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Applied Thermal Engineering 75 (2015) 748e755

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Applied Thermal Engineering

journal homepage: www.elsevier .com/locate/apthermeng

Thermal protection from a finite period of heat exposure e Heatsurvival of flight data recorders

Ruhul Amin Rana, Ri Li*

School of Engineering, The University of British Columbia, Kelowna, BC V1V 1V7, Canada

h i g h l i g h t s

� We study the thermal design of flight data recorders for heat survival.� Consecutive heating and cooling of 3-layer configuration is investigated.� Influences of sizes and material properties on thermal protection are explored.

a r t i c l e i n f o

Article history:Received 28 August 2014Accepted 28 September 2014Available online 8 October 2014

Keywords:Thermal protectionThermal insulationHeat conductionPhase change materialThermal designFlight data recorder

* Corresponding author. Tel.: þ1 250 807 9578; faxE-mail address: sunny.li@ubc.ca (R. Li).

http://dx.doi.org/10.1016/j.applthermaleng.2014.09.071359-4311/© 2014 Elsevier Ltd. All rights reserved.

a b s t r a c t

This work relates to developing thermal protection for a finite period of exposure to a high temperatureenvironment. This type of transient heat transfer problem starts with a heating period, which is thenfollowed by a cooling period once the high temperature environment disappears. The study is particu-larly relevant to the thermal protection of flight data recorders from high temperature flame. In thiswork, transient heat conduction through a three-concentric-layer configuration is numerically studied,which includes a metal housing, a thermal insulation, and a phase change material. The thermal per-formance is evaluated using the center temperature changing with time. It is found that the centertemperature reaches a peak during cooling period rather than heating period. Time taken to reach thepeak and the peak value depend on the sizes and properties of the layers. The properties include latentheat of fusion, melting temperature, heat capacities, and thermal conductivities. Parametric study isconducted to analyze and distinguish the influence of these parameters. The study provides generalguidance for determining sizes and selecting materials for the thermal design of flight data recorders.Additionally, the study is also useful for other similar applications, for which thermal management andprotection over a period of time is needed. In this paper, analysis starts with a baseline configurationcomposed of specific materials and sizes. Finite changes are applied to sizes, properties of the materials,and the results are compared to understand the roles of the varied parameters in affecting the thermalprotection performance.

© 2014 Elsevier Ltd. All rights reserved.

1. Introduction

Thermal protection is needed in many applications to protectdevices from thermal damage when the device is exposed to a hightemperature environment for a finite period of time. This type ofproblem can be briefly described as follows. A device initially at alow temperature is suddenly exposed to a high temperature envi-ronment for a time period, and then the initial ambient conditionreturns due to the disappearance of the high temperature envi-ronment. The design of thermal protection is to ensure that the

: þ1 250 807 9850.

7

highest temperature of the device reached during the transientprocess is within the safe temperature limit of the device.

One example is the thermal protection of flight data recorders.Flight data recorders, often called “black boxes”, are devicesdeployed in aircraft to record aviation data, which are highlyimportant for accident investigation and developing appropriatepreventive measures [1,2]. To survive a crash, flight recorders mustbe able to withstand the intense heat of post-crash fuel fire at1100 �C. During this fire exposure the temperature of interiormemory boards or small data storage chips shall not exceed theirsafe temperature limits, ~100 �C. Thermal test criteria have been setfor flight data recorders [3,4]. The recorder for large aircraft needsto survive high temperature flame for 60 min [3], while 15 min isrequired for the recorder of small aircraft [4].

Nomenclature

C volume-specific heat capacityh convection heat transfer coefficientk thermal conductivityL volume specific latent heat of fusionr radial locationR radius of layerst timeth time period of heatingTg ambient gas temperatureTs surrounding temperatureTc temperature at the center of PCMTh temperature distribution at the end of heating periodTR temperature at layer interface

Greek symbolsdC1 modification factor of shell heat capacitydk1 modification factor of shell thermal conductivitydR1 modification factor of outer radius of shell ε emissivitys StefaneBoltzmann constantq temperature

Superscript0 dimensional

Subscriptsi ¼ 1 shell layeri ¼ 2 insulation layeri ¼ 3 PCM layerb baseline configurationmax temperature peak

R.A. Rana, R. Li / Applied Thermal Engineering 75 (2015) 748e755 749

New legislation is putting more challenges on the design ofblack boxes. On one hand, new black boxes are required to containmore flight information. On the other hand, black boxes aremandated to be installed in small aircraft, for which the recordersmust have smaller size and lighter weight. To develop black boxesthat can store more information in ever-shrinking packages,optimal design of thermal protection is needed. Here the challengeis to effectively insulate and absorb heat with small thermal mass toprevent interior temperature from excessive rise.

