Fundamental Study Of Heat Pipe Design For High Heat Flux S - Nasa
FUNDAMENTAL STUDY OF HEAT PIPE DESIGN FOR HIGHHEAT FLUX SOURCERyoji Oinuma, Frederick R. BestDepartment of Nuclear Engineering, Texas A&M UniversityABSTRACTAs the demand for high performance small electronic devices has increased, heatremoval from these devices for space use is approaching critical limits. A loop heatpipe(LHP) with coherent micron-porous evaporative wick is suggested to enhance theheat removal performance for the limited mass of space thermal management system.The advantage of LHPs to have accurate micron-order diameter pores which will givelarge evaporative areas compared with conventional heat pipes per unit mass. Also thisdesign make it easy to model the pressure drop and evaporation rate in the wickcompared with the evaluation of the heat pipe performance with a stochastic wick. Thisgives confidence in operating limit calculation as well as the potential for the ultra highcapillary pressure without corresponding pressure penalty such as entrainment of theliquid due to the fast vapor flow. The fabrication of this type heat pipe could beachieved by utilizing lithographic fabrication technology for silicon etching. Thepurpose of this paper is to show the potential of a heat pipe with a coherentmicron-porous evaporative wic k from the view point of the capillary limitation, theboiling limitation, etc. The heat pipe performance is predicted with evaporation modelsand the geometric design of heat pipe is optimized to achieve the maximum heatremoval performance per unit mass.INTRODUCTIONIn recent years, the high thermal performance requirements for integrated circuits incomputers, telecommunications, networking, and power -semiconductor markets aremaking high heat flux( 100W / cm2 ) and improved thermal management critical needs.
Heat pipes are promising devices to remove thermal energy and keep the integratedcircuits at the proper working temperature. The advantage of the heat pipe is in usingphase change phenomena to remove thermal energy since the heat transfer coefficient ofthe phase change is normally 10-1000 times larger than typical heat transfer methodssuch as heat conduction, forced vapor or liquid convection. Even though a heat pipe hasa big potential to remove the thermal energy from a high heat flux source, the heatremoval performance of heat pipes cannot be predicted well since a first principles ofevaporation has not been established.22R pVaporPlate Heat SourceVapor PathConducting PostPorous Wick51Liquid ReservoirLiquid643CondenserFigure 1: Loop Heat Pipe with coherent porous wickSince the porous material used for current heat pipes is usually stochastic structure, it ishard to apply analytical or numerical methods for design optimization. A loop heat pipewith coherent pores integrated to the heat source is considered as a calculation model inthis paper(Fig.1). The advantage of this de sign is to have accurate micron-orderdiameter pores which will give large areas of evaporative thin film more than inconventional heat pipes. Also this design make it easy to calculate pressure drop andevaporation rate in the wick compared with the evaluation of the heat pipe performancewith the stochastic wick, which bring us to the confidence in operating limit andpotentially the ultra high capillary pressures w ithout corresponding pressure penaltysuch as entrainment of the liquid due to the fast vapor flow.
