Hi, my point is whether the Maximum Power Transfer Theorem should apply?

If not, why ?

Not. Because the theorem applies to a constant-voltage source with infinite current capability. The effects of the theorem appear when the load impedance is nearly equal to the source impedance. If we assume that the battery output impedance (ESR) is 0.1 ohm, and the load is 14.4 ohms, then clearly the majority of the circuit energy (10 W) will be dissipated in the load rather than the ESR. But that is not the maximum power available.

To see the MPTP in action, let's change to a larger battery, with a 12 V output at up to 500 amps, and an internal impedance of 0.1 ohm.

Now let's decrease the load to 0.2 ohm. The circuit current is 40 A, the power dissipated in the load is 320 W, and the power dissipated in the battery's internal resistance is 160 W.

Now let's decrease the load to 0.1 ohm. The circuit current increases to 60 A, the power dissipated in the load increases to 360 W, and the power dissipated in the battery's internal resistance increases to 360 W.

Keep going, and decrease the load impedance even more, to 0.05 ohm. The circuit current is 80 A, the power dissipated in the load is *decreases* to 320 W, and the power dissipated in the battery is 640 W Decreasing the load impedance more causes the load power to decrease more. With a theoretically perfect zero ohm load, the circuit current is 120 A, but the power in the load is zero watts.

And, your math is off.10 W at 12 V >> i =0.833 A

2 Ah / 0.833 A = 2.4 hours

ak