7.2 KiB
| title | chunk | source | category | tags | date_saved | instance |
|---|---|---|---|---|---|---|
| Convection | 5/7 | https://en.wikipedia.org/wiki/Convection | reference | science, encyclopedia | 2026-05-05T10:54:52.394392+00:00 | kb-cron |
The convection zone of a star is the range of radii in which energy is transported outward from the core region primarily by convection rather than radiation. This occurs at radii which are sufficiently opaque that convection is more efficient than radiation at transporting energy. Granules on the photosphere of the Sun are the visible tops of convection cells in the photosphere, caused by convection of plasma in the photosphere. The rising part of the granules is located in the center where the plasma is hotter. The outer edge of the granules is darker due to the cooler descending plasma. A typical granule has a diameter on the order of 1,000 kilometers and each lasts 8 to 20 minutes before dissipating. Below the photosphere is a layer of much larger "supergranules" up to 30,000 kilometers in diameter, with lifespans of up to 24 hours.
=== Water convection at freezing temperatures === Water is a fluid that does not obey the Boussinesq approximation. This is because its density varies nonlinearly with temperature, which causes its thermal expansion coefficient to be inconsistent near freezing temperatures. The density of water reaches a maximum at 4 °C and decreases as the temperature deviates. This phenomenon is investigated by experiment and numerical methods. Water is initially stagnant at 10 °C within a square cavity. It is differentially heated between the two vertical walls, where the left and right walls are held at 10 °C and 0 °C, respectively. The density anomaly manifests in its flow pattern. As the water is cooled at the right wall, the density increases, which accelerates the flow downward. As the flow develops and the water cools further, the decrease in density causes a recirculation current at the bottom right corner of the cavity. Another case of this phenomenon is the event of super-cooling, where the water is cooled to below freezing temperatures but does not immediately begin to freeze. Under the same conditions as before, the flow is developed. Afterward, the temperature of the right wall is decreased to −10 °C. This causes the water at that wall to become supercooled, create a counter-clockwise flow, and initially overpower the warm current. This plume is caused by a delay in the nucleation of the ice. Once ice begins to form, the flow returns to a similar pattern as before and the solidification propagates gradually until the flow is redeveloped.
=== Nuclear reactors === In a nuclear reactor, natural circulation can be a design criterion. It is achieved by reducing turbulence and friction in the fluid flow (that is, minimizing head loss), and by providing a way to remove any inoperative pumps from the fluid path. Also, the reactor (as the heat source) must be physically lower than the steam generators or turbines (the heat sink). In this way, natural circulation will ensure that the fluid will continue to flow as long as the reactor is hotter than the heat sink, even when power cannot be supplied to the pumps. Notable examples are the S5G and S8G United States Naval reactors, which were designed to operate at a significant fraction of full power under natural circulation, quieting those propulsion plants. The S6G reactor cannot operate at power under natural circulation, but can use it to maintain emergency cooling while shut down. By the nature of natural circulation, fluids do not typically move very fast, but this is not necessarily bad, as high flow rates are not essential to safe and effective reactor operation. In modern design nuclear reactors, flow reversal is almost impossible. All nuclear reactors, even ones designed to primarily use natural circulation as the main method of fluid circulation, have pumps that can circulate the fluid in the case that natural circulation is not sufficient.
== Mathematical models of convection == A number of dimensionless terms have been derived to describe and predict convection, including the Archimedes number, Grashof number, Richardson number, and the Rayleigh number. In cases of mixed convection (natural and forced occurring together) one would often like to know how much of the convection is due to external constraints, such as the fluid velocity in the pump, and how much is due to natural convection occurring in the system. The relative magnitudes of the Grashof number and the square of the Reynolds number determine which form of convection dominates. If
G
r
/
R
e
2
≫
1
{\displaystyle {\rm {Gr/Re^{2}\gg 1}}}
, forced convection may be neglected, whereas if
G
r
/
R
e
2
≪
1
{\displaystyle {\rm {Gr/Re^{2}\ll 1}}}
, natural convection may be neglected. If the ratio, known as the Richardson number, is approximately one, then both forced and natural convection need to be taken into account.
=== Onset ===
The onset of natural convection is determined by the Rayleigh number (Ra). This dimensionless number is given by
Ra
=
Δ
ρ
g
L
3
D
μ
{\displaystyle {\textbf {Ra}}={\frac {\Delta \rho gL^{3}}{D\mu }}}
where
Δ
ρ
{\displaystyle \Delta \rho }
is the difference in density between the two parcels of material that are mixing
g
{\displaystyle g}
is the local gravitational acceleration
L
{\displaystyle L}
is the characteristic length-scale of convection: the depth of the boiling pot, for example
D
{\displaystyle D}
is the diffusivity of the characteristic that is causing the convection, and
μ
{\displaystyle \mu }
is the dynamic viscosity. Natural convection will be more likely and/or more rapid with a greater variation in density between the two fluids, a larger acceleration due to gravity that drives the convection, and/or a larger distance through the convecting medium. Convection will be less likely and/or less rapid with more rapid diffusion (thereby diffusing away the gradient that is causing the convection) and/or a more viscous (sticky) fluid. For thermal convection due to heating from below, as described in the boiling pot above, the equation is modified for thermal expansion and thermal diffusivity. Density variations due to thermal expansion are given by: