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This work is the first in a series of articles addressing the energyoptimization in ice hockey halls. Here we adopt an analytical method, calledfunctional optimization, to find which design and operating conditions maximizethe Coefficient Of Performance of the entire cooling system (brine pumps andcooling tower), which we call ${\rm COP}_{sys}$. This is addressed as afunction of several variables, like electric consumption and brine physicalproperties. By maximizing such function, the best configuration and brinechoices for the system can thus be determined accurately and rigorously. Weinvestigate the importance of pipe diameter, depth and brine type (ethyleneglycol and ammonia) for average-sized ice rinks. An optimal brine density isfound, and we compute the weight of the electric consumption of the brine pumpson ${\rm COP}_{sys}$. Our formulas are validated with heat flow measurementdata obtained at an ice hockey hall in Finland. They are also confronted withtechnical and cost-related constraints, and implemented by simulations with theprogram COMSOL Multiphysics. The multivariable approach here discussed isgeneral, and can be applied to the rigorous preliminary study of diversesituations in building physics and in many other areas of interest.

Energy optimization in ice hockey halls I. The system COP as a multivariable function, brine and design choices