Mathematical Modeling of Heat Transfer and Energy Efficiency in Above-Ground Outdoor Pools

Above-ground outdoor swimming pools are increasingly popular due to their affordability and ease of installation, yet maintaining optimal water temperature under variable climate conditions remains challenging. Our study develops a theoretical and mathematical modeling framework to quantify heat gains and losses in residential frame pools, focusing on convection, radiation, and evaporation as dominant mechanisms. The analysis demonstrates that daytime water circulation enhances solar heat gains but increases nighttime losses, while opaque covers reduce evaporation at the expense of solar input. Heating during colder months in Central and Eastern Europe is highly energy-intensive due to low ambient temperatures, strong winds, and reduced solar radiation. Based on these findings, the paper proposes cost-effective strategies, including optimized pool geometry, wind protection, transparent covers, and operational adjustments such as daytime-only circulation. The model provides a foundation for advanced simulations and supports the design of sustainable heating solutions, aiming to extend the swimming season and reduce operational costs.