Below is a mathematical representation of the MHD equations. We expect they make absolutely no sense to you and this is not surprising. We spent several years at university before we really learned the mathematical meaning of them. So just take them as a form of abstract art! You can always ask your friends if they have seen this "masterpiece"...
Even if the mathematics is to difficult to understand, the concepts behind them are not to unfamiliar to you.
In the following you should try to imagine that we have put a cube (a hollow box) around the plasma at a particular location in the solar atmosphere. The sides of the cube are special in that they allow the atmosphere to move through them without effecting the plasma. The MHD equations then describe how the physical quantities such as mass, velocity, temperature and magnetic field change in time inside the box.
The first equation then describes how the mass in the cube changes in time due to the difference in any mass flowing in and out through the 6 surface.
The second equation tells us how the velocity (speed) of the plasma within the cube changes as a result of the different forces that act on it. Each term on the right hand side of the = represents a particular force (friction, gas pressure, magnetic force and gravity). In other words this is a special way of writing Newton's second law.
The third equations describes how the temperature of the plasma within the cube changes as energy is injected into or escapes from the plasma. The temperature may also change because plasma with a different temperature suddenly blows through the box (just think of a hot air hairdryer blowing in different directions, it is only some times that it blows hot air into one particular spot of your head). The temperature may also change temperature if the volume of a given amount of gas suddenly changes (When you put air into the tire on your bike with a hand pump, the valve gets hot, this is because of the compression of air in the pump before it enters the tube).
The last three equations describe how the magnetic field within the cube changes in response to the plasma motions relative to the orientation of the magnetic field.
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