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.