The 1854 Shaw engine, is a hot air engine of a new type.
Unlike is predecessor, Philander Shaw took into account the physical fact that the air conductor; which means that it heats up slowly. In usual air engine like the Stirling engine, the air that comes from the cold side to the hot side, has little time to heat up. If the engine rotates at 120 rpm, the batch of cold air will have only a quarter of a second to heat up (included the running through the regenerator).
Shaw built a special heater where the air was stored and heat up with time before entering the acting piston. This was indeed a superior improvement and allowed the Shaw engines to be more powerful.
A later shaw engine, exhibited at the Paris exhibition in 1867, was a 20 hp air engine.
To economize on fuel, Shaw did not use a regenerator but effective common sense. He used the expanded air to feed the fire, and doing so effected considerable saving of fuel.
Confusion should be avoided. The Shaw engine was not a furnace air engine, but an external combustion air engine. Although the working fluid was mixed with the product of combustion, it did so after having acted upon the working piston with the sole purpose to take less heat to the combustible and not to gain in pressure and then expand.
This engine had nevertheless some drawbacks.
It was a intricate engine, with many parts, though increasing its fragility and side effects like friction and performances losses.
Moreover there was a non explainable feature: the working fluid in the compression chamber was cooled down.
In an air engine the cooling happens during the compression, in order to save work given to the fluid. But once the compression is done, there is no reason to cool the working fluid.
Why Shaw did such a feature remains mysterious.
Finally, Shaw brought up a good machine, complicated, but working, at a time when the Ericsson adventure finished by a tremendous failure and Stirling had abandonned the building of hot air engine.