1990 or the interfacial instability limit proposed by Gerner 1992 should begoverned by evaluating the shape and physical dimensions of the specific micro heat pipe being considered.Khrus
Trang 1differential and then combined with the continuity expression The result was a first order ordinary ferential equation that related the radius of curvature of the liquid–vapor interface to the axial positionalong the pipe Building upon this model, Peterson (1988a) and Babin et al (1990) developed a steady-statemodel for a trapezoidal micro heat pipe using the conventional steady-state modeling techniques outlined
dif-by Chi (1976) and described earlier in this chapter The resulting model demonstrated that the capillarypumping pressure governed the maximum heat transport capacity of these devices
The performance limitations resulting from the models presented by Cotter (1984) and by Babin et al.(1990) were compared and indicated significant differences in the capillary limit predicted by the two models These differences have been analyzed and found to be the result of specific assumptions made inthe initial formulation of the models [Peterson, 1992]
A comparative analysis of these two early models was performed by Gerner et al (1992), who indicatedthat the most important contributions of Babin et al (1990) were the inclusion of the gravitational bodyforce and the recognition of the significance of the vapor pressure losses In addition, the assumption thatthe pressure gradient in the liquid flow passages was similar to that occurring in Hagen–Poiseuille flow wasquestioned, and a new scaling argument for the liquid pressure drop was presented In this development,
it was assumed that the average film thickness was approximately one-fourth the hydraulic radius, ing in a modified expression for the capillary limitation
result-Evaporator
Cond
enser
120 µm
FIGURE 11.4 Micro heat pipe operation (Reprinted with permission from Peterson, G.P., Swanson, L.W., and
Gerner, F.M (1996) “Micro Heat Pipes,” in Microscale Energy Transport, C.L Tien, A Majumdar, and F.M Gerner eds.,
Taylor-Francis Publishing Co., Washington D.C.)
Trang 2A significant contribution made by Gerner et al (1992) was the recognition that the capillary limit maynever actually be reached due to Kelvin–Helmholtz type instabilities occurring at the liquid–vapor interface.Using stability analysis criteria for countercurrent flow in tubes developed by Tien et al (1979) and mini-mizing the resulting equations, the wavelength was found to be approximately 1 cm for atmospheric waterand methanol Since this length was long with respect to the characteristic wavelength, it was assumed thatgravity was the dominant stabilizing mechanism The decision as to whether to use the traditional capillarylimit proposed by Babin et al (1990) or the interfacial instability limit proposed by Gerner (1992) should begoverned by evaluating the shape and physical dimensions of the specific micro heat pipe being considered.Khrustalev and Faghri (1994) presented a detailed mathematical model of the heat and mass transferprocesses in micro heat pipes that described the distribution of the liquid and the thermal characteristics
as a function of the liquid charge The liquid flow in the triangular corners of a micro heat pipe with gonal cross-section was considered by accounting for the variation of the curvature of the free liquid sur-face and the interfacial shear stresses due to the liquid vapor interaction The predicted results were comparedwith the experimental data obtained by Wu and Peterson (1991) and Wu et al (1991) and indicated theimportance of the liquid charge, the contact angle, and the shear stresses at the liquid vapor interface inpredicting the maximum heat transfer capacity and thermal resistance of these devices
poly-Longtin et al (1994) developed a one-dimensional steady-state model for the evaporator section of themicro heat pipe The governing equations were solved, assuming a uniform temperature along the heatpipe The solution indicated that the maximum heat transport capacity varied with respect to the cube ofthe hydraulic diameter of the channel
An analytical model for the etched triangular micro heat pipe developed by Duncan and Peterson (1995)
is capable of calculating the curvature of the liquid–vapor meniscus in the evaporator This model wasused to predict the capillary limit of operation of the heat pipe and to arrive at the optimal value of theliquid charge In a subsequent work, a hydraulic diameter was defined, incorporating the frictional effects
of the liquid and the vapor, and was used in a model for predicting the minimum meniscus radius andmaximum heat transport in triangular grooves [Peterson and Ma, 1996b] The major parameters influ-encing the heat transport capacity of the micro heat pipe were found to be the apex angle of the liquid arter-ies, the contact angle, heat pipe length, vapor velocity and the tilt angle Ma and Peterson (1998) presentedanalytical expressions for the minimum meniscus radius and the maximum capillary heat transport limit
in micro heat pipes that were validated with experimental data
A detailed steady-state mathematical model for predicting the heat transport capability of a micro heatpipe and the temperature gradients that contribute to the overall axial temperature drop as a function
of the heat transfer was developed by Peterson and Ma (1999) The unique nature of this model was that itconsidered the governing equation for fluid flow and heat transfer in the evaporating thin film region Themodel also consisted of an analytical solution of the two dimensional heat conduction in the macro evapo-rating regions in the triangular corners The effects of the vapor and liquid flows in the passage,the flow and condensation of the thin film caused by the surface tension in the condenser, and the capillaryflow along the axial direction of the micro heat pipe were considered in this model The predicted axialtemperature distribution was compared with experimental data, with very good agreement The model wascapable of calculating both the heat transfer distribution through the thin film region and the heat transfer-operating temperature dependence of the micro heat pipe It was concluded from the study that the evap-orator temperature drop was considerably larger than that at the condenser and that the temperaturedrops increased with an increase in input power when the condenser is kept at a constant temperature.The maximum heat transfer capacity of copper–water micro heat pipes was also explored by Hopkins
