Why don't we see the glow of jet engines at night
 

Some technology here.

Much documentation about the inner workings tell that the operating temperature inside jet aircraft engines is about 1900 C, hotter than molten steel, which appears bright yellow hot.
Passengers sitting in the very front can peep into the front of the engines and in the very rear into the back of the engines, so one would expect to see reddish / orangish incandescense due to an indirect view to the combustion chamber of the engine. Unlike a car engine, a jet engine is more 'open'.

But during a night flight not any glow is seen, even not indirectly.

Why is that ?

Because the combustion chamber is occluded by compressor rotors and stators on one end and turbine rotors and stators on the other. And the outer shell of the engine is cold metal.

What you are seeing on the front is the fan blade, which really isn't anywhere near the core of the engine. It may be more open but there's still a lot of metal in the way... If you look through an engine from behind you can see light, but that's light shining past the fan and through the bypass route, not the engine core (where combustion occurs).

http://i.stack.imgur.com/ghnkw.jpg

Yes, many, many compressor and turbine blades before and after the combustion chamber, respectively. Turbine blades have the specific purpose of taking the heat energy from the combustion and turning it into rotational energy for the fan and compressors. Bypass air is also mixed in before exiting the engine, so the air coming out is only 500-800C or so.

As noted, combustion is hotter than molten steel, so since the engine is actually made of steel (various complex alloys, actually) there are many insulating and cooling systems that keep the visible shell much, much cooler.

You really don't want to see it
http://4.bp.blogspot.com/-8FA0u7UyP1...ngine-Fire.jpg

To be fair to Rolls-Royce and AA, that photo was proven to be faked. (You can see the reflection in the polished aluminum fuselage...no fire).

That said, when testing a turbojet (not turbofan) engine on a test cell, you can indeed see the turbine case's dull glow with the lights off. However, the glowing parts are hidden by the engine cowling when installed on an aircraft. High-bypass turbofans have so much airflow going around the turbine case, they're kept cool enough to not glow.

The hottest parts of the engine can operate at temperatures above the melting point of the metals they're constructed of thanks to some pretty clever manufacturing techniques, which circulates air through the turbine blades and vanes, as well as envelopes the outer surface of the components with a thin layer of cool air. ('Cool' air being a relative term...still >500 degrees F). That's one reason why volcanic ash is such a big deal...it can clog these tiny air passages.
If the turbine blades got hot enough to glow bright yellow, something has gone horribly wrong...and will likely get much worse. If the blades get that hot, they will stretch because of centripetal forces of the turbine rotating at roughly 10,000 RPM. Ultimately, the blade tips will contact the outer walls of the engine. Boom.

You can see the flames from engines with afterburners lit. - Concorde takeoff, for example. Normally it is military AC with ABs, however. - multiple F-22 takeoffs.

Afterburners are extremely inefficient with fuel.

You can see the last stage turbine disc glow at night but you have to be behind the engine so that you can see far enough up the tailpipe. The angle is too great from a window seat.

Fuel essentially dumped straight into the exhaust.

I had thought the old low bypass engines that powered the early 707s may have showed some flames but apparently not (long time since I last saw one take off).

If you flew on a 737-200 back in the day, the old JT8D engines would squirt out a momentary flash of flame visible at night if you were seated near, but just behind the engine if the start was on the 'warm' side....other than that, I don't think you want to see any commercial jet engine with visible flames :)

If you could regularly see flames/glow from a jet engine, that engine would be very inefficient.

Fun though...