Much work has been published regarding the thermal design offlight data recorders [5e10]. For example, Groenewegen [5] dis-closed a heat shield enclosure with a three layers configuration ofphase transition material (PCM), thermal insulator and metalhousing. The protected memory device is encapsulated in a heatsink formed of a synthetic amide wax, which changes phase at atemperature below the device's acceptable temperature. Theenclosure can protect the solid state memory or other solid statedevices from damage due to high temperature. A similar enclosurefor crash survivable protection [6] was disclosed, for which a syn-thetic wax having a relatively high heat of fusion is also proposed.

Currently, most work done in this area is mainly published aspatents, which center on the three-layer configuration. However,almost no research has been conducted to investigate the heattransfer of the configuration. As a result, there is lack of under-standing regarding the relations between configuration parametersand thermal protection performance. In the present work, a para-metric study is carried out based on a numerical model. In themodel, configuration parameters are varied and tested, whilethermal boundary conditions remain unchanged.

From a fundamental perspective, the present work explores atransient heat transfer problem through a composite configuration,which include a finite period of heat storage process followed by aheat discharging process. The results are useful for understandingthe roles of insulation and phase change in this type of heat transferproblem.

Fig. 1. Schematic of a thermal protection design composed of three layers: (1) metalshell; (2) insulation; (3) phase change material. The outer surface is exposed to bothradiation and convection heat transfer.

2. Thermal model

Cylindrical shape is commonly used as the geometric design forsmall flight data recorders. The major reason is that the shapeprovides good mechanical strength for surviving impact shock andstatic crush. For a cylindrical shape, short path for heat transferexists in radial or lengthwise dimensions, or both. However, nomatter how a data storage chip is placed inside the cylindrical

enclosure, the radial path for heat transfer is always a majorconcern. And many data recorders are packaged such that the datachip is closer to the cylinder's radial surface than to its top andbottom surfaces. Hence, a typical three-layer configuration for thethermal protection of flight data recorders is schematically shownin Fig. 1, which is a cylinder and has been reduced to two-dimensional for the simplicity of analysis.

In Fig. 1, the three layers are represented by subscript i ¼ 1, 2, 3.The outer layer (i ¼ 1) is a metal shell, which is needed for me-chanical protection. The middle layer (i ¼ 2) is an insulation layer,which has low thermal conductivity and can withstand high tem-perature. The inner layer (i ¼ 3) is a PCM (phase change material).The outer surface of the metal shell is exposed to both convectionand radiation heat transfers. Details of the boundary conditions willbe provided later on. For simplicity, no room for the protecteddevice is considered in the model. Instead, the temperature at thecenter of PCM is used to evaluate thermal protection.

A few important assumptions are made for the present study. 1)Uniform boundary conditions are assumed on the outer surface ofthe metal shell. 2) For heat transfer inside the three layers, onlyheat conduction is considered. In reality, natural convection existsin melted PCM. Usually, the melting temperature of PCM is close to

Table 1Dimensional sizes and properties of the baseline configuration. The melting tem-perature of PCM Tm,3 ¼ 82 �C.

Layer R0i;b(mm)

k0i;b(W/m �C)

C0i;b

(W/m3 �C)L0i;b(J/m3)

ε0b

i ¼ 1 (metal shell) 50.8 6.2 2.48 � 106 e 0.5i ¼ 2 (insulation) 48.3 0.028 3.15 � 104 e e

i ¼ 3 (PCM) 35.6 0.22 1.88 � 106 1.32 � 108 e

R.A. Rana, R. Li / Applied Thermal Engineering 75 (2015) 748e755750

the safety temperature limit of the protected device. Hence formost of the entire transient process, the PCM layer could be partlymelted with relatively viscous liquid phase, and convection heattransfer, therefore, could be insignificant. 3) Thermal contactresistance between layers is not considered. 4) The thermo-physical properties (specific heat and thermal conductivity) ofeach layer are assumed to be constant. It should be noted that, formost PCMs, the solid phase usually is more thermally conductive.However, there is lack of information regarding the liquid proper-ties of PCMs.