et al (1999) using a one-dimensional model for predicting the capillary limitation In this analysis, theliquid–vapor meniscus was divided into two regions depending on whether the contact angle can betreated as a constant at the evaporator or as a variable along the adiabatic and condenser sections
11.2.1.2 Transient Modeling
As heat pipes diminish in size, the transient nature becomes of increasing interest The ability to respond torapid changes in heat flux coupled with the need to maintain constant evaporator temperature in modern
Trang 3high-powered electronics necessitates a complete understanding of the temporal behavior of these devices.The first reported transient investigation of micro heat pipes was conducted by Wu and Peterson (1991) Thisinitial analysis utilized the relationship developed by Collier (1981) and used later by Colwell and Chang(1984) to determine the free molecular flow mass flux of evaporation The most interesting result fromthis model was the observation that reverse liquid flow occurred during the start-up of micro heat pipes.
As explained in the original reference [Wu et al., 1990], this reverse liquid flow is the result of an imbalance
in the total pressure drop and occurs because the evaporation rate does not provide an adequate change
in the liquid–vapor interfacial curvature to compensate for the pressure drop As a result, the increasedpressure in the evaporator causes the meniscus to recede into the corner regions forcing liquid out of theevaporator and into the condenser During start-up, the pressure of both the liquid and vapor are higher
in the evaporator and gradually decrease with position, promoting flow away from the evaporator Oncethe heat input reaches full load, the reverse liquid flow disappears and the liquid mass flow rate into theevaporator gradually increases until a steady-state condition is reached At this time the change in the liquidmass flow rate is equal to the change in the vapor mass flow rate for any given section [Wu and Peterson,1991] The flow reversal in the early transient period of operation of a micro heat pipe has also been cap-tured by Sobhan et al (2000) using their numerical model
Several more-detailed transient models have been developed Badran et al (1993) developed a conjugatemodel to account for the transport of heat within the heat pipe and conduction within the heat pipe case.This model indicated that the specific thermal conductivity of micro heat pipes (effective thermal con-ductivity divided by the density) could be as high as 200 times that of copper and 100 times that of Gr/Cucomposites
Ma et al (1996) developed a closed mathematical model of the liquid friction factor for flow occurring
in triangular grooves This model, which built upon the earlier work of Ma et al (1994), considered the facial shear stresses due to liquid–vapor frictional interactions for countercurrent flow Using a coordinatetransformation and the Nachtsheim–Swigert iteration scheme, the importance of the liquid vapor inter-actions on the operational characteristics of micro heat pipes and other small phase change devices wasdemonstrated The solution resulted in a method by which the velocity distribution for countercurrentliquid–vapor flow could be determined, and it allowed the governing liquid flow equations to be solved forcases where the liquid surface is strongly influenced by the vapor flow direction and velocity The results ofthe analysis were verified using an experimental test facility constructed with channel angles of 20, 40, and
inter-60 degrees The experimental and predicted results were compared and found to be in good agreement [Maand Peterson 1996a, 1996b; Peterson and Ma 1996a]
A transient model for a triangular micro heat pipe with an evaporator and condenser section was sented by Sobhan et al (2000) The energy equation as well as the fluid flow equations were solved numer-ically, incorporating the longitudinal variation of the cross-sectional areas of the vapor and liquid flows, toyield the velocity, pressure, and temperature distributions The effective thermal conductivity was com-puted and characterized with respect to the heat input and the cooling rate under steady and transientoperation of the heat pipe The reversal in the liquid flow direction as discussed by Wu and Peterson (1991)was also obvious from the computational results
pre-11.2.1.3 Transient One-Dimensional Modeling of Micro Heat Pipes
A flat micro heat pipe heat sink consisting of an array of micro heat pipe channels was used to form a pact heat dissipation device to remove heat from electronic chips Each channel in the array served as anindependent heat transport device The analysis presented here examined an individual channel in such
com-an array The individual micro heat pipe chcom-annel com-analyzed had a tricom-angular cross-section The chcom-annel wasfabricated on a copper substrate and the working fluid used was ultrapure water
11.2.1.3.1 The Mathematical Model
The micro heat pipe consisted of an externally heated evaporator section and a condenser section subjected
to forced convective cooling A one-dimensional model was sufficient for the analysis, as the variations in thefield variables were significant only in the axial direction, due to the geometry of the channels A transient
Trang 4model that proceeded until steady-state was utilized to analyze the problem completely In this problem,the flow and heat transfer processes are governed by the continuity, momentum, and energy equations forthe liquid and vapor phases A nonconservative formulation can be utilized because the problem deals withlow velocity flows As phase change occurs, the local mass rates of the individual liquid and vapor phasesare coupled through a mass balance at the liquid–vapor interface The cross-sectional areas of the vaporand liquid regions and the interfacial area vary along the axial length due to the progressive phase changeoccurring as the fluid flows along the channel These variations in the area can be incorporated into themodel through the use of suitable geometric area coefficients, as described in Longtin et al (1994) The localmeniscus radii at the liquid–vapor interface are calculated using the Laplace–Young equation The frictionfactor, which appears in the momentum and energy equations is incorporated through appropriate modelsfor fluid friction in varying area channels, as described in the literature.