The thermal energy from the heat source conducts through the post to the body ofevaporator and the heat is removed by evaporation of working fluid in pores driven bycapillary forces. The post connecting the heat source and the evaporator is made ofsilicon and the evaporator consists of silicon around the evaporative region and silicondioxide below it to prevent boiling in the liquid reservoir (Figure 2). The diameter ofevaporative pores is micron order and the pitch between pores is a few times larger thanthe pore diameter. The height of the post, thickness of evaporator body is order ofhundreds microns. The fabrication of this type heat pipe could be achieved by utilizingmicro electro mechanical systems (MEMS) fabrication technology which is siliconetching. Also the evaporator will have micro-machine multiple layers to prevent boilingat the bottom of the wick.Plate Heat SourceVapor PathConductingPost (Si)Height of post: hThickness ofBodyEvaporator: t(SiO 2)LiquidCapillaryReservoirPoreFigure 2: Coherent Porous Evaporator (Side View)DEFINITION OF GEOMETRIC PARAMETERSFigure 3 shows the top view of the coherent porous evaporator. The evaporator consistsof a number of unit cells which has a unit length of w, pitch of P and number of pores ofn, pore diameter of d. The width of conducting post connecting between the heat sourceand the evaporator is b. These parameters have relations:
w b nPh (1)3nP2Evaporator Length: LPitch: PNumber of Pores perPost Width: bEvaporative PoreUnit Cell Length: wUnit Cell: nConducting PostFigure 3: Top view of Coherent Porous EvaporatorTo simplify the problem, the following parameters are definedCp P / dCb b / w(2)and parameters will be given again asb nC p d(1 Cb 1)(3)33h nP nC p22In the calculation, n and d are fixed and Cb , C p will be varied to change the geometry.
METHODOVERVIEW OF CALCULATIONSaturation CurveP1P1P2243wickline Pvap Pvap Pliqwick Pliqline5P66TT1 T2Figure 4: Operating Cycle of Loop Heat PipeFigure 4 shows the operating cycle of a Loop Heat Pipe 1. The heavy line is thesaturation curve for the working fluid. Point 1 corresponds to the vapor condition justabove the evaporating meniscus surface and Point 2 corresponds to the bulk vaporcondition in the vapor path. Point 3 corresponds to the vapor pressure at the exit of thevapor path and the Point 4 corresponds to the vapor in the condenser. Point 5corresponds to the liquid state in the condenser and Point 6 corresponds to thesuperheated liquid just below the meniscus interface. The heat pipe will satisfy thefollowing conditions to operate.wicklineP 2 P6 Pliqwick Pvap Pliqline Pvap Pwickliq, Pwickvap(4)are the liquid pressure and vapor pressure drops in the evaporator.line Pliqline, Pvapare the liquid and vapor pressure drops in the transport line. All ofpressure drops are supposed to be a function of a heat flux generated by the heat sourceand geometric parameters such as w, b, n, P in Figure 3. Since the evaporation rate in apore can be determined by pressure and temperature of liquid and vapor near the
interface, the evaporation rate in a pore is a function of these values. If we define theeffective evaporation rate per unit pore area, q evap′ , we will have a relation of′ ( P 2, T 2, P6 ,T 6) N ( w, b , n, P ) A pore ( d ) .q ′source Asource q ′evap(5)′q ′sourceis heat flux generated by the heat source. Asource and Apore are the area of theheat source and a pore. N is the total number of pore in an evaporator and will be givenasN L2nwP(6)Since the area of a pore is a function of the diameter of pore and the number of the poreis a function of geometry parameter of evaporator (Figure 3), N varies due to thegeometry of the evaporator. It will be assumed that the temperature increase(T2-T1) ofthe steam in the vapor path due to the heat transfer from the conducting wall or the heatsource is small so that T1 T 6 T 2 . We set T2 T6 constant. P6 is assumed to beequal to the saturation pressure at the temperature of condenser(T5). This is ba sed onthe fact that Point 5 could not be far from the saturation curve and