Conventional refrigeration requires comprehensive power, control, and maintenance systems, all at high costs. As a result it is promising to have an alternative method, which is capable of creating cryogenic refrigeration with no moving parts, a clean energy source, and with a relatively simple design and cheap components. This could be achieved through thermoacoustic cooling techniques, which is based on the oscillation of sound waves to circulate heat between high and low heat exchangers within a well-designed thermoacoustic device. In this study an inclusive acoustic model has been proposed, in which the main parameters have been determined to build up a matrix of constituted engineering-mathematical equations that form the main structure of the modelling process. This modelling has coupled with its associated thermodynamical parameters to form the appropriate thermoacoustic model, which allows for the scaling of parameters, determination of performance rate, and enables refrigeration-performance enhancement. Our results show that the model can provide a precise margin of applications for each parameter of thermoacoustic refrigeration for different working fluids. Also, it is possible to determine the numerical ranges of efficient cooling for absorbed and released heat (qc, qH ), maximum-pressure amplitude (Pm) and sound intensity (I), respectively.