble the Nacelle.
• the water of the secondary circuit of engine of the nuclear plants is cooled in large the Cheminée S by using the capacity of extraction of heat of the convection associated with heat with evaporation with particularly high water.

## Geophysics

### In the atmosphere

The convection is a frequent phenomenon in the terrestrial atmosphere. It can be started by a warming of the ground by the sun, the movement of a Masse of cold air above a relatively hot water level, or by other phenomena which cause the relative warming of the bottom of an atmospheric layer compared to its top.

One gives to the class Nuage S of convective origin the generic name of cumulus .

In its benign form, the convection can give to the Planeur S and other not motorized aircraft the ascending push which they need to be maintained in vol. the Montgolfière S use as the convection as means of lift, by imprisoning a quantity of hot air (less dense as the surrounding air) inside a balloon.

The ascending convectif movement is accompanied by the downward movement of denser a corresponding volume of air (colder). The mass of the air going down is higher than that of the ascending air; there is thus a fall of the center of gravity of the system, interpretable like a conversion of potential energy gravitational, in kinetic energy. Moreover, when the air in ascent contains sufficient steam, this one while condensing its Latent heat releases, which increases thermal contrast and the convective push. The quantities of energy implied in this conversion can be considerable and result in strong blows of Vent, Tornade S, Grêle, and Foudre. For more details on this subject, see the article on the Orage S.

### In the ocean

The ocean is animated marine currents which have as an engine the convection: the water heated and evaporated in the Gulf of Mexico goes up in the Atlantique, the Gulf Stream, and cools brutally in contact with the Arctic polar icecap. Because of their salinity and of their temperature, it plunges at the ocean floor.

### In the volcanos

Magmatic room, volcanic clouds.

### In the lithosphere

Convection with small scales, destabilization.

### In the coat

The terrestrial coat consists of rocks (polycrystalline aggregate) which on a geological scale of time (the million year) behaves like a fluid. Same manner that a glacier creeps in a solid state on the side of a mountain, the convection takes place in the coat with large scales.

This convectif phenomenon is held for person in charge of displacement on the surfaces of tectonic plates. However the relation between Plate tectonics convection and is always under discussion.

### In the external core

Deeper still, under the coat, the terrestrial core is. It is composed of a metal seed (also called internal core, kind of aggregate of liquids solidified under the effect of the pressure) surrounded by a thick shell, metal it also but remaining in the liquid state: the external core. One can consider here that the liquid contained in the external core is confined between two solids. The external core in question is animated mysterious movements of convection to the unusual forms. Several physical phenomena of different nature (thermics, mechanics, magnetic) act in concert to animate the fluid core. In preoccupations with a simplification, we present these different cause separately.

Simplest and most obvious among all these causes is certainly the Poussée of Archimedes which causes rises of pieces in the fluid core. The core as a whole cools and crystallizes slowly with the interface between the internal core and the external core: light heat and elements are salted out by places at the base of the fluid. This one, lighter than its entourage (see higher), is put naturally at convecter. It is a form of convection whose two thermal and chemical aspects are as important one as the other. One speaks about thermochemical convection.

Two other forces then come to embellish mechanics by deviating the trajectory of the fluid pieces. First of all, the Force of Coriolis. Indeed, contrary to the case of the coat which surrounds it, the viscosity of the fluid constituting the external core is very low (near to that of water). Consequently, and since the shell which encapsulates the metal fluid is in rotation (day-night-day…) the movement of convection describes higher very strongly undergoes the action of the force of Coriolis. This one becomes dominant compared to the viscous forces and constrained the fluid to be organized in more or less regular rotary columns. At this stage one can represent the convection in the core by imagining ascending/downward pieces of fluid convectant with trajectories with the spiral forms (?? image convection cockles rotation).

Then the force comes from Laplace. Let us not forget it, the fluid considered here is metal! (Iron + Nickel + some light elements - link geochemistry?). It is very good conducting of électricté, kind of fluid electrified, which is the seat of hydromagnetic phenomena not elucidated to date, in particular the effect Dynamo thanks to which we bathe in a Terrestrial magnetic field. Remain however a certainty, the phenomena in question give birth to in the core from the sufficiently important magnetic forces (taking into account the intensity of the ambient terrestrial magnetic field and the strength of the flow describes earlier) to also modify they in their turn the movements of convection of which it is question here. (image magneto-convection??). The convection in the external core then seems to become more and more complex of advantage.