the pressure dropfrom Point 5 to 6 is not large compared with the saturation pressure at T5. P2 will beobtained for a provided geometry to satisfy equations (4) and (5). This chapter shows′ ) and thethe way to calculate the effective evaporation rate per unit pore area( q evappressure drops(P2-P6) to solve equations (4) and (5).PHENOMENA IN A POREAccording to Potash and Wayner (1972) 2 , in a micron scale pore, a meniscus is formed.The meniscus is divided into three regions: non-evaporating region, thin film region andintrinsic region (Figure 4) . In the non-evaporating region, the intermolecular dispersionforce (Van der Waals force) between liquid molecules and wall molecules are strongenough to prevent evaporation from the liquid -vapor interface. The intermolecular forceis also known as the disjoining pressure. In the thin film region, the intermolecular forceholds the liquid molecules, but not as strong as to prevent evaporation, so evaporation isoccurring. If we assume the heat conduction between the wall and the liquid interface isone dimensional, the interfacial temperature is dependent on the distance between thewall and the interface and liquid properties. The interfacial temperature gives theevaporation rate . The liquid thickness of this region is about the order of nano-meter. In
the intrinsic meniscus region, the surface tension is dominant and the meniscus isformed. The evaporation rate per unit area is relatively smaller than in the thin filmregion.2RpThermal EnergyI : Non-Evaporating RegionII : Transient RegionEvaporationIII : Meniscus RegionFigure 4: Classification of Evaporating RegionGOVERNING EQUATIONThe meniscus profile and the evaporation rate along the meniscus interface can becalculated by solving Navier-Stokes equation (DasGupta, 1993) 3. The momentumequation in Cartesian coordinate in the transition region is given by lubrication theory asµ 2 u Pl y 2 z(7)The boundary conditions are u( R pore) 0 at the wall and u y 0 at the interface.Integrating the momentum equation from y R pore δ (x ) to y R pore yields1 p l 2 y 2 ( R pore δ ( z )) y R pore ( R pore 2δ ( z )) .2 µ z {u ( y) }(8)The mass flow rate at z z will beΓ ρ y Rporey Rpore δ ( z )u ( y) dy .(9)
From the mass balance, the evaporation rate from the interface matches the differentialof the flow ratedΓ m& .dz(10)A evaporation model based on statistical rate theory has been suggested recently byWard(1999) 4. Since this model doesn’t contain a evaporation or condensationcoefficient as in the kinetic theory, we can avoid using an empirical value to evaluatethe evaporation rate. The mass flux based on the statistical rate theory is given asm& M P (Tli ) S S exp exp N A 2 mkTli kk (11), where µ 1 S 1µ 1 exp l v hv kk Tvi Tli Tli Tvi T 1 ν l 1 3 ΘΘl2σA 4 1 vi l Psat (Tli ) 3 . Pv Rcδ Tli Tvi Tli l 1 2 exp (Θ l Tvi ) 1 k Tli T 4 P (T ) q (T ) ln vi sat li ln vib vi Pv Tli q vib (Tli ) 3q vib (T ) l 1exp ( Θ l 2T ).1 exp ( Θ l T )(12)k ( moleculeK / J ) is Boltzmann constant. µ l , µ v (J/molecule ) are the liquid andvapor chemical potential. T li , T vi are the interfacial liquid and vapor temperature. hv(J/molecule ) is the vapor enthalpy. q vib (T ) is the vibrational partion function and Θ lis the vibrational characteristic temperature which are 2290, 5160 and 5360(K)5 forwater. v l ( m 3 / molecule ) is the specific volume of the saturated liquid( m 3 / molecule ).The pressure balance between the liquid and the vapor at the interface is related by theaugmented Young-Laplace equation asPv Pl σK ΠΠ is the disjoining pressure given asΠ AA,A 3δ6π(13)
