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

ABSTRACT

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.

KEYWORDS:

• Transient heat conduction
• cooling
• theoretical models
• analytical solutions
• ice rinks
• energy efficiency

Acknowledgments

This paper is dedicated to the memory of Professor Martti Viljanen.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 Toomla et al. (2018) have performed an extended study in a different ice hockey arena.

2 At first sight the plot in Figure 5 seems to suggest an exponential, however the accuracy is that case would be much lower, with $R^2=0.8552$.

3 This is precise enough for our purposes, notice anyway that one has some freedom in setting the upper limit of integration in (10(10) $q_B={\int }_0^{2300}{\dot{q}}_B\left(t\right)\mathrm{d}t=127.88\frac{\mathrm{k}\mathrm{J}}{{\mathrm{m}}^2},$(10) ). The order of magnitude is anyway what matters.

Additional information

Funding

The authors acknowledge financial support by the Estonian Research Council (Eesti Teadusagentuur) with Institutional research funding grant IUT1-15 and by the European Regional Development Fund through the Estonian Centre of Excellence in Zero Energy and Resource Efficient Smart Buildings and Districts, ZEBE, grant 2014-2020.4.01.15-0016.