Figures of Merit for Hybrid Thermal Energy Storage Units

Two figures of merit for hybrid Thermal Energy Storage (TES) units are developed: the volumetric figure of merit, V~ , and the temperature control figure of merit, T~ ∆ . A dimensional analysis shows that these quantities are related to the performance specification of the storage unit and its physical design. A previously benchmarked semi-empirical finite volume model is used to study the characteristics of various plate-type TES-unit designs. A parametric study is used to create a database of optimal designs, which is then used to form simple correlations of V~ and T~ ∆ in terms of design requirements and attributes. A preliminary design procedure utilizing these figures of merit is suggested. Sample calculations show that these correlations can be used to quickly determine the design attributes of a plate-type TES-unit, given design requirements. NOMENCLATURE Ab Footprint area (m) fm Metal fraction of the TES unit H Height (m) htr Latent heat (joule/gm) k Thermal conductivity of the conducting plate (watt/m⋅K) L Length of the TES unit base (m) m Mass of the PCM (kg) N Number of plates Qss Initial heat loading (watt) q Input energy (watt) Rmetal Metallization thermal resistance (°C/watt) metal R Normalized Rmetal (as defined in Eq. 6) Rtotal Total thermal resistance of TES unit at steady state (°C/watt) s Plate fin spacing (m) Ttr Transition temperature (°C) T0max Maximum TES unit’s base temperature (°C) Tss(0) Steady state temperature of the TES unit’s base (°C) Ta Heat sink temperature (°C) tpl Plate fin thickness (m) (UA) Heat exchanger conductance (watt/°C) Vstorage Storage volume of PCM (m) Vthermo Thermodynamic volume of PCM (m) V~ Volumetric figure of merit (as defined in Eq. 5) W Width of the TES unit base (m) δts Storage time (min) 1 ∆Q Heat loading increment (watt) Q ∆ Dimensionless heat loading (as defined in Eq. 6) T~ ∆ Dimensionless maximum temperature excursion (as defined in Eq. 5) ρ Packing density of the PCM (kg/m) τs Characteristic time (min) INTRODUCTION Many multi-chip modules such as portable electronic devices have variable power dissipation rates. As a consequence, conventional electronics module coolers must be designed for peak power operation. Incorporation of a Thermal Energy Storage (TES) mechanism into the module cooler will allow for a smaller and quieter cooling system that is sized for some intermediate heat load. Then, heat is stored in the TES-system during periods of high power operation, and it is subsequently released from the system during periods of reduced power operation. Phase Change Materials (PCM) formulated to undergo phase transition at key temperatures can provide this load-leveling capability via the latent heat effect. TES units have been employed in a variety of temperature stabilization applications including thermal control of electronics. Leoni and Amon [1997] reported a transient thermal design of wearable computers with embedded electronics using PCMs. Fossett et al. [1998] investigated the avionics passive cooling with microencapsulated PCMs. They demonstrated that microencapsulated PCM technology can be used to provide an effective passive heat sink for remotely located, intermittently operated avionics and suitable analysis may be used with confidence to design passive heat sinks. Wirtz et al. [1999] developed a simple mathematical model that simulates the performance of a cooler/heater storage unit. Alawadhi and Amon [2000] numerically studied the effectiveness of the PCM thermal storage unit under various operating conditions. They found that for varying power conditions, the thermal balance is a function of the varying power magnitude, period and PCM quantity. Gurrum et al. [2000] reported the work on thermal management of high temperature pulsed electronics using solid-liquid PCMs. Based on numerical modeling, they investigated the feasibility of using solid-liquid PCMs for microwave power transistors, which are periodic power dissipating devices. By experiments, Hodes et al. [2000] quantified the effectiveness of transient thermal management of a handset as a function of PCM material, power dissipated, orientation and wind in terms of increased talk-time and recovery time. Zheng and Wirtz [2000] developed a thermal model for optimizing the design of the hybrid TES-unit. Copyright  2001 by ASME Thermal analysis of a TES unit will give design guidelines. However, these analyses involve complicated numerical calculations or experiments to determine the design. For engineering application purpose, a simple algorithm is needed for a preliminary assessment of the feasibility of a hybrid TES-unit. The objective of this paper is to develop figures of merit that can be used to quickly evaluate various design alternatives of plate-type TES units. A modification of a previously benchmarked semiempirical finite volume model [Zheng and Wirtz, 2000] is used to study the characteristics of various TES-unit designs. A series of optimal designs, subject to various design constraints, is obtained by linking the model to an optimization algorithm. This database of optimal designs is used to develop two figures of merit that can be used to characterize the physical attributes of TES-units proposed for specific applications. TES-UNIT CONFIGURATION Figure 1 shows the general layout of these energy storage devices. One side of the storage volume is in thermal contact with the heat source (the electronics). The other side connects to the system’s heat exchanger, which is sized for some nominal heat load. The storage volume contains the PCM and a metal conducting path that is in thermal contact with the PCM. The metallization is necessary since the PCM that may be employed for this application generally have low thermal conductivity. The metallization is designed so that it can convey a nominal heat load through the storage volume to the hybrid cooler’s heat exchanger while at the same time it facilitates heat transfer to the PCM. The conducting path might consist of discrete elements such as parallel pins or plates, or it might be aluminum foam or honeycomb material. Or, the “metallization” could involve impregnation of the PCM mass with a conductivity enhancer. The thermal performance of the TES-unit is characterized by the metallization thermal resistance, Rmetal and the TES-unit thermal capacity. These quantities are functions of the physical attributes of the TES-unit. A plate-type TES-unit, shown in Figure 2, is studied in the current work. Thin, conductive plates span the gap between heat Fig. 1 General concept of the TES-unit 2 spreader plates that are in thermal contact with the heat source and the system heat exchanger, respectively. The conducting plates, of thickness, tpl and spacing, s, are the “metallization” of this design. The PCM fills the spaces between the plates, forming the thermal storage volume, Vstorage. The lower base plate (heat spreader plate) is assumed to be in contact with the heat source such that a time dependent heat load, Q(t) is imposed on the lower boundary. The upper heat spreader plate is in contact with the system heat exchanger, which is characterized by its overall thermal conductance, (UA). (UA) is sized for the nominal heat load of the application such that at steady state operation