Take a planet with an atmosphere similar to Earth's but, say, 9-10x as dense. What is this going to mean for the performance and design of the heat engines that are so familiar to us? Higher oxygen partial pressure... easier to burn? But higher air density means more heat conducted away... easier engine cooling, yes, but does it also hurt their performance? An internal combustion engine, instead of having something like 10:1 compression ratio, will only have about 2:1 (edit; assuming the engine is constructed to the same strength). Does this actually make a big difference, or does only the absolute difference in pressure matter? Likewise for a steam engine. Or (because I'm thinking particularly about aircraft here) a jet engine.
The effects won't be as dramatic as you might think
For piston engines increasing atmospheric pressure will cause a similar situation to turbo charging. You will create 10 times the power per density, compression ratio will remain the same. This means to get the same power your engines will have 1/10th the displacement, but that does not mean they will actually be smaller. Since your engines will be operating at higher pressures, they will be creating more mechanical stress on the engine block, which will need to be reinforced. Contrary to what others have said, you will not have to deal with increased fuel consumption. Fuel consumption per unit power will be the same since your displacement will be smaller. Only when you try to keep 1 atm engine displacements will you see a jump in fuel consumption (but power will rise equally). Of course trying to move quickly through such an atmosphere would require more power due to drag, but stationary engines will not have this concern. Similarly, back-pressure caused directly from the atmosphere will not be a problem, the concern here will be that drag through the exhaust pipe may build up easier, so you will want freer flowing exhausts.
Moving towards aircraft and jet engines in particular get a little more interesting. Let us start with how the atmosphere works. The higher you go up, the thinner the air. That atmosphere above the point where it reaches 1 atm pressure will look identical to our atmosphere. Planes will simply fly higher when speed or long distances are required. Most planes that reach high speeds at altitude can not do the same at sea level. Mach 2.5 fighter jets are often limited to Mach 1.2 at sea level. If you do want to fly fast at low altitude, besides the rules for piston engines, you will likely see changes to nozzle design. If your exhaust is supersonic, then the higher the pressure the smaller the nozzle. Aircraft that operate at many altitudes will need nozzles that adjust in size dramatically.
Higher oxygen partial pressure... easier to burn?
It means higher fuel consumption and higher produced power per cycle
But higher air density means more heat conducted away... easier engine cooling, yes, but does it also hurt their performance?
An ICE is based on the expansion of the gas. That the gas is heated is just a nuisance, since one has to cool the combustion chamber. Indeed there have been design were water is injected into the chamber to absorb the heat and increase expansion thanks to the formation of vapor. So additional cooling is not an issue.
An internal combustion engine, instead of having something like 10:1 compression ratio, will only have about 2:1.
Wrong. The compression ratio of an ICE doesn't depend on the intake pressure, but on the volume ratio between the upper and lower point of the cycle. Those do not change with air pressure.
Same general reasoning holds for steam engine and jet engine.
Incidentally, increasing the intake pressure is the exact reason for applying a turbo to ICE.
Have you ever done something particularly foolish as a child?
I have. Oh, yes... I've done some whoppers. And one of them was pounding a potato into a tail pipe. As you can imagine, the engine failed to start.
1. Increased Fuel Consumption
Engine efficiency drops like a rock. That means small engines we love today (like my weed trimmer) might not even start, because the back-pressure on the exhaust is too high. The solution? A bigger bang. That means I'm increasing fuel consumption to overcome the increased back pressure.
2. Increased Cooling Required
I believe (I could be wrong) that higher air pressure does not improve cooling. In fact, it makes heat dissipation worse. If increasing surrounding density helped with cooling, computers would have a rock sitting on top of them rather than a fan. Heat propagates fairly slowly through a static atmosphere, which acts (like pretty much all things) as a thermal insulator. Increasing its density is like adding more insulation to the walls of your house. In fact, air-gap insulation is very effective. It's why people staple plastic over their windows during the winter. That gap of static air is an insulator. Therefore, you have a bigger problem with heat removal, which means a bigger radiator.
3. Decreased need for air flow
You are correct that greater air density means more oxygen per cubic centimeter. Therefore, the air draw requirements would not be as large.
4. Increased air filtering
But, as a nasty byproduct, you need a larger air filter because the higher density of air will push crap through an air filter more readily than here on good ol' Earth. You need a way to disperse that pressure, too. That means a bigger filter (more surface area) with greater density filtration. So, in the long run, #3 and #4 are a wash.
5. Increased Fuel Consumption — Again
Finally, you're pushing whatever the engine is moving through thicker air. This might not have a massive impact, but the reality is that the higher the pressure (air density), the harder it is to push an object through it. That means you need an even bigger bang than #1 requires to overcome the additional air resistance.