Convection
![[url=https://pixabay.com/en/hurricane-irene-1049612/]"Hurricane Irene"[/url] by skeeze is in the [url=http://creativecommons.org/publicdomain/zero/1.0/]Public Domain, CC0[/url]
Hurrican Irene (2011) as viewed from space.](https://www.geogebra.org/resource/YDEnPmYP/S4yP6tBKEOMLlilR/material-YDEnPmYP.png)
Convection is heat transfer by the flowing and mixing of materials such as occurs when you turn on an air conditioner. The whole room gets cooled by the mixing of cool air with the relatively warmer ambient air. Convection is also needed to make a hot bath tub uniformly hot. Water, like most non-metallic materials, is a poor conductor. It would take too long for conduction to cause the cool side of the tub to become warm. Instead we know instinctively to stir the water, or use convection to warm the whole tub.
Convection occurs naturally to some extent due to the fact that hotter fluids tend to be less dense as compared to colder fluids. The colder ones fall and hotter rise. The consequence is convection and mixing of the cold and hot. Weather patterns are driven by convection since there are no hands to otherwise stir the atmosphere. Hot air will rise and get filled in by surrounding air. The ocean currents are also largely driven by variations in temperature (and also salinity) which drive convection.
In southern California, the Santa Ana winds blow when ocean currents bring warm water toward the coast. This water warms the air overhead, which causes it to rise. The rising air creates low pressure which pulls air off the inland land mass toward the coast to fill in the space it leaves behind. The low pressure draws air from the great basin (with the Sierra Nevadas on its west) down to orange county. While this air starts rather cold and at high altitude, it gets adiabatically compressed as it descends, and warms by roughly 10 degrees Celsius per thousand meters of altitude descended. "Adiabatically" is a fancy way of saying that the heat is trapped in the air and has no place to go due to the poor conductivity of air. So with trapped air, and rising atmospheric pressure as the air descends in altitude, the cool mountain air becomes very hot by the time it arrives at the sea-level coast.
By the time the Santa Ana winds arrive at the coast, they are very hot indeed, but they are also extremely dry, owing to the fact that the relative humidity of air with constant water volume will drop as the air warms up. Relative humidity is just a measure of how much water vapor is in the air as compared to the maximum it could hold. For instance, if the air right now has half the water that it could possibly hold, the relative humidity is r=0.5, which would often be written 50%. Warmer air can hold more moisture, so as the air gets adiabatically heated, and the water it contains doesn't change, its relative humidity will drop.
When temperatures drop, it is why we get fog or dew at night. Whatever water was in the air during the day can often be too much for the air to hold at night when the temperatures drop. As a consequence, it condenses onto the surfaces in contact with the night air, or might even form fog.
Regarding heat transfer via convection, there is no simple way to describe it mathematically. It is the realm of computational fluid dynamics. This is why weather and storm predictions are so hard. Such fluid dynamic calculations are beyond the scope of our course.
I should note here that many books on heat transfer attempt to treat convection just like conduction via Newton's law of cooling which we'll describe in the next section. The trouble is that it requires the determination of a constant that's called the convective heat constant. This constant is notoriously difficult to know well in all but the simplest conditions. As you'd expect, it depends on both the properties and geometries of the materials in contact as well as the flow field in the event that one of them is a liquid or gas. For this reason, doing convection right involves computer simulation of fluid flow.