Solar-type stars are characterized by an outer convecting zone where heat is transported by fluid motions resulting from the Rayleigh-Bénard instability. The convection in these stars appears because of surface cooling: the surface material cools too rapidly to be reheated by the radiative conductivity of the fluid; the fluid at the surface is too cold and sinks till a depth where the conductivity is high enough to smear out the "superadiabatic gradient" thus built up by the cooling. This critical depth where the convective zone ends is given by the famous Schwarzschild criterium. For our sun this place is 200000 km below the surface.
         Because of the size of the stars the fluid motions are characterized by very high Reynolds numbers which means that the flows are turbulent. This turbulence is the basic difficulty which astrophysicist must face to model  solar-type stars. Making progress is very hard because we have no general theory of turbulence at hand. One way in this jungle is to do direct simulations of these flows (using Reynolds number around 1000), understand the important properties of these flows and then extrapolate to the real sun where the Reynolds number is 10^12. Then we may test our results and conjectures on some observables like the differential rotation or the magnetic activity of the sun.

More on direct simulations:

More on extrapolation: