Numerical optimization of small-scale thermo-acoustic refrigerators considering maximum cooling

The use of sound wave to remove heat could potentially contribute significantly to the development of a more affordable, sustainable search of an effective solution for electronics coolers. This work provides details of the implementation of a lexicographic optimization scheme in order to address the issue of dimensional optimization of a small-scale standing-wave thermo-acoustic refrigerator system. The cooling load has been considered as main criteria in the formulation and the measurement of the performance of the system. The dimensional parameters describing the heart of the device, namely the porous media (or the stack), where the heat pumping takes place are the variables to optimize. The problem has been formulated as a non-linear programming problem with discontinuous derivatives and implemented in the General Algebraic Modelling Systems (GAMS). The main contributions of the work are the detailed GAMS model and the clarity about the most preferred position and length of the stack considering prior knowledge of its porosity. This work reveals that shorter stack perform relatively better with respect to the cooling load performance. In addition, it appears that the position of the stack within the resonator tube is closely related to its length for maximum performance of the device.