References: - sites: - WikiArticles: - books, theses:

## Astrophysics

Movements in stars.

# Physical principle

A particle of fluid heated at the base becomes lighter because of its thermal dilation and goes up under the action of the Poussée of Archimedes. Arrived at the top of the layer, the fluid exchanges its heat, cools and is weighed down. It goes down again then and creates a return transfer of heat.

The first physical approach was installation by Henri Bénard, with the study of the convection in a layer of fluid subjected to a vertical Gradient of temperature. These experiments are known under the name of Cellules of Bénard.

Two great convection types are distinguished: the natural convection where the movement of the fluid carrying heat spontaneously sets up because of anomaly of Density of thermal origin; the forced convection : the movement of the fluid is caused by an external actor.

## Natural convection

The natural convection is a phenomenon of the Mécanique fluids, which occurs when a zone changes Température and that it moves then vertically under the effect of the Poussée of Archimedes. The change of temperature of a fluid indeed influences its Density, which is modified compared to the density of the surrounding fluid.

Such displacement are called movements of convection . They are at the origin of certain oceanographical phenomena (current sailors), weather (Orage S), geological (increase of magma) for example.

# Convection of Rayleigh-Bénard

It is the academic case studied by Henri Bénard and Lord Rayleigh. A simple system is considered.

## Physical assumptions

One supposes a fluid Newtonian, incompressible, in the Approximation of Boussinesq, i.e. the only physical property which exchange is the Density.

## Conservation equations

• Conservation of the mass
$\ nabla \ cdot \ mathbf \left\{U\right\} =0$
• Conservation of the momentum
• Conservation of energy

## Starting of the convection

The transfer of heat in a horizontal layer of fluid is carried out by the thermal Conduction and the movement of the fluid. When one starts to impose a heat gradient between surfaces of the layer, a heat gradient settles. In experiments, it is observed that at the end of a certain time, the fluid is put moving spontaneously: it is the starting of the convection. This one is controlled by a number without dimension:
$Thorough Ra= \ frac \left\{\ mathrm \left\{\, of Archimedes\right\}\right\} \left\{\ mathrm \left\{dissipation\right\}\right\} = \ frac \left\{\ rho G \ alpha \ Delta T d^3\right\} \left\{\ kappa \ eta\right\}$
with $\ rho$ the Density, $g$ the force of gravity, $\ alpha$ the thermal coefficient of expansion, $\ T$ Delta the difference in temperature between the top and the bottom of the layer, $\ kappa$ thermal diffusivity and $\ eta$ characteristic dynamic viscosity (to be noted: these values can be variable in the fluid and it is important to check that one uses many characteristic sizes)
Starting is carried out for a number of Rayleigh of 657,5 for free faces and 1770 for rigid surfaces.

## Convectif Pattern

Rollers, cells, plumes.

## Heat flow

### Expression of the heat flow in convection (Law of Newton)

For a flow at a temperature $T_ \ infty$ around a structure at a uniform temperature $T_S$ of surface S, the expression of the heat flow in convection is the following one:

$\ phi=h S \ big \left(T_S - T_ \ infty \ big\right)$

Where H is the Coefficient of heat exchange

### Resolution of the problem

The dimensional Analyze makes it possible to show that, in forced convection, the Nombre of Nusselt is expressed according to the Reynolds number and of the Nombre of Prandtl.

*$Nu_x=C \left\{Re_x\right\} ^m Pr^n$, local Nusselt with a X-coordinate X

*$\ overline \left\{Nu_L\right\} =C \left\{Re_L\right\} ^m Pr^n$, average Nusselt over a length L

Where C, m and N depend on the characteristics of the fluid, the geometry and the mode of flow.

The engineer then has a series of empirical formulas established on typical configurations (plane plate, flow around a cylinder…) in order to deduce the coefficient of heat exchange from it.

# See too

• Convection in the coat

Simple: Convection

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