The dimensional outer radius of each layer is R0i as shown inFig. 1. In the present work, all the radii are normalized by R01, i.e.Ri ¼ R0i=R

01, and r ¼ r0=R01. So, T1 is the temperature distribution of

the metal shell within R2 � r � 1, T2 is the temperature distributionof the insulation layer within R3 � r � R2, and T3 is the temperaturedistribution of PCM within 0 � r � R3.

Since only heat conduction is considered, three thermo-physicalproperties, thermal conductivity k0i, volume-specific heat capacity,C0i , and volume-specific latent heat of fusion, L0i, are used. The non-

dimensional forms of thermal conductivity and heat capacity aredefined by ki ¼ k0i=k

01, Ci ¼ C0

i=C01. The latent heat is normalized by

the heat capacity of metal shell, i.e. Li ¼ L0i=C01, the unit of which is

temperature. The non-dimensional form of time is t ¼ t0k01=C01R

021 ,

which actually is a Fourier number based on the thermal diffusivityand outer radius of the metal shell.

The heat transfer processes can be described as follows. Initially,the cylinder has a uniform temperature T0. At t ¼ 0, the outersurface r¼ 1 is exposed to a high temperature environment by bothconvection and radiation heat transfer for a time period th, which isthe heating period. At t ¼ th, the high temperature environment isreplaced with a room condition, and the cooling period begins. Theheating period ends up with non-uniform temperature distributionin each layer, denoted by Th,i, which then becomes the initial con-dition for the cooling period. To clearly describe the two consecu-tive heat transfer processes, the governing equations for theanalysis are expressed in their integral forms. Assuming constantproperties, the equations are

Zth

0

1r

v

vr

�rvTivr

�dt ¼ Ci

kiðqi � T0Þ (1a)

Zt

th

1r

v

vr

�rvTivr

�dt ¼ Ci

ki

�qi � Th;i

�(1b)

where t is used as a dummy variable to represent time. Eq. (1a) isfor the heating period, while Eq. (1b) is for the cooling period. BothT and q are dimensional with the unit of temperature. And q isdefined as

qi ¼ Ti for Ti � Tm;i

qi ¼ Ti þLiCi

for Ti > Tm;i

(2)

Here Tm,i is the melting temperature of each material. It shouldbe noted that, for the current thermal problem, phase change oc-curs only to the layer i ¼ 3.

For Eq. (1), the following conditions at the interfacial boundariesr ¼ R2 and R3 need to be satisfied. Neglecting contact thermalresistance, the two conditions are temperature continuity and heatflux continuity, which are given by.

½Ti ¼ Tiþ1�r¼ R2;R3�kivTivr

¼ kiþ1vTiþ1vr

�r¼ R2;R3

(3)

where i ¼ 1, and 2. For the PCM, the other boundary condition is

vT3vr

����r¼0

¼ 0 (4)

The boundary condition on the outer surface of the metal shellis.

εsT4s � T4R1

þ h

�Tg � TR1

� ¼ vT1vr

����r¼1

(5)

Here Ts is the surrounding temperature, and Tg is the tempera-ture of gas flow over the cylinder. The modified emissivity ε isdefined as ε ¼ ε

0R01=k01 with the unit of m2 K/W, where ε

0 is emis-sivity. And the non-dimensional heat transfer coefficient ish ¼ h0R01=k

01, where h0 is dimensional heat transfer coefficient.

Based on the geometric model shown in Fig.1 and the governingequations given by Eq. (1), a 2-D finite element model is con-structed to simulate the transient heat transfer problem. A 2-Dtriangle element with six nodes is employed for meshing. Consid-ering the operating temperature limit for most data chips, theallowed increase of center temperature is ~100 �C. Using aconvergence tolerance of 10�3, the convergence criterion for tem-perature is set to be 0.1 �C. The time step is set to be 0.005th so thatthere are two hundred time steps for the heating period. Themeshing resolution dependency is checked by refining the meshuntil the maximum difference of temperature was within 0.5 �C.The number of nodes is around eight thousand.

