On a theory for system-level cooling of close electronics enclosures by PCM-filled heat sinks-Exact solution and second law performance limits

This paper takes a fundamental approach on the simple, however widespread, application of closed electronics enclosures that are passively cooled by internally mounted heat sinks filled with phase change material (PCM) and exposed to periodic temperature environments. The regime of interest is that of periodic steady state (PSS). A model that allows for an analytical solution of the Stefan-like problem in the finite PCM domain and of the energy balance coupling of the closed enclosure is devised in dimensionless terms by using a lumped formulation for the enclosure and for the PCM domain, the later being known as zero-phase modeling (Naaktgeboren, 2007). The model is one that allows for internally reversible heat transfers in the PCM and in the enclosure domains, while retaining the finiteness (irreversibilities) of the heat interactions between the environment, the enclosure, and the PCM-filled heat sinks, as well as the heat sources irreversibilities, so as to allow for meaningful outcomes. Results include melting and freezing interface location history-conversely, melting and freezing times-and a design condition for perpetual occurence of phase change; hence, latent heat interactions. Moreover, a figure of merit for passive temperature regulation of real (irreversible) electronics enclosures is proposed as a temperature attenuation effectiveness. The limit imposed by the second law of thermodynamics on the temperature attenuation effectiveness is analytically derived and shown to depend on only two (out of the four) dimensionless parameters of the model. The original expression for the enclosure temperature attenuation effectiveness in the reversible limit, obtained herein, is of theoretical and practical significance.