The origins of the steam engine

It's not efficient at all. Without condensing the solar input, there simply isn't enough energy to heat the water fast enough to create enough steam to push a fan.

However, what you have described is similar to the basic design of closed-loop industrial solar thermal systems: they concentrate solar power to heat a liquid or other medium and use the heat (or heat differential) conventionally (see, for example the Ivanpah Solar Power Facility near Las Vegas).

Here on HN I read about the theory, that one of the main reasons that the time of the steam engines came, was the rise of the cannon. Over generations, every king wanted to have the best cannons as that translated into power - and once you can build a cannon, you can build something that can contain high pressures and give that pressure a direction. In other words, to take that toy further, they would have also had to greatly improve their metallurgy first. Otherwise a smart greek inventor would have just created spectacular (and dangerous) booms, but nothing that could reliable do more work, than a ordinary slave.

It's possible, but solar thermal has proven to be less efficient than photovoltaic at capturing energy from the sun. The only advantage is that you can coast on stored heat after the sun sets to keep making energy. Other than some pilot plants solar thermal is going nowhere.

Condensing the steam down and trying to extract energy from the condensation flowing downhill is orders of magnitude away from being worth it. The sun is boiling a few gallons of water per minute at best, while hydroelectric systems are measured millions of gallons per minute.

What is concentrated solar thermal?

    Concentrated solar thermal (CST) is a solar energy technology that uses sunlight to generate heat.

    Spain is the world leader in the use of CST to produce electricity, with around 2.3 GW in operation, followed by the United States with around 1.7 GW in operation.

https://arena.gov.au/renewable-energy/concentrated-solar-the...

    The Australian Renewable Energy Agency (ARENA) has announced it has approved $65 million in funding to Vast Solar to construct VS1, a first-of-a-kind 30 MW / 288 MWh concentrated solar power (CSP) plant in Port Augusta, South Australia.

    ARENA’s funding for VS1 is conditional upon the project reaching financial close, which is targeted to occur in late 2023. VS1 is expected to take two years to build with commercial operations commencing late 2025.

    CSP uses mirrors to concentrate and capture heat from the sun in solar receivers, with high temperature heat transferred via sodium and stored in molten salt. The stored heat can then be used to heat water to create steam to power a turbine and produce electricity, or the heat can also be used directly to decarbonise some industrial processes.

    One of the benefits of CSP is that the captured heat can be stored cost-effectively for long periods with little loss of energy. This means that CSP can be used to generate electricity or provide heat on demand, including overnight.

https://arena.gov.au/news/one-step-closer-towards-australias...

    Vast's modular CSP v3.0 technology has been proven at its 1.1 MW, grid-synchronised demonstration project in Australia and will be used in a growing pipeline of zero-carbon power projects globally.

https://www.vast.energy/about-technology

That's Hero's aeolipile, mentioned near the end of the article.

Most scholars tend to agree that Rome [1] was nowhere near an Industrial Revolution. One take on it is here: https://acoup.blog/2022/08/26/collections-why-no-roman-indus..., but the general tl;dr is that a) even if you backported a fully working Watt steam engine to Classical Antiquity and they could manufacture it, there's nothing that they could use it for [2], and b) the Roman economy isn't really in a shape that encourages the kind of industrial innovation feedback loop you see in the Industrial Revolution.

[1] Side note: at the time the aeolipile is developed, there is no independent Greece; Rome thoroughly conquered all the polities in the Balkans in the 2nd century BC. Classical Greece is largely 5th century BC. The aeolipile dates to 1st century AD, rather late in Roman history.

[2] The historical motivation for the steam engine was of course draining coal mines, and the Romans weren't really using coal in enough quantities to require it. The Industrial Revolution itself was initially jumpstarted with textile production, which Rome was even further behind in--the spinning wheel wasn't developed until after 1000!