Analytical expression of electric power was deduced in case of the large-scale
thermoelectric device that consists of the multiple cylindrical tubes like roll
cake exposed to two thermal fluids. The output powers of the four arrangements
were mathematically solved from heat transfer theory. The maximum output power
of roll-cake module was practically the largest for the system of the counter
flow with a single thermoelectric tube (V1C system), but 1/4 of the ideal output
power (V1II system). The multiplication of thermoelectric tubes can shorten
significantly the device length, although the output power decreases only a
little. For example, the double vortical tubes (V2CC system) can generate 95.7
pct output power by 38.5 pct diameter, compared with the single tube (V1C system).