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Highlights • Operational frequency deduced both analytically and computationally. • Previously untested cooling configuration found to be the optimal. • Development of validated computer model of physical system. • Liquid piston instability linked to Rayleigh-Taylor phenomenon. • Liquid piston maximum acceleration limit identified. Abstract The objective of this research project is to develop a solar-powered refrigerator in the lower capacity range of up to 5 kW of cooling power. With the use of liquid pistons and one of the most efficient thermodynamic cycles known, the Stirling cycle, this product has the potential to outperform rival solar cooling technologies while providing inexpensive, reliable, quiet, environmentally-friendly, and efficient solar cooling for residential use, due to its straightforward manufacturing, simple design and inert working gas. Presented in this paper are the newest results of the theoretical and experimental investigation into deducing the key design parameters and system configuration of the so-called Liquid Piston Stirling Cooler (LPSC), which will help lead to optimal performance. Computer models of the complex unconstrained system have been constructed and validated using the modelling software Sage and shown to replicate system behavior with reasonable accuracy in experiments. The models have been used to predict system improvements and identify limitations imposed by the use of liquid pistons. The results to date provide a unique insight into a relatively little studied area in Stirling cycle research. [ABSTRACT FROM AUTHOR]