The curvature for the interface is give as d 2δ 1 1dy 2K .1/2322 dδ 2 dδ 2 ( Rc δ ) 1 1 dz dz (14)Combining equations (7) through (14), we haveδ ′′′′ {}3ρσδ 4 δ ′δ ′′′ ρA δδ ′′ m& (δ ) µδ 2 .ρσδ 5(15)If the heat conduction between the wall and the interface through the thin film is onedimensional, the interface temperature isTli Tw m& h fg δkl.(16)The procedure to obtain the thickness of the film and the evaporation rate is as follows:1. Determine the non-evaporating film thickness for m& 0 .2. Determine the film thickness at the next vertical location ( z k 1 z k z ) by solvingequation (15) with fourth-order Runge-Kutta method.3. By using the determined film thickness , obtain the evaporation.4. Repeat 2 and 3 until the thin film region ends.5. Determine the meniscus profile by the hemi-spherical shapeIn the non-evaporation area, the temperature at the interface is equal to the walltemperature ( Tli Tw ). The total evaporation rate per a pore is kk 1Rc z m& ( z ) m& ( z ) Qtotal h fg (Tli )(17) .k 1k2 δ δ k cos a tan z If the total number of pores in evaporator is equal to N, the evaporation rate per unitevaporation area isN′′ Qtotal, N NApore .qevapn 1(18)
PRESSURE DROPSLiquid Pressure Drop in the evaporatorThe liquid is sucked due to the capillary pressure of pore from the bottom liquidreservoir to the top of the pore. To compensate the loss by the evaporation, the massflow rate of the liquid in the pore should be balanced to the evaporation rate. The liquidpressure drop of the capillary tube in the evaporator for laminar flow is Pliquid fV p2tρld2(19)Re ρ l V pdµ(20).The mass flow rate in a unit cell of the evaporator is given asq ′sourceLw h fg m& cell .(21)Since the number of pores in a unit cell isn L (w b ).P2(22)Form the relationship between the mass flow rate per unit cell and one per pore, themass flow in the pore is shown asm& cell nm& pore Lw bL m& pore 2 P 1(23)′ LWq ′sourceP 2 q ′sourceLw .h fg( w b ) h fgThe velocity in a pore becomesVp 4m&pρ lπ d 2 ′ wq ′source4P 2.2ρ l πd (w b ) h fg(24)Reynolds’s number is also deformed toRe ′ w′ wρl dq ′source4 P 2 q ′source4P 2 .2µ ρ l πd ( w b ) h fgµ l πd ( w b )h fgFor laminar flow, the friction factor is(25)
f 64.Re(26)Substituting from equation (24) to (19), the liquid pressure drop isV p264 t32 µ lP 2 wt′ . Pliquid ρl L q ′sourceRe d2ρ l h fg π d 4 ( w b )(27)Vapor pressure drop in the evaporatorAs shown in Figure 2, the cross sectional shape of the vapor path in the evaporator partis triangle, which is constrained due to the current lithographic technology. The flowrate is given asm& v ρ vVv A ρ vV vw bh.2(28)Therefore, the vapor velocity isVv &v&′ Lwmmq ′source22 v .ρ v A ρ v ( w b )h ρ v (w b )h h fg(29)It will be checked whether the vapor velocity will exceed the speed of sound or notwhen the maximum heat removal ability is determined. If it exceed, the vapor velocityis set to the sound of speed and the maximum heat removal ability of the evaporator iscalculated with it.The friction factor for the equilateral triangle (White, 1991) 5 isCf 13 .333 µ v ρ v ( w b )h h fg13 .33313 .333 Re Dhρ Vv Dh µ vρ v Dh2q ′sourceLw(30), whereDh a3 2h3(31)Actually, the some vapor is generated at the middle of evaporator and others aregenerated near the exit of the vapor path and the pressure drop is dependent on thelocation where the vapor is generated. Since we want to know the performancelimitation due to the pressure drop and the sonic limitation, the maximum pressure dropshould be considered to evaluate the heat pipe performance. The vapor generated in themiddle of the evaporator should be experienced the maximum pressure drop and we will
calculate it. The path length for this vapor isL 2 until the exit and the hydraulicdiameter for the equilateral triangle is given as Dh a3 2h 3By using above equations, the vapor pressure drop is given as Pvapor 4C f22L 2 Vv51 .96 µ v L wρv K q ′sourceDh2h 4 ρ v h fgρ VDRe V v hµv.(31)Vapor and Liquid Pressure Drop in Transport LineThe vapor and liquid pressure drop in the transport line are given asline Pvap 32 µv l′ ,q ′sourceDv4 ρ vπh fg(32) Pliqline 32 µ l l′ .q ′sourceDlv4 ρ l πh fg(33)LIMITATION OF HEAT PIPE PERFORMANCEThere are some limits to control the heat transfer of heat pipes (Faghri 1995)1: Capillarylimitation, Sonic Limitation, Boiling Limitation, Viscous Limitation, EntrainmentLimitation. These give information of the heat transfer limit due to the parameters sucha pore diameter, a pitch between pores, number of pores between posts, thermophysicalproperties of working fluid (Figure 3).For instance, the total pressure drop in the system is supposed to be lower than thecapillary pressure to make the heat pipe work. The total pressure drop in the system isgiven by the sum of the pressure drop of liquid in pore, vapor in the exiting path overthe evaporator, liquid and vapor transportation line to or from the condenser.wickline Pcap Pliqwick Pvap Pliqline Pvap,(34)If these pressure drops are expressed in geometric and thermophysical parameters ofworking fluid stated above, the equation (34) is expressed as
