Current work proposes a novel design methodology using curve-fitting approach for a non-axisymmetric airfoil convergent nozzle used in small-sized cryogenic turboexpander. The curves used for designing the nozzle are based on a combination of fifth and third order curve at upper and lower surface respectively. Four different turbulence model such as k-ε, SST, BSL and SSG Reynolds stress turbulence model is used to visualize and compare the fluid flow characteristics and thermal behaviors at various cross-sections. It is interesting to observe that the Mach number obtained at the outlet of the nozzle is highest and temperature drop is maximum for SSG model under similar boundary conditions. It is also observed that the designed nozzle with curve fitting approach is appropriate for impulse type turbine with a small amount of reaction. The key feature of this implementation is to obtain subsonic velocity at the nozzle exit and reduce the irreversible losses through the nozzle, which can affect the performance of a turboexpander.