Modelling of thermo-acoustic refrigerators using general algebraic modelling system

Abstract: While thermo-acoustic refrigeration is new among emerging technology, it shows strong potential towards the development of sustainable and renewable energy systems by utilising a sound wave to remove the heat. This work discusses a new mathematical programming approach that provides fast initial engineering estimates to initial design calculations, describing the optimal geometry of thermo-acoustic refrigerators. Three different criteria describing their performances were taken into account: maximum cooling, best coefficient of performance and acoustic power loss. As the stack has been identified as the heart of the device where heat transfer takes place, this new approach aims to optimise its geometrical parameters: namely, the stack position, the stack length, the blockage ratio and the stack pore sizes. Hence, the optimisation task is formulated as a three-criterion nonlinear programming problem with discontinuous derivatives. This approach was implemented in the General Algebraic Modelling Systems. The unique characteristic of this research is the computation of all efficient optimal solutions, allowing the decision maker to identify the most efficient solution. The proposed modelling approach was investigated experimentally to evaluate its ability to predict the best parameters describing the geometry of the stack. Similar trends were obtained to support the use of the proposed approach in the design of thermo-acoustic refrigerators