This paper presents numerical study on dynamic characteristics of evaporator to control evaporator superheat and compressor capacity with optimum condition in refrigeration system. It is very important to reduce energy consumption and to keep room temperature within a very restricted range with minimum oscillation in some special applications of the refrigeration system. Heat exchange is mainly happened in the evaporator. So, making mathematical model of evaporator and analyzing evaporator characteristics are necessary in order to control the superheat and the capacity of the system. A mathematical model based on the one dimensional partial differential equations representing mass and energy conservation and a tube-wall energy is described. A set of ordinary differential equation is formulated by integrating separately over the two regions(two-phase and vapor) generally presented in a heat exchanger.