2σq ′source r 1 32 µl P 2 wt51 .96 µ v L2 w32 µ l32 µ l 4 v 4 l , 44ρ v h fg Dv ρ v πh fg Dl ρ l πh fg h ρ l h fg πd ( w b )where w nP b .(35)µ l and µ v are the liquid and vapor viscosities,P is the pitch between pores, ρ land ρ v are the liquid and vapor densities, d is the diameter of pore, Dl and Dvare the pipe diameter in the liquid and vapor transport lines, b and h are the widthand height of the conducting post, l is the length of transport line, L is the horizontallength of evaporator, n is the number of pores between conducting posts. In the similarway for other limitations, the heat transfer limit will be calculated with theseparameters.TEMPERATURE DIFFERENCE BETWEEN HEAT SOUCE AND EVAPORATORSince the shape of vapor path is the right triangle, the height(h) can be determined ifother parameters such as P, n, d, b are known. Therefore, the shape of the conductingpost will be determined as well(Figure 2 and 3). The temperature difference betweenheat source and evaporator is given as′ (b T wall 0 .5q ′source3 3b 2 3h . ln 3b3 k wall L 2h)(36)RESULTGEOMETRY AND ASSUMPTIONSWe assume that we want to design the loop heat pipe which can remove the thermalenergy from a heat source which generates a uniform heat flux and has the size of 1cmby 1cm, thus L 1cm. The evaporative pore diameter(d) is 10µm and the working fluidis water. The number of pores per unit cell(n) is set to 10. The thickness of theevaporator(t) is 200µm. Pitch between pores will be changed from P 1.1d toP 6dand the width of conducting post(b) varies between b 0 .01w and
b 0.09w . T2 is set to from 323.15 to 373.15K and P6 is assumed to be equal to thesaturation pressure at 300K( 4200 Pa ). To simplify the problem, the temperature isuniform for the horizontal direction, the thermal contact resistances at the connectionbetween the heat source and the conducting post or between the conducting post and theevaporator are ignored. The heat loss from the heat source by the radiation andconvection is ignored also.EVAPORATION AND MENISCUS PROFILE IN A POREThe evaporation rate profiles along the axial position in a pore were calculated. Figure 5shows the profile of the evaporation rate for the pore diameter of 10µm at T6 373.15Kand Pv 9.0 10 4 Pa.6.00Evaporation RateMeniscus .001.002.003.004.005.006.00Position( µm)Figure 5: Profile of Evaporation Rate and Meniscus(d 1.0e -5m,T6 373.15K, Pv 9.0e4Pa)Profile(µm)Evaporation Rate(kg/m2/s)25.0
Heat Removal Capability per unit pore area (W/cm2 )25002000T6 373.15KT6 363.15KT6 353.15KT6 343.15KT6 333.15KT6 323.15K1500100050000.02.0e 44.0e 46.0e 48.0e 41.0e 51.2e 5Vapor Pressure(Pa)Figure 6: Heat Removal Capability per Pore Area(d 1.0e -5m)Based on the calculation of evaporation rate in a pore, the heat removal capability in apore is determined by using equations (17) and (18) and the results are shown on Figure′6 for several temperatures. Now we go back to equations (4), (5) and find q ′sourcetosatisfy these equations. The results for several geometries are shown for T6 373.15 andT6 363.15K. Both figures show that the maximum heat flux is given at Cp(P/d) 2.1′and Cb(b/w) 0.01. In addition, we will find in both figures that q ′sourceincreases as Cbdecreases. This is reasonable as Cb is smaller, the vapor path is relatively larger, whichcause to decrease the pressure drop. However, if the width of the conducting post arereduced too much, the temperature difference between the heat source and theevaporator will be large and the heat source temperature may exceed the limit.
