A Stirling engine (https://en.wikipedia.org/wiki/Stirling_engine) is an engine which uses temperature differences to turn. In space it is hard to conduct heat so very often the sunny side of an object is really hot while the other side in the shade is ice could. Could a Stirling engine be placed behind a solar panel and used to produce more electricity?
The first boring problem is that most space based solar implementations are weight limited, and it is hard to conceptualize an array of heat engines that are lighter weight than just a slightly larger array.
Weight aside ideally you keep solar cells cool for peak electrical performance so ideally you let any heat radiate away on the backside as easily as possible and using IR reflective coatings on the front, 'insulating' the back face with heat harvesting hardware is going to reduce that cooling effect and loose electricity and probably array life.
The next problem is that a properly designed solar panel is cool - we want to turn as much of the incoming light into electricity, not waste it heating up the panel.
A possible use case for heat engines is to skip the solar panels entirely and just collect heat. While low efficiency if we are in the situation of making power harvesting equipment from local resources of a moon or asteroid it may be easier to ship 'stuff to make stuff' for large heat collector than solar cells. Heat collection involves making metal into some sort of pipe and painting it black while solar cells involves rather complex high purity silicon processing.
NASA’s interest in Sterling engine generators dates back to the 1980’s https://ntrs.nasa.gov/api/citations/19880003045/downloads/19880003045.pdf .
NASA developed a free piston Sterling alternator which (as of 2020) had run continuously for 14 years; an all-time record for a heat engine. https://www.nasa.gov/feature/glenn/2020/stirling-convertor-sets-14-year-continuous-operation-milestone .
NASA’s Sterling engine was powered by a radioisotope heat source. It could potentially also function on solar thermal energy for inner solar system missions.
It is possible for Sterling engines to operate on very small temperature differences, but these “low temperature difference” engines have very low specific power (watts/kilogram). Not a good choice for spacecraft. Your proposal to run a Sterling engine in the shade of a solar panel is a non-starter.
As a rule, the greater the temperature difference between the “hot end” and “cold end” of a Sterling engine, the higher the specific power. Optimally, the engine is designed with as high a temperature as can be tolerated by the engine’s materials and working gas. Typically, this is over 600C. This means a spacecraft’s Sterling would need a solar concentrator, a radiator and support structure, all of which add mass.
