Energy analysis in ice hockey arenas and analytical formula for the temperature profile in the ice pad with transient boundary conditions

The energy efficiency of ice hockey arenas is a central concern for the administrations, as these buildings are well known to consume a large amount of energy. Since they are composite, complex systems, solutions to such a problem can be approached from many different areas, from managerial to technological to more strictly scientific. In this paper we consider heat transfer processes in an ice hockey hall, during operating conditions, with a bottom-up approach based upon on-site measurements. Detailed heat flux, relative humidity and temperature data for the ice pad and the indoor air are used for a heat balance calculation in the steady-state regime, which quantifies the impact of each single heat source. We also solve the heat conduction equation for the ice pad in transient regime, and obtain a general analytical formula for the temperature profile that is suitable to practical applications. When applied to the resurfacing process for validation, it shows good agreement with an analogous numerical solution. Since our formula is given with implicit initial condition and boundary conditions, it can be used not only in ice hockey halls, but in a large variety of engineering applications.