why jet have convex exhust, while rockets have concave exhust?

Answer 1

I believe you're referring to whether the nozzle is converging (cross sectional area gets smaller as the flow approaches the exit) or diverging (area gets larger as flow approaches exit).

If a converging nozzle is used, the speed of the flow at the exit cannot exceed the speed of sound (Mach number less or equal to 1). For supersonic flows, a converging nozzle followed by a diverging nozzle is needed to achieve supersonic speeds. This is called a Laval nozzle. So for the space shuttle for instance, which is supersonic, the nozzles are bell shaped as that is the diverging portion of the nozzle. Commercial jets are sub-sonic and therefore have converging nozzles.

Photographs of supersonic planes on the outside seem like the nozzle is converging but they're not. If you were able to look at the insides, you would see that they are Laval nozzles.

Answer 2

You are mistaken.

Turbojet engines share with liquid fuel rocket engines an overall venturi shape with an exhaust duct that is roughly in the shape of a parabolic section. Both are shaped in general the same way.

For lots of information including pictures and diagrams, do an internet search on "jet propulsion" or "rocket engine."