thermal and mechanical characteristics of a multi-functional thermal

THERMAL AND MECHANICAL CHARACTERISTICS OF A MULTI-FUNCTIONAL THERMAL ENERGY STORAGE STRUCTURE Richard Wirtz, Tianwen Zhao and Yanyao Jiang Mechanical Engineering Department, MS312 University of Nevada, Reno Reno, NV 89557

ABSTRACT Thermal Energy Storage (TES) sandwich-structures that combine the heat storage function with structural functionality are described. The structure consists of a Thermal Interface (TI) connected to a hollow plate lamination. Each laminate is a hollow aluminum plate having a series of mm-scale channels or compartments that are filled with Phase Change Material (PCM). Heat storage is via the latent heat of the PCM. A generalized thermal response model that is applicable to a wide range of channel geometrical configurations is described. The model couples the thermal response of the TI to that of the aluminum/PCM lamination. It gives rise to closed-form solutions for the spatial temperature distribution within the TES-volume. The temporal response of the system is easily obtained via numerical solution of two ordinary differential equations. Thermal analysis delineates geometrical configurations that have good thermal response characteristics. The mechanical properties of the laminated structure were determined experimentally. Four-point bending experiments were conducted using specimens made with three layers of hollow plates laminated using a structural adhesive. An energy method was developed to model the deformation and strength of the laminated structure. The energy method can correctly simulate the experimental results. Experiments and modeling indicate that these laminated structures have an excellent performance-to-weight ratio.

NOMENCLATURE A Ac h k L mc MC P q Rk Ri S t T W x Greek β δ ε

Eq. (14b) Cross section area Comductance or latent heat Thermal conductivity Length Thermal capacity Eq. (11b) Perimeter Heat transfer rate Eq. (12b) Interfacial resistance Shape factor Thickness Temperature width coordinate Specific surface area “melt” region extent Volume fraction

0-7803-8357-5/04/$20.00 ©2004 IEEE

τ Subscripts f i p n ref tr v

Time Aluminum heat spreader plate Interfacial TES-volume Number of laminates Reference value Phase transition Volumetric

INTRODUCTION A Thermal Energy Storage (TES) capability incorporated into the temperature control system of an electronics module having a variable heat dissipation rate will improve system reliability and allow for a smaller, less-power-consuming module cooler 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. Materials formulated to undergo phase transition at key temperatures (Phase Change Materials, PCM’s) can provide this loadleveling capability via the latent heat effect. Space limitations often preclude the incorporation of this technology into avionics thermal control systems so that TESsystems must be such that they add no mass (or volume) to existing systems. TES-systems having multiple functionality can satisfy this constraint. For example, TES-composites that combine the heat storage function with a structural function can be configured into a system as structural elements while at the same time they are part of the temperature control system. A system that possesses dual functionality, such as thermal storage together with structural functionality, will save weight and space in an avionics system. Phase Change Materials having transition temperatures and latent heats appropriate to the electronics thermal control application can be categorized according transition process: solid-to-liquid, solid-to-solid, etc. Most of these materials are organics having relatively poor thermal conductivity. In addition, their performance when the PCM is in the liquid phase could be sensitive to system orientation or g-loading. The most widely used solid-liquid materials are the paraffins, although other materials have been considered [1]. Fossett and co-workers [2] used micro-encapsulated PCM powder; and, Wirtz et al [3] employed an immobilizing agent (SEBS) to inhibit paraffin liquid motion. Recently, Wirtz et al [4] showed that liquid paraffin in graphite foam is effectively immobilized by the small cell size of the foam. Pai and Joshi [5] used a

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2004 Inter Society Conference on Thermal Phenomena

honeycomb structure; O’Connor and Weber [6] employed foam metal; and, Wirtz et al [4] used foam graphite to enhance conduction in the PCM mass. Bauer and Wirtz [7] developed laminations where the TES-volume consisted of Pentaglycerine impregnated aluminum foam. Pentaglycerine is a PCM that undergoes solid-state phase transition, so the issue of PCM mobility was obviated. This work focuses on development of light-weight TES sandwich-structures where the structural/thermally-conductive elements are a metal; typically a mm-scale hollow aluminum extrusion or casting. The TES-volume is a solid-solid or solid-liquid PCM, which may include a thermal conductivity enhancer or other property modifier such as a paraffin immobilizer. The short conduction lengths of the TES-volume are effective in ameriolating the adverse effect of low PCM thermal conductivity; and, the small compartmentalization of the PCM minimizes buoyancy-driven motion. A variety of TES-system configurations have been considered, ranging from simple laminations that maximize the storage volume to fairly complex systems that include additional elements for improved structural performance. Previously benchmarked analytical models[4] that predict the thermal and structural response of plate-like TES-structures have been developed and used to assess performance.

Fig. 1 Aluminum meso-channel TES-composite.

The principal application is thermal control of variable-power avionics systems such as intermittently operated radar. The primary advantage of this approach is that such multifunctionality results in a smaller, less massive thermal control/structural system. In addition, the TES component of the system is passive, having essentially no moving parts.

SYSTEM GEOMETRY Consider the laminated TES-structure shown in Fig. 1. It consists of PCM-impregnated mm-scale aluminum plates of thickness t and length Lf attached to a thermal interface (TI) of length xo. The TI’s are presumed to be in thermal contact with a heat source or sink, so the temperature of the source/sink will be directly related to the TI temperature. Heat input per unit width to the TI is q’n where n is the number of laminations. Each plate of the lamination is hollow, with a number compartments that contain phase change material. The figure shows a plate that has a series of parallel channels of periodicity W running in the x-direction. We designate this configuration a 2D Box Structure. In storage mode, excess heat flows into the thermal interface, and then outward in the x-direction from the TI through the conductive (heat spreader) plates and to the TES-volume. Since the thermal conductivity of the aluminum heat spreader plate (kf) is much greater than that of the PCM contained in the compartments (kp), heat flow is primarily from the TI along the aluminum, and then into the PCM.

THERMAL RESPONSE MODEL An operable unit cell for analysis of the configuration shown in Fig. 1 is shown in Fig. 2. It consists of a single lamination heat spreader/TES-volume of width, W in thermal contact with a segment of TI. The heat spreader has length Lf, cross sectional area Acf and thermal conductivity kf. The TESvolume has length Lf, cross sectional area Acp, thermal

Fig. 2 Slab-shaped TES structure: a) unit cell, b) section end view. conductivity kp, volumetric latent heat hv and transition temperature Ttr. The TES-volume may contain a thermal conductivity enhancement or a paraffin immobilizer, so kp and hv could be “effective” properties. The heat transfer to/from one TI segment is

q1 (τ ) = qref F (τ )

(1)

where qref is a reference quantity and τ is time. The TI temperature is assumed to be spatially uniform and it is characterized by its sensible heat capacity (mc-product). An energy balance gives mc

dTTI = q1 (τ ) − q f ,0 dτ

(2)

where TTI is the TI temperature and qf,o is the heat transfer rate from the TI volume. Assume kpAcp