that flow path increases and other channels become a path of less resistance.
flow that makes their resistance equal. You could get all the flow going up the first few channels if they were very wide.
If you want to pursue the electrical resistance analogy, then you'll have to extend it to include convection.
You could do that by putting a voltage source in each channel, pushing flow up that channel. The voltage of the sources will depend on the temperature difference across their channel. In practice, the first channel will have its bottom end much hotter than its top end, so its voltage source will be large and most of the current will be driven up that channel. Any current that sneaks along the bottom tank will raise the temperature at the bottom of the second channel, increasing the voltage of the source in that channel and causing it to suck up any remaining current that the pump, strangled by the lockshield valve, can provide.
Cheers,
Colin.