I cannot believe how many baseless assumptions you just made, but we'll hit a few.
First, we don't know exactly what is in the earth's core whether it be flat or a globe. Really, we have no clue.
Second, I haven't seen any convection currents in a bar magnet, but perhaps you have. Clearly, a convective dynamo is not required to produce a magnetic field.
Third, Herndon convincingly shows how convection is impossible in a globe's mantle and core -- except perhaps in the very small region of a molten inner-core at the very center of a globe. Wholly insufficient to cause any "dynamo" effect as posited by mainstream science.
First, we aren't completely sure, but it is not accurate at all to say that we have no clue. Seismic waves can't go through a solid core, so using measurements from these, we can tell that there is something solid down there, and that it is, predictably, a sphere.
Second, there are no convection currents in a bar magnet, because it is made of magnetic material whose atoms are aligned easily. This is not the same for the Earth. Here is an explanation of convection:
As magma falls to the core of the Earth, it is heated up (because it's hotter down there). You may have heard that "heat rises." This is because heat is the speed of particles. When they're faster, they sort of push outwards and begin to take up more space, making the magma less dense (because density is how packed together something is; if the same amount of mass is in more space, it is less dense). We know that buoyancy (what makes things float) is caused when something less dense is in something more dense. Wood is less dense than water, so it floats. Really small rocks, like in Monty Python, will never float, despite being light, because things only float if they're less dense. So when the magma becomes less dense, it rises. Then it cools, and falls again, repeating the cycle.
The magnetic field is caused because the outer core is molten iron (inner core is solid, which is what I've been talking about) which is highly conductive to electricity. Electric fields also create magnetic fields. Magnetic fields resist the motion of the fluid, which is why convectional currents are needed to keep it going.
The rotation of the Earth causes a north-south alignment of the field.
Third, let me see this? Convection is completely possible in the mantle; so long as it's fluid, it will be affected by convectional currents, just like water in a pot on a heat source.
Hence, heat rises. I don't see how this couldn't happen in the mantle; in fact, I don't think the outer core is wide enough for this to occur en masse, like you suggest.