Small Transport; Low Wing; 2 Turbojet Eng
Flight Crew Instrument; Flight Crew Multiengine
Situational Awareness; Troubleshooting
Aircraft Equipment Problem Less Severe; Flight Deck / Cabin / Aircraft Event Smoke / Fire / Fumes / Odor
Flight Crew Overcame Equipment Problem
Aircraft
As I came to a complete stop on the south side of the ramp; my Right Brake was very soft; or weak. It felt like there was no pressure. In order to determine if if I needed to write the brake up I pumped the brakes and tried to see if I could obtain any pressure in the right brake. I was trying to determine if the pressure had just bled out; or if it was gone completely. I was able to get a little pressure; but determined that something didn't feel right and decided to shut down with plans to write up the brake and call maintenance. I chocked the nose gear and went to spin down the right engine when I noticed a small puddle underneath the brake reservoir in between tire 3 and 4. This wasn't a big surprise as I had noticed that something was wrong prior to shutdown. I decided to go inspect the situation further and complete the walk around. As I got to the back side of the right wing I saw the entire gap between both tires completely up in flames. I immediately went back into the he airplane and got the fire extinguisher. I extinguished the fire with in a minute of noticing it was on fire. The brake fluid was pouring out from the reservoirs for several addition minutes until maintenance arrived and helped monitor the situation.
Pilot reported they noticed a loss of brake pressure while taxiing and after parking observed flames from the leak. Pilot extinguished the flames.