The governing differential equations can be described as follows:
11.2.1.3.2 Laplace–Young Equation
11.2.1.3.3 Vapor phase equations
Vapor continuity equation: evaporator section
冢 d2⫺ βl r2冣 ⫺ 2βl u v r ⫹ βi rV il⫽ 0 (11.31)Vapor continuity equation: condenser section
1ᎏ2
∂T v
ᎏ
∂x
兹3苶ᎏ4
∂u v
ᎏ
∂x
兹3苶ᎏ4
4ᎏ3
∂ᎏ
∂x
兹3苶ᎏ4
∂ᎏ
1ᎏ2
1ᎏ2
∂P v
ᎏ
∂x
兹3苶ᎏ4
∂u v
ᎏ
∂t
兹3苶ᎏ4
ρ
l
ᎏρ
ρ
l
ᎏρ
σᎏ
r
Trang 5Vapor Energy equation: condenser section
11.2.1.3.4 Liquid Phase Equations
Liquid continuity equation: evaporator section
The vapor and liquid pressures can be computed as follows:
1 The ideal gas equation of state is utilized for computing the pressure in the vapor Because the vapor
is either saturated or super heated, the ideal gas state equation is reasonably correct and is used sively in the analysis
exten-1ᎏ2
1ᎏ2
∂ᎏ
∂x
∂ᎏ
1ᎏ2
∂ᎏ
∂x
∂ᎏ
l
1ᎏ2
β
lw
ᎏβ
l
1ᎏ2
1ᎏ2
∂T v
ᎏ
∂x
兹3苶ᎏ4
∂u v
ᎏ
∂x
兹3苶ᎏ4
4ᎏ3
∂ᎏ
∂x
兹3苶ᎏ4
∂ᎏ
Trang 62 For the liquid phase the Hagen–Poiseuille equation is used as a first approximation, with the localhydraulic diameter for the wetted portion of the liquid-filled region adjacent to the corners The val-ues of pressure obtained from this first approximation are substituted into the momentum equationsand iterated for spatial convergence.
The initial conditions are
at t ⫽ 0 and for all x
11.2.1.3.6 Area Coefficients in the Computational Model
Figure 11.5 illustrates the geometric configuration of the vapor and liquid flow in the cross-section of themicro heat pipe, along with the meniscus idealized as an arc of a circle at any longitudinal location Thedefinitions of the area coefficients, as derived for this configuration, are given below:
Referring to Figure 11.5, the cross section is an equilateral triangle with φ ⫽ π/3 ⫺ α, and η ⫽ r sin φ.
