The Cryogenic Extruder (CE) is an extruder technology which can continuously produce solid rods of hydrogen and its isotopes. The solid rod is further cut into small cylindrical pieces called pellets, which are used for the fuelling of the long-pulse fusion reactors by injecting at high velocity into the magnetically confined, hot plasma, for the core-fuelling and D-T reaction. The design and analysis of a cryogenic extruder involves optimization of the various parameters of its different components such as precoolers, liquefier and solidifier compatible with cryogenic temperature operation. In this work, a design approach and Computation Fluid Dynamics (CFD) analysis of the components of extruder system is presented. The liquefier is designed to operate at a temperature of < 21 K and cooled using the 2nd stage of the cold head of a GM cryocooler. It has a compact shell which has an array of fins for the cooling down and liquefaction of the hydrogen gas to liquid. Theoretically, the surface temperature of 20.4 K is sufficient to produce liquid for the extrusion rate of 500 mm3/s of solid hydrogen but the CFD studies showed that the liquefier can produce the liquid for up to 1.75E-5 kg/s i.e., equivalent to 200 mm3/s of solid hydrogen based on the available cooling capacity of a cryocooler.