Refrigeration systems require optimal amount of refrigerant for maximum system performance. Undercharged or overcharged systems experience reduced efficiency and accessories deterioration. Optimal amount of refrigerant to be charged in a refrigeration system depends on the physical and thermal dynamic properties of the evaporator and the refrigerant. This paper presents formulation of a numerical model that can be used in determination of optimal amount of refrigerant charged in a system for maximum cooling rate as hence maximum system performance. Rayleigh’s method of dimensional analysis was used obtain the relationship between the maximum cooling rates of direct expansion evaporators as a function of thermodynamic properties of refrigerant R-134a, Different sizes of evaporator were fitted in the refrigeration system and charged with systematically varying amount of refrigerant until a maximum cooling rate was determined. The variation of pressures and temperatures both at the inlet and exit of the evaporator were observed and analyzed. The cooling rate of the numerical model formulated was compared with the cooling rate the actual physical refrigeration system. A t-test of 95% confidence interval indicated no significance difference between the numerical model, and the physical refrigeration system.