The total area of the liquid in the cross section is
Where, βl⫽ 3冤兹3苶sin2冢 ⫺ α冣⫹ 0.5 sin 2冢 ⫺ α冣⫺冢π ⫺ α冣冥
ᎏ3
πᎏ3
πᎏ3
σᎏ
r o
D2
H
ᎏ4
∂P l
ᎏ
∂x
Trang 7The total area of interface in length dx is
A i⫽ βi rdx, where β i⫽ 6冢 ⫺ α冣 (11.46)The total wetted perimeter for the three corners ⫽ βlw r,
11.2.2 Testing of Individual Micro Heat Pipes
As fabrication capabilities have developed, experimental investigations on individual micro heat pipeshave been conducted on progressively smaller and smaller devices, beginning with early investigations onwhat now appear to be relatively large micro heat pipes, approximately 3 mm in diameter and progress-ing to micro heat pipes in the 30 m diameter range These investigations have included both steady-stateand transient investigations
11.2.2.1 Steady-State Experimental Investigations
The earliest experimental tests of this type reported in the open literature were conducted by Babin et al.(1990), who evaluated several micro heat pipes approximately 1 mm in external diameter The primarypurposes of this investigation were to determine the accuracy of the previously described steady-state mode-ling techniques, to verify the micro heat pipe concept, and to determine the maximum heat transportcapacity The fabrication techniques used to produce these test articles were developed by Itoh Research andDevelopment Company, Osaka, Japan (Itoh, 1988) As reported previously, a total of four test articles wereevaluated, two each from silver and copper Two of these test pipes were charged with distilled deionizedwater, and the other two were used in an uncharged condition to determine the effect of the vaporization–condensation process on these devices’ overall thermal conductivity Steady-state tests were conducted over
a range of tilt angles to determine the effect of the gravitational body force on the operational tics An electrical resistance heater supplied the heat into the evaporator Heat rejection was achieved throughthe use of a constant temperature ethyl–glycol solution, which flowed over the condenser portion of the heatpipe The axial temperature profile was continuously monitored by five thermocouples bonded to the
characteris-πᎏ3
πᎏ3
d
2
r
FIGURE 11.5 Cross-sectional geometry of the triangular micro heat pipe for determining the area coefficients (Reprinted with permission from Longtin, J.P., Badran, B., and Gerner, F.M [1994] “A One-Dimensional Model of a
Micro Heat Pipe During Steady-State Operation,” ASME J Heat Transfer 116, pp 709–15.)
Trang 8outer surface of the heat pipe using a thermally conductive epoxy Three thermocouples were located onthe evaporator, one on the condenser, and one on the outer surface of the adiabatic section Throughoutthe tests, the heat input was systematically increased and the temperature of the coolant bath adjusted tomaintain a constant adiabatic wall temperature (Babin et al., 1990).
The results of this experiment have been utilized as a basis for comparison with a large number of heatpipe models As previously reported [Peterson et al., 1996], the steady-state model of Babin et al (1990)over-predicted the experimentally determined heat transport capacity at operating temperatures below40°C and under-predicted it at operating temperatures above 60°C These experimental results representedthe first successful operation of a micro heat pipe that utilized the principles outlined in the original con-cept of Cotter (1984) and, as such, paved the way for numerous other investigations and applications.There has been a large amount of experimental research work on micro heat pipes under steady-stateoperation following the early experimental studies reported by Babin et al (1990) Fabricating micro heatpipes as an integral part of silicon wafers provided a means of overcoming the problems imposed by thethermal contact resistance between the heat pipe heat sink and the substrate material, and Peterson et al.(1991) in their first attempt to study the performance of an integral micro heat pipe, compared the tem-perature distributions in a silicon wafer with and without a charged micro heat pipe channel The wafer withthe integral micro heat pipe showed as much as an 11% reduction of the maximum chip temperature,which worked out to a 25% increase in effective thermal conductivity, at a heat flux rate of 4 W/cm2 Moreextensive experimental work and detailed discussions on triangular and rectangular micro heat pipes and
on micro heat pipe arrays fabricated on silicon wafers can be found in Mallik et al (1992) and Peterson
et al (1993) Peterson (1994) further discussed the fabrication, operation, modeling, and testing aspects ofintegral micro heat pipes in silicon Steady-state experiments on a micro heat pipe array fabricated in siliconusing the vapor deposition technique were also reported by Mallik and Peterson (1995)
In an attempt to conduct visualization experiments on micro heat pipes, Chen et al (1992) fabricated aheat transport device by attaching a wire insert to the inner wall of a glass capillary tube, so that capillaryaction is obtained at the corners formed by the two surfaces This was also modeled as a porous medium.The device was highly influenced by gravity, as revealed by comparisons of the experimental and pre-dicted results for maximum heat flow with horizontal and vertical orientations It appears that this devicefunctioned more like a thermosyphon than a capillary driven heat pipe
