how is heat transferred into work in a stirling engine?

Answer 1

Usually, a dynamic fluid is involved. Thermal differential is used to expand and contract the fluid, commonly to actuate a reciprocating piston.

You can think of it as being very similar to a steam engine or even a traditional internal-combustion engine in terms of how the fluid acts on the piston, and how useful energy is extracted from the device.

Ideally, Stirling engines are hermetically sealed; however, some may have valves.

The short answer to your question, though, is that heat (thermal differential) energy acts on the working fluid in accordance with the combined gas law; the pressure differential multiplied by the area of the piston determines the available force.

Geometry (and other mechanical losses) determine the fraction of force that is recoverable.

Work then derives from the rate of expansion and contraction, and applied force. The formulae are very basic, but going into that is beyond the scope of your question.

Answer 2

the Sterling is a piston engine the only difference between it and the typical internal combustion engine is where the combustion takes place ( the cylinder pressures in both come from heat - the sterling uses an external source of heat instead of an internal burn )
it is heavier and only a little more efficient than your typical gas engine - the advantage is you can use any heat source !

The basic process is very much a sophisticated redesign of the steam engine - but it has a zero loss fluid system ( steam is total loss ) so the best comparison would be a piston driven compressor ( the fluid system works like your refrigerator compressor )