To carry out a parametric study, a baseline configuration isdefined. The dimensional radii and properties of the three layersare given in Table 1, where the subscript b represents baseline. Thebaseline materials are selected from commercially available mate-rials. Both the baseline sizes andmaterials are decided based on theavailable information of commercially available flight data re-corders. Titanium is used for metal shell, for which emissivity ε

0b ¼

0:5 is assumed. At the end of the paper, it will be shown that theemissivity is an insignificant property for the current thermalproblem. Micro-porous silica (Rath Incorporated) is used for insu-lation. An organic material (A82, Phase Change Material ProductsLimited) is selected as PCM, which has a melting temperatureTm,3 ¼ 82 �C and maximum operating temperature 300 �C. Likemany other PCMs, the selected PCM has the properties for its solidphase available, but not for its liquid phase. Hence, the solid-phaseproperties are used for both phases.

Normalized sizes and material properties of the baselineconfiguration are provided in Table 2. Starting from the baselineconfiguration, configuration parameters including sizes and mate-rial properties will be modified with finite changes, and themodified configurations will be numerically tested. Despite thefinite changes to the material properties, some combinations of the

Table 2Normalized sizes and properties of the baseline configuration.

Layer Ri,b ki,b Ci,b Li,b (�C) εb (m2 K/W)

i ¼ 1 (metal shell) 1 1 1 e 0.004i ¼ 2 (insulation) 0.95 0.005 0.013 e e

i ¼ 3 (PCM) 0.7 0.035 0.76 53 e

Fig. 2. Transient temperatures of the baseline configuration exposed to high thermalload for a time period of th ¼ 0.9. The PCMmelting point Tm,3 is indicated. Separated bythe vertical dotted line, left side is heating period, while right side is cooling period.(TR1: surface temperature of metal shell; TR2: shell-insulation interface temperature;TR3: insulation-PCM temperature; Tc: center temperature of PCM).

R.A. Rana, R. Li / Applied Thermal Engineering 75 (2015) 748e755 751

modified properties might not be available currently in real life. Theobjective of the present work is to investigate the thermal effects ofchanging the properties. The results will be useful for guiding theselection of real materials for actual designs to achieve optimalthermal protection.

The model requires initial condition, boundary conditions dur-ing heating period, and boundary condition during cooling period.The boundary conditions are provided in Table 3. All the conditionsare defined according to the industrial criteria for high temperatureflame testing of flight data recorders [4]. Initially, the concentriccylinder has a uniform temperature of T0¼ 20 �C, which is the sameas the ambient. The cylinder is exposed to a high temperatureimpinging flame of 1100 �C for a time period of 900 s, which cor-responds to a non-dimensional time th ¼ 0.9. This heating time isused for most of the analysis in the present work unless indicatedotherwise.

The convection and radiation heat transfer of flame impinge-ment depend on many factors [11], and no specific information isprovided in the test standard regarding each heat transfer modes.There is almost no previous research work on the flame testing offlight data recorders except a previous experimental report [12],which present temperature measured at the center a metal slugexposed to a flame. We numerically simulate the metal slug usingε0 ¼ 0.5 and changing convection heat transfer coefficient.Reasonable agreement with the experimental datawas foundwhenh0 ¼ 35 W/m2 K.

At t ¼ th the flame stops, and the cylinder returns to a roomcondition with ambient temperature 20 �C to naturally cool downwithout any forced convection. For cooling period, the ambienttemperature is used for both Ts and Tg. For air cooling with naturalconvection, it is reasonable to assume the convection heat transfercoefficient to be 10 W/m2 K. At the end of the paper, it will beshown that, for the present thermal problem radiation is not themajor heat transfer mode as compared with convection heattransfer.

3. Results and discussion

3.1. Results of baseline configuration

The cylinder with baseline configuration is exposed to the flamefor a heating period of th ¼ 0.9. The transient temperatures at fourlocations: center (Tc), insulation-PCM interface (TR3), shell-insulation interface (TR2), and shell outer surface (TR1), are plottedversus time for both heating and cooling periods in Fig. 2. Themelting temperature of PCM, Tm,3, is indicated in the figure. Sig-nificant increases are visible for TR1, TR2, TR3 during the heatingperiod. The temperatures TR1 and TR2 show fast increase toward theflame temperature. The TR3 curve shows that phase change starts

Table 3Transient boundary conditions for heating and cooling periods.