Experimental studies were performed on triangular grooves fabricated in a copper substrate withmethanol as the working fluid in order to determine the capillary heat transport limit [Ma and Peterson,1996a] A parameter, “the unit effective area heat transport,” was defined for the grooves (qeff⫽ q/Aeff,where Aeff⫽ DH/Le) to be used as a performance index An optimum geometry was found that gave themaximum unit effective area heat transport Further, this maximum depended on the geometricalparameters, namely the tilt angle and the effective length of the heat pipe
Modifying the analytical model for the maximum heat transport capacity of a micro heat pipe developed
by Cotter (1984), a semiempirical correlation was proposed by Ha and Peterson (1998b) The methodused was to compare the results predicted by Cotter’s model with experimental data and then modify themodel to incorporate the effects of the intrusion of the evaporator section into the adiabatic section ofthe heat pipe under near dry-out conditions With the proposed semiempirical model, a better agreementbetween the predicted and experimental results was obtained
Hopkins et al (1999) experimentally determined the maximum heat load for various operating tures of copper–water micro heat pipes These micro heat pipes consisted of trapezoidal or rectangular microgrooves and were positioned in vertical or horizontal orientations The dry-out condition also was studiedexperimentally The effective thermal resistance was found to decrease with an increase in the heat load
tempera-11.2.2.2 Transient Experimental Investigations
While the model developed by Babin et al (1990) was shown to predict the steady-state performance tations and operational characteristics of the trapezoidal heat pipe reasonably well for operating temper-atures between 40 and 60°C, little was known about the transient behavior of these devices As a result,
limi-Wu et al (1991) undertook an experimental investigation of the devices’ transient characteristics This
Trang 9experimental investigation again utilized micro heat pipe test articles developed by Itoh (1988); however,this particular test pipe was designed to fit securely under a ceramic chip carrier and had small fins at thecondenser end of the heat pipe for removal of heat by free or forced convection, as shown in Figure 11.3.Start-up and transient tests were conducted in which the transient response characteristics of the heat pipe
as a function of incremental power increases, tilt angle, and mean operating temperature were measured.Itoh and Polásek (1990a, 1990b), presented the results of an extensive experimental investigation on aseries of micro heat pipes ranging in size and shape from 1 to 3 mm in diameter and 30 to 150 mm in length.The investigation utilized both cross-sectional configurations, similar to those presented previously or aconventional internal wicking structure (Polásek, 1990; Fejfar et al., 1990) The unique aspect of this par-ticular investigation was the use of neutron radiography to determine the distribution of the working fluidwithin the heat pipes [Itoh and Polásek, 1990a; Itoh and Polásek, 1990b; Ikeda, 1990] Using this tech-nique, the amount and distribution of the working fluid and noncondensale gases were observed duringreal time operation along with the boiling and/or reflux flow behavior The results of these tests indicatedseveral important results [Peterson, 1992];
● As is the case for conventional heat pipes, the maximum heat transport capacity is principallydependent upon the mean adiabatic vapor temperature
● Micro heat pipes with smooth inner surfaces were found to be more sensitive to overheating thanthose with grooved capillary systems
● The wall thickness of the individual micro heat pipes had greater effect on the thermal performancethan did the casing material
● The maximum transport capacity of heat pipes utilizing axial channels for return of the liquid tothe evaporator were found to be superior to those utilizing a formal wicking structure
The experimental work on the micro heat pipe array fabricated in silicon using vapor deposition nique [Mallik and Peterson, 1995] was extended to also include the performance under transient condi-tions The results of this study were presented in Peterson and Mallik (1995)
Apart from theoretical and experimental research on individual micro heat pipes, modeling, fabrication,and testing of micro heat pipe arrays of various designs also have been undertaken Significant work onthese subjects is presented in the following sections
11.3.1 Modeling of Heat Pipe Arrays
The initial conceptualization of micro heat pipes by Cotter (1984) envisioned fabricating micro heat pipesdirectly into the semiconductor devices as shown schematically in Figure 11.6 While many of the previouslydiscussed models can be used to predict the performance limitations and operational characteristics of indi-vidual micro heat pipes, it is not clear from the models or analyses how the incorporation of an array of thesedevices might affect the temperature distribution or the resulting thermal performance Mallik et al (1991)
x y z
FIGURE 11.6 Array of micro heat pipes fabricated as an integral part of a silicon wafer.
