Furnace and Water Heater Ventilation pipe
A chimney cap is a good idea, as it reduces the water heading down.  Water can affect the flames and rust the pipe.

For better answers we need to know what type of pipe (ceramic? metal? plastic?). In general chimneys are not to be insulated.  Tap on the pipe, what does it sound like?  Post pictures.  What era are the heating appliances: that matters also.  Old ones send a lot of heat up the chimney, drying it out.