Time h0 (W/m2 K) h Tg (�C) Ts (�C)

0 � t � th (heating period) 35 0.3 1100 1100th � t (cooling period) 10 0.08 20 20

when the local temperature reaches Tm,3. For the center tempera-ture, Tc, a slight increase of 4 �C can be seen during the heatingperiod. At time th, the flame stops. Immediate drop can be seen forall the temperatures except Tc. The center temperature keepsincreasing to a peak value Tc,max ¼ 81.8 �C at t ¼ 7.5. Major increaseof Tc occurs during the cooling period rather than during theheating period. Solidification occurs at the insulation-PCM inter-face when TR3 decreases below the melting temperature. Thetemperature peak at the insulation-PCM interface TR3,max is themaximum temperature of the PCM, which does not exceed themaximum operating temperature of the PCM.

The heating period is varied from 0.45 to 2.7, and the centertemperature is plotted versus time in Fig. 3. For all the cases, thetemperature peak occurs during cooling periods. For th ¼ 0.45 and

Fig. 3. Transient temperature at the center of the baseline configuration exposed tothermal load for varied heating periods th.

R.A. Rana, R. Li / Applied Thermal Engineering 75 (2015) 748e755752

0.9, no phase change occurs at the center. For th ¼ 1.8, the entirePCM melts, and Tc stabilizes at the melting temperature for a longtime. For th ¼ 2.7, melting occurs at the center, and temperaturecontinues to increase in the liquid phase and reaches a peak~150 �C. Fig. 3 clearly indicates that the duration of heating periodwould significantly affects the design of thermal protection.

Fig. 5. Peak values of Tc and TR3 reached during the transient process for R3 varyingfrom 0 (no PCM, only metal shell and insulation) to 0.95 (no insulation, only shell andPCM). The dotted line is the maximum operating temperature 300 �C of the PCM.

3.2. Varying sizes

Smaller size of thermal protection is preferred for the benefit ofsaving space and reducing weight. However, the size must be largeenough to provide sufficient strength andwithstand high heat load.In this section, the sizes of different layers are varied, and theireffects on thermal protection will be discussed.

The thickness of PCM R3 is varied from 0 to 0.95, and the outerradius of the insulation layer R2,b¼ 0.95 remains constant. Since theouter radius of insulation is fixed, increasing the thickness of PCMresults in reducing the insulation material. For R3 ¼ 0, there is onlythe shell and insulationmaterial, and no PCM. For R3¼ 0.95, there isonly the shell and PCMwithout insulation in between. Fig. 4 showsthe development of Tc for four cases. When R3¼ 0 without PCM, thetemperature shows a fast rise toward a very high peak value andthen cools down quickly. When there is PCM, the temperature in-creases slowly with lower peaks. However, both the temperaturepeak and the time taken to reach the peak are not in a monotonictrend with the PCM thickness. For example, the peak temperaturefor R3 ¼ 0.2 is higher than that for R3 ¼ 0.7 but lower than that forR3 ¼ 0.95.

To understand the trend, a few values of R3 are tested. Tem-perature peaks at the center and outer surface of the PCM layer,TR3,max and Tc,max, are plotted in Fig. 5 for 0 � R3� R2,b. Both tem-perature peaks decrease first and then increase with increasingPCM and reducing insulation. There is a range of PCM thickness,from ~0.3 to ~0.85, where Tc,max remains low. Attention should alsobe paid to the interfacial temperature TR3,max, which cannot exceedthe maximum operating temperature of PCM. For the PCM in thebaseline configuration, the maximum operating temperature isindicated by the horizontal dotted line. For example, althoughR3¼ 0.85 looks promising in terms of Tc,max, the temperature TR3,max

Fig. 4. Transient temperature at the center for PCM radius varying from R3 ¼ 0 (noPCM, only metal shell and insulation) to R3 ¼ 0.95 ¼ R2,b (no insulation, only shell andPCM).

almost exceeds the operating temperature. Hence, the insulationmaterial helps bring down the outer temperature of PCM TR3 andensure PCM is within its safe temperature range, while the PCM isimportant for maintaining the center temperature low. It can beseen that the insulation and PCM jointly can provides satisfactorythermal protection within the given design size R2 ¼ 0.95.