Trang 10developed a three-dimensional numerical model capable of predicting the thermal performance of an array
of parallel micro heat pipes constructed as an integral part of semiconductor chips similar to that illustrated
in Figure 11.7 In order to determine the potential advantages of this concept, several different thermalloading configurations were modeled and the reductions in the maximum surface temperature, the meanchip temperature, and the maximum temperature gradient across the chip were determined [Peterson, 1994].Although the previous investigations of Babin et al (1990), Wu and Peterson (1991), and Wu et al (1991)indicated that an effective thermal conductivity greater than ten times that of silicon could be achieved, addi-tional analyses were conducted to determine the effect of variations in this value Steady-state analyses wereperformed using a heat pipe array comprised of nineteen parallel heat pipes Using an effective thermal con-ductivity ratio of five, the maximum and mean surface temperatures were 37.69°C and 4.91°C respectively.With an effective thermal conductivity ratio of ten, the maximum and mean surface temperatures were35.20°C and 4.21°C respectively Using an effective thermal conductivity ratio of fifteen, the maximum andmean surface temperatures were 32.67°C and 3.64°C respectively [Peterson, 1994] These results illustrate howthe incorporation of an array of micro heat pipes can reduce the maximum wafer temperature, reduce thetemperature gradient across the wafers, and eliminate localized hot spots In addition, this work high-lighted the significance of incorporating these devices into semiconductor chips, particularly those con-structed in materials with thermal conductivities significantly less than that of silicon, such as gallium arsenide.This work was further extended to determine transient response characteristics of an array of micro heatpipes fabricated into silicon wafers as a substitute for polycrystalline diamond or other highly thermallyconductive heat spreader materials [Mallik and Peterson 1991; Mallik et al 1992] The resulting transientthree-dimensional numerical model was capable of predicting the time dependent temperature distribu-tion occurring within the wafer when given the physical parameters of the wafer and the locations of theheat sources and sinks The model also indicated that significant reductions in the maximum localized wafertemperatures and thermal gradients across the wafer could be obtained through the incorporation of anarray of micro heat pipes Utilizing heat sinks located on the edges of the chip perpendicular to the axis ofthe heat pipes and a cross-sectional area porosity of 1.85%, reductions in the maximum chip temperature
of up to 40% were predicted
FIGURE 11.7 (See color insert following page 2-12 ) Silicon wafer into which an array of micro heat pipes has been
fabricated.
Trang 1111.3.2 Testing of Arrays of Micro Heat Pipes
Peterson et al (1991) fabricated, charged, and tested micro heat pipe arrays incorporated as an integral part ofsemiconductor wafers These tests represented the first successful operation of these devices reported in theopen literature In this investigation, several silicon wafers were fabricated with distributed heat sources onone side and an array of micro heat pipes on the other as illustrated in Figure 11.7 Since that time, a number
of experimental investigations have been conducted to verify the micro heat pipe array concept and determinethe potential advantages of constructing an array of micro heat pipes as an integral part of semiconductordevices [Peterson et al 1993; Peterson 1994] The arrays tested have typically been fabricated in silicon andhave ranged in size from parallel rectangular channels 30 µm wide, 80 µm deep, and 19.75 mm long, machinedinto a silicon wafer 20 mm square and 0.378 mm thick with an interchannel spacing of 500 µm to etched arrays
of triangular channels 120 µm wide and 80 µm deep machined into 20 mm square silicon wafers 0.5 mmthick [Peterson et al 1993] In addition, arrays of micro heat pipes fabricated using a vapor depositionprocess first proposed by Peterson (1990) and illustrated in Figure 11.8 were tested by Mallik et al (1995)
In this work, wafers with arrays of 34 and 66 micro heat pipes were evaluated using an IR thermalimaging system in conjunction with a VHS video recorder These arrays occupied 0.75% and 1.45% ofthe wafer cross-sectional area respectively The wafers with micro heat pipe arrays demonstrated a 30%
to 45% reduction in the thermal time constant when compared to that obtained for plain silicon wafers,which led to a significant reduction in the maximum wafer temperature The experimental results werethen used to validate the transient numerical model described previously [Peterson and Mallik, 1995]
11.3.3 Fabrication of Arrays of Micro Heat Pipes
Considerable information is available on the methods used to fabricate micro heat pipes with hydraulicdiameters on the order of 20 to 150 µm in diameter into silicon or gallium arsenide wafers These early inves-tigations included the use of conventional techniques such as the machining of small channels [Peterson,1988b; Peterson et al., 1991]; the use of directionally dependent etching processes to create rectangular ortriangular shaped channels [Peterson, 1988b; Gerner, 1990; Mallik et al., 1991; Gerner et al., 1992]; or othermore elaborate techniques that utilize a multisource vapor deposition process illustrated in Figure 11.8[Mallik et al., 1991; Weichold et al., 1992] to create an array of long narrow channels of triangular cross-section lined with a thin layer of copper Peterson (1994) has summarized these The earliest fabricated
Metallic layer Square grooves
Step 3 Seal ends and charge
Step 2 Vapor deposit metallic layer
Silicon
Step 1 Machine square grooves Construction process
FIGURE 11.8 Vapor deposition process for fabricating micro heat pipes.
