Many space agencies like NASA, SPACE-X have promised to send humans into the red planet in future. So, considering their project of mars colonization, nuclear rocket propulsion would be the better option. Replacing chemical rockets by nuclear rockets may reduce the mission duration and also can reduce the mass of the propellant used. In chemical rockets, propellant releases energy through combustion but in case of nuclear rockets, propellant i.e. hydrogen is heated up in controlled fission reaction in nuclear reactor inside the rocket engine. Specific impulse of the nuclear rocket is greater than chemical rocket. This helps in providing gigantic thrust as a result mission duration is decreased. The challenging parameter of increasing specific impulse is solved by maximizing specific impulse which is done by increasing the exhaust core temperature. The fuel is selected in such a way so that the exhaust temperature would be obtained. The (U, Zr) Cgraphite fuel is selected because it has high uranium density and melting point is equivalent to exhaust core temperature which is sufficient enough to enhance the reactivity of the fissile material and thus to increase the rocket performance. A mathematical analysis shows that the percentage of mass of propellant used in mars mission will be lesser than the chemical rockets because the specific impulse is expected to be more in nuclear propulsion. The specific impulse obtained from the CFD Analysis of rocket nozzle is 979 sec with exit velocity of 9604m/s.