This paper deals with the modeling and miniaturization of a thermoacoustic refrigerator that is run by a thermoacoustic heat engine. This coupling eliminates all moving parts and hence leads to increased reliability. The refrigerator is designed to produce 1W cooling power at 90 K and operates at a frequency of 80 KHz. Two different numerical models are considered for the design and the necessary inputs to the model are derived from existing literature. The results indicate that it is possible to design a thermoacoustically driven refrigerator that operates at an acceptable efficiency.