Trang 12arrays were machined into a silicon wafer 2 cm square and 0.378 mm thick, with an interchannel spacing
of 500 µm Somewhat later, Adkins et al (1994) reported on a different fabrication process used for anarray of heat pipes with a segmented vapor space Peterson (1988b), Gerner (1990), Peterson et al (1993),Ramadas et al (1993), and Gerner et al (1994) have described other processes All of these techniques weresimilar in nature and typically utilized conventional photolithography masking techniques coupled with
an orientation dependent etching technique
Perhaps the most important aspects of these devices are the shape and relative areas of the liquid andvapor passages A number of investigations have been directed at the optimization of these grooves Theseinclude investigations by Ha and Peterson (1994), which analytically evaluated the axial dry-out of theevaporating thin liquid film; one by Ha and Peterson (1996), which evaluated the interline heat transfer; andothers that examined other important aspects of the problem [Ha and Peterson 1998a, 1998b; Petersonand Ha, 1998; Ma and Peterson 1998] These studies and others have shown both individual micro heat pipesand arrays of micro heat pipes to be extremely sensitive to flooding [Peterson, 1992] For this reason, severaldifferent charging methods have been developed and described in detail [Duncan and Peterson, 1995].These vary from those that are similar to the methods utilized on larger more conventional heat pipes toone in which the working fluid is added and then the wafer is heated to above the critical temperature ofthe working fluid so that the working fluid is in the supercritical state and exists entirely as a vapor Thearray is then sealed and allowed to cool to below the critical temperature, allowing the vapor to cool andcondense When in the critical state, the working fluid is uniformly distributed throughout the individ-ual micro heat pipes, so the exact charge can be carefully controlled and calculated
11.3.4 Wire Bonded Micro Heat Pipe Arrays
One of the designs that has been developed and evaluated for use in both conventional electronic cations and for advanced spacecraft applications consists of a flexible micro heat pipe array fabricated bysintering an array of aluminum wires between two thin aluminum sheets as shown in Figure 11.9 In thisdesign, the sharp corner regions formed by the junction of the plate and the wires act as the liquid arteries.When made of aluminum with ammonia or acetone as the working fluid, these devices become excellentcandidates for use as flexible radiator panels for long-term spacecraft missions, and they can have a ther-mal conductivity that greatly exceeds the conductivity of an equivalent thickness of any known material
appli-A numerical model combining both conduction and radiation effects to predict the heat transfer formance and temperature distribution of these types of radiator fins in a simulated space environment hasbeen developed [Wang et al., 2001] Three different configurations were analyzed, experimentally evaluated,and the results compared Each of the three configurations were modeled both with and without a workingfluid charge in order to determine the reduction in the maximum temperature, mean temperature, and tem-perature gradient on the radiator surface.Table 11.1 lists the physical specifications of the three micro heatpipe arrays fabricated Acetone was used as the working fluid in both the modeling effort and also in the actualexperimental tests The flexible radiator with the array of micro heat pipes was found to have an effective ther-mal conductivity of more than 20 times that of the uncharged version and 10 times that of a solid material.The results of the preliminary tests conducted on these configurations are shown in Figure 11.10 As indi-cated, the heat transport was proportional to the temperature difference between the evaporator and con-denser; that is, the effective thermal conductivity of the micro heat pipe array was constant with respect tothe temperature From the temperature difference and heat transport obtained as shown in Figure 11.10,the effective conductivity was calculated As illustrated in Figure 11.11, the effective thermal conductivities
per-of micro heat pipe arrays No 1, No 2, and No 3 were 1446.2 W/Km, 521.3 W/Km, and 3023.1 W/Km, tively For the micro heat pipe arrays without any working fluid, the effective conductivities in the x-directionwere 126.3 W/Km, 113.0 W/Km, and 136.2 W/Km respectively Comparison of the predicted and experi-mental results indicated these flexible radiators with the arrays of micro heat pipes have an effective thermalconductivity of between fifteen and twenty times that of the uncharged version This results in a more uni-form temperature distribution that could significantly improve the overall radiation effectiveness, reduce theoverall size, and meet or exceed the baseline design requirements for long-term manned missions to Mars
Trang 13respec-Wang and Peterson (2002a) presented an analysis of wire-bonded micro heat pipe arrays using a dimensional steady state analytical model that incorporated the effects of the liquid–vapor phase interactionsand the variation in the cross-section area The model was used to predict the heat transfer performanceand optimum design parameters An experimental facility was fabricated, and tests were conducted to
one-Wires
Condenser
Al Av.
a
R R
Evaporator
FIGURE 11.9 Flexible wire bonded heat pipe (Reprinted with permission from Wang, Y., Ma, H.B., and Peterson,
G.P (2001) “Investigation of the Temperature Distributions on Radiator Fins with Micro Heat Pipes,” AIAA J.
Thermophysics and Heat Transfer 15(1), pp 42–49.)
TABLE 11.1 Configuration of Micro Heat Pipe Reprinted with Permission from [Wang, Y., Ma, H.B., and Peterson, G.P (2001) “Investigation of the Temperature
Distributions on Radiator Fins with Micro Heat Pipes,” AIAA J Thermophysics and
Heat Transfer 15(1), pp 42–49.]