The outer radius of the metal shell is changed. This change isnecessary when the mechanical strength is not sufficient to survivea crash. The ratio shown in Fig. 6 is the ratio of new radii to theradius of the baseline configuration, i.e. dR1 ¼ R01=R

01;b. The hori-

zontal axis is defined as td2R1 so that the three temperature curvesare shown on the same time scale. Comparison is made betweenthe baseline configuration dR1 ¼ 1 with two other configurationswith thicker shells dR1 ¼ 1.05, and 1.1. The rapid temperature in-crease at the early stage of the transient process is almost the same

Fig. 6. Transient development of center temperature for varied outer radii of metalshell (dR1 ¼ R01=R

01;b).

R.A. Rana, R. Li / Applied Thermal Engineering 75 (2015) 748e755 753

for all the three cases. Major difference is visible at the later stage ofcooling period, and a thicker shell slows down the decrease ofcenter temperature. One major reason is that the thicker shellstores more heat during the heating period, and that heat storagewill affect the temperature change during the cooling period. Thiswill be confirmed by varying the heat capacity of shell material,which will be presented later on. Another reason is that a thickershell could increase thermal impedance for the heat transfer to theambient during cooling period.

3.3. Varying properties

The purpose of the three concentric layers is to provide thermalprotection from high temperature thermal load. A proper combi-nation of the layer properties is essential for thermal protection. Inthis section, the important thermal properties of insulation, PCMand shell materials are modified in small ranges, and the centertemperature of PCM is used to evaluate their effects.

The properties of the insulation material are changed to studythe thermal performance. The thermal conductivity k2 is changedfrom half to three times of the baseline value k2,b. For k2 ¼ k2,b, theheat capacity C2 is changed from half to three times of the baselinevalue C2,b. In Fig. 7, the center temperature shows high sensitivity tothe thermal conductivity, and peak temperature is 62 �C for 0.5k2,band 112 �C for 3k2,b. In contrast, the effect of changing heat capacityis very small. This can be seen from the temperature curves of k2,bwith four varied heat capacities, and all the four curves are too closeto be distinguished. The thermal conductivity is the major propertyof the insulation that affects the heat flow into the PCM.

The properties of PCM including thermal conductivity, heat ca-pacity, latent heat, are changed. They are varied from half to threetimes of their baseline values. The benefits of decreasing thermalconductivity and increasing heat capacity are clear from Fig. 8a andb. However, higher sensitivity of center temperature is observed toheat capacity than to thermal conductivity. Comparing the 2k3,bline (Fig. 8a) with the 0.5C3,b line (Fig. 8b), one can see thatdecreasing specific heat showsmore negative effect than increasingthermal conductivity. Comparing the 0.5k3,b line (Fig. 8a) with the2C3,b line (Fig. 8b), increasing specific heat shows more positiveeffect than decreasing thermal conductivity. As shown in Eq. (3),

Fig. 7. The thermal conductivity of insulation material is varied. The heat capacityC2 ¼ C2,b for all cases except for k2 ¼ k2,b where 4 lines (C2 ¼ 0.5C2,b, C2,b, 2C2,b, 3C2,b)cluster together.

the thermal conductivity affects both the inward heat flow duringheating period and outward heat flow during cooling period. Asshown in Fig. 2, major rise of the center temperature occurs duringthe cooling period.

Fig. 8c shows the effects of changing latent heat of fusion. It issurprising to see the minor effect as compared to that of changingheat capacity. The major reason is that only a limited portion of thePCM melts in the baseline configuration during the transient pro-cess. This can be observed in Fig. 2, which shows that at t ¼ th thePCM melts at R ¼ R3 with its center temperature well below themelting temperature Tm,3. It is expected that if th is longer or Tm,3 islower, the role of latent heat would become significant.

The melting temperature of PCM is also changed with twovalues lower and the other two higher than the baseline value of82 �C. Fig. 8d shows that melting occurs at center for Tm,3 ¼ 60 �Cand 70 �C, but not for 90 �C and 100 �C. Lowering the meltingtemperature slows down the increase of center temperature at theearly stage of the transient. Additionally, the center temperaturepeak decreases with decreasing the melting temperature of PCM,showing the benefit of having phase change across the PCM layer atlow temperatures. However, the concern regarding low meltingtemperature is that having the entire PCM layer in liquid phasewellabove its melting temperature would cause significant free con-vection. Also, it cools down slowly as compared to high meltingpoint.