Prototype
Total dimension (mm) 152 ⫻ 152.4 152 ⫻ 152.4 152 ⫻ 152.4 Thickness of sheet (mm) 0.40 0.40 0.40
Trang 140 40 80 120 160 200 240 280
FIGURE 11.10 (See color insert following page 2-12 ) Temperature difference of micro heat pipe arrays with or
with-out working fluid (Reprinted with permission from Wang, Y., Ma, H.B., and Peterson, G.P (2001) “Investigation of the
Temperature Distributions on Radiator Fins with Micro Heat Pipes,” AIAA J Thermophysics and Heat Transfer 15(1),
pp 42–49.)
0 500 1000 1500 2000 2500 3000 3500
FIGURE 11.11 (See color insert following page 2-12 ) Effective thermal conductivity of micro heat pipe arrays.
(Reprinted with permission from Wang, Y., Ma, H.B., and Peterson, G.P (2001) “Investigation of the Temperature
Distributions on Radiator Fins with Micro Heat Pipes,” AIAA J Thermophysics and Heat Transfer 15(1), pp 42–49.)
Trang 15verify the concept as well as to validate the proposed model The results indicated that the maximum heattransport capacity increased with increases in wire diameter and that the overall value was proportional
to the square of the wire diameter The numerical model indicated that the maximum heat transportcapacity increased with increases in the wire spacing and predicted the existence of an optimal configu-ration for the maximum heat transfer capacity Further optimization studies on a wire-bonded microheat pipe radiator in a radiation environment were reported in Wang and Peterson (2002b) A combinednumerical and experimental investigation was performed in order to optimize the heat transfer per-formance of the radiator The optimal charge volume was found to decrease with increasing heat flux Theoverall maximum heat transport capacity of the radiator was found to be strongly governed by the spacing
of the wires, the length of the radiator, and the radiation capacity of the radiator surface The numericalresults were consistent with experimental results, which indicated that the uniformity of the temperaturedistribution and the radiation efficiency both increased with increasing wire diameter Among the speci-mens tested, the maximum heat transport capacity of 15.2 W was found to exist for radiators utilizing awire diameter of 0.635 mm Comparison of the proposed micro heat pipe radiators with solid conductorsand uncharged versions indicated significant improvements in the temperature uniformity and overall radia-tion efficiency Aluminum–acetone systems of wire-bonded micro heat pipes were tested in this study
A flat heat pipe thermal module for use as a cooling device for mobile computers was analyzed by Petersonand Wang (2003) It consisted of a wire-bonded heat pipe and a fin structure to dissipate heat The tem-perature and heat flux distributions were calculated, and a performance analysis was done using a resis-tance model Effects of the wire diameter, mesh number of the wire configuration, and the tilt angle of theheat pipe on the maximum heat transport capacity were investigated The effect of the air flow rate onthe thermal resistance and the influence of the operating temperature and air flow velocities on the heatdissipation capacity were also studied Larger wire diameters were found to lead to a significant increase
in the maximum heat transport capacity
While arrays of micro heat pipes can significantly improve the effective thermal conductivity of silicon wafersand other conventional heat spreaders, they are of limited value in that they provide heat transfer only alongthe axial direction of the individual heat pipes To overcome this problem, flat plate heat spreaders capable
of distributing heat over a large two-dimensional surface have been proposed by Peterson (1992, 1994) Inthis application, a wicking structure is fabricated in silicon multichip module substrates to promote the distri-bution of the fluid and the vaporization of the working fluid (Figure 11.12) This wick structure is the key ele-ment in these devices, and several methods for wick manufacture have been considered [Peterson et al 1996]
In the most comprehensive investigation of these devices to date, a flat plate micro heat pipe similar to thatdescribed by Peterson et al (1996) was fabricated in silicon multichip module (MCS) substrates 5 mm ⫻
5 mm square [Benson et al 1996a; Benson et al 1996b] These devices, which are illustrated in Figure 11.12,utilized two separate silicon wafers On one of the two wafers, the wick pattern was fabricated leaving
a small region around the perimeter of the wafer unpatterned to allow the package to be hermeticallysealed The other silicon wafer was etched in such a manner that a shallow well was formed corresponding
to the wick area The two pieces were then wafer bonded together along the seal ring Upon completion
of the fabrication, the flat plate micro heat pipe was filled through a small laser drilled port located in onecorner of the wafer Because the entire wicking area was interconnected, the volume of the liquid required tocharge was of sufficient volume that conventional charging techniques could be utilized [Benson et al 1996]
11.4.1 Modeling of Micro Heat Spreaders
Analytical investigations of the performance of these micro heat spreaders or flat plate heat pipes have beenunderway for some time; Benson et al (1996a), Benson et al (1996b), and Peterson (1996) have summarizedthe results These investigations have demonstrated that these devices can provide an effective mechanismfor distributing the thermal load in semiconductor devices and reducing the localized hot spots resulting