The metal shell mainly serves as a mechanical housing. Its ef-fects on thermal protection are investigated by changing its ther-mal conductivity and heat capacity. Two ratios are defined in Fig. 9to compare the new values of the two properties to their baselinevalues, which are dC1 ¼ C0

1=C01;b and dk1 ¼ k01=k

01;b. To compare all

the transient temperature curves on the same time scale, they areplotted versus a modified time tdC1/dk1. For dC1 ¼ 1, two thermalconductivities dk1 ¼ 1, 2 are tested, and for dC1 ¼ 2, three thermalconductivities dk1¼1, 2, 3 are tested. The center temperature showshigher sensitivity to the change of heat capacity than to the changeof thermal conductivity. There is benefit from a lower heat capacityof shell material, which reduces the thermal storage in the shelllayer during heating period and shows faster cooling process. Thereis minor benefit from having a high thermal conductivity of shellmaterial, which assists the heat transfer to the ambient duringcooling period.

To evaluate the effect of surface emissivity, the emissivity of theshell material is changed from twice to 0.4 of the baseline value,which correspond to a range of ε0 from 1 to 0.2. Fig. 10 shows thatthe effect is almost invisible at early stage of the transient. However,increasing the emissivity can slightly reduce the center tempera-ture peak. This means that during cooling period the emissivityassists heat transfer from the hot shell to the ambient and thereforereduces the inward heat flow. After the center temperature reachesits peak, a higher emissivity cause the center temperature to dropfaster. Therefore, as compared to the heating period, the emissivityis more effective for the cooling period. This is because, in thepresent case, convection heat transfer is less dominant duringcooling period than heating period. Generally speaking, Fig. 10 in-dicates that, for the present thermal protection problem, convec-tion is the major mode for the heat transfer from the hightemperature flame to the thermal protection unit.

4. Conclusions

A parametric study is numerically conducted on the heattransfer in a three-concentric-layer configuration, which is exposedto a high temperature environment for a finite period of time. Thisconfiguration is a typical thermal protection for electronic devices,and has been commonly considered for the thermal design of flight

Fig. 8. The development of center temperature for varied PCM properties: (a) varied thermal conductivity; (b) varied heat capacity; (c) varied latent heat of fusion; (d) variedmelting point.

Fig. 9. Three heat capacities of the shell material are tested with varied thermalconductivities: dC1 ¼ 1 (dk1 ¼ 2, 1); dC1 ¼ 2 (dk1 ¼ 3, 2, 1); dC1 ¼ 3 (dk1 ¼ 1).

Fig. 10. The emissivity of the shell material is changed. ε ¼ 2εb indicates a blackbodysurface.

R.A. Rana, R. Li / Applied Thermal Engineering 75 (2015) 748e755754

R.A. Rana, R. Li / Applied Thermal Engineering 75 (2015) 748e755 755

data recorders. The thermal conditions employed in the presentwork are based on the flame testing standard of flight datarecorders.

The heat transfer process contains a finite heating period fol-lowed by a long cooling period. It is found that the center tem-perature continues to rise until reaching its peak during the coolingperiod rather than the heating period. The center temperature isused to evaluate the thermal protection performance.

The study first focuses on the relations between layer thick-nesses and thermal performance. With a fixed total space forinsulation and PCM, the thermal protection does not change in amonotonic trend with varying the volumes of PCM and insulation.It is shown that having both materials is necessary to provideoptimal thermal performance and at same time protect PCM fromexceeding its maximum operating temperature. Although a thickmetal shell is beneficial for mechanical strength, increasing itsthickness causes negative effect on thermal protection.

Material properties are changed to investigate their impacts onthermal protection. For the insulation layer, changing its thermalconductivity shows more significant effect than changing its heatcapacity. For PCM, the results show the benefits of decreasingthermal conductivity, increasing heat capacity, and increasinglatent heat. Higher sensitivity of the center temperature is observedto the heat capacity than to the thermal conductivity. With otherproperties fixed, lowering the PCM melting temperature reducesthe center temperature. Changing the properties of shell materialalso show minor effects on the thermal performance. Increasing itsthermal conductivity or emissivity assists outward heat transferduring cooling period.

Acknowledgements

This work was supported by NSERC (Natural Sciences and En-gineering Research Council of Canada) Engage Grant (EGP#445102-12).

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