2402201801601400.101200.08100800.0660400.04Cb ( b/w)q"source (W2/cm )200204060801001201401601802002202402050.024Cp( P32/d)′ ) to satisfy the operating condition for a givenFigure 7: Heat Flux ( q ′sourcegeometry(T1 T6 373.15K and P6 Psat(T5 300K))Usually thermal analysis requires designing a cooling system to keep the limittemperature of the heat source. For instance, the computer chips are required to sustainbelow the operating temperature and it is useless to design to exceed the limittemperature. Figure 9 shows the heat removal capability and the heat sourcetemperature. If there is a heat source which has the limit temperature of 373K andgenerate the heat flux of 100W/cm2, this heat pipe may satisfy these limitations.Since our loop heat pipe system is operated only by the capillary force in the evaporator,the total pressure drop in the system cannot exceed the capillary pressure. Thecomparison between the total pressure drop and the capillary force are shown in Figure10. The total pressure drops do not exceed the capillary pressure. The vapor pressuredrop in evaporator is dominant and the liquid pressure drop is much lower than the
saturation pressure at T5 ( 4200 Pa ), which supports the assumption that the pressureat Point 5 is close to the pressure at Point 6.1801402)q"source (W/cm1601200.10100600.06400.04Cb ( b/w)0.08802054Cp( P/d)204060801001201401601800.0232′ ) to satisfy the operating condition for a givenFigure 8: Heat Flux ( q ′sourcegeometry(T1 T6 363.15K and P6 Psat(T5 300K))
q" sourceSource Temperature4003002002q"source (W/cm ) or Source Temperature(K)5001000320330340350360370380T6 (K)′ ) and Heat Source Temperature for d 1.0e-5 mFigure 9: Heat Flux ( q ′source(Cb 0.01, Cp 2.1, P6 Psat(T5 5.010.050005.00Pressure Drop for Both Liquid andVapor in Transport Line (Pa)Vapor Pressure Drop in Evaporator orCapillary Pressure (Pa)30000Total Pressure DropVapor Pressure Drop inEvaporatorCapillary PressureLiquid Pressure Drop inPoreLiquid Pressure Drop inTransport LineVapor Pressure Drop inTransport Line0.0320340360380T6 (K)Figure 10: Total Pressure Drop and Capillary Pressure for d 1.0e -5 m
CONCLUSIONA loop heat pipe(LHP) with coherent micron-porous evaporative w ick is suggested toenhance the heat removal performance and it is demonstrated that this design couldachieve the high heat removal capability( 100W/cm2) with keeping the reasonable heatsource temperature( 373.15K) and satisfy the pressure limitation due to the pressuredrop. The optimized geometric parameters can be found and the maximum heat flux isgiven at Cp(P/d) 2.1 and Cb(b/w) 0.01 for d 1.0 10 5 m and n 10. In this paper,there are several assumptions which may not match the real condition. The mostimportant things are that the temperature is uniform in evaporator. As far as our briefestimation with computational fluid dynamics calculation, the temperature across theevaporator varies and the evaporation rate of pores close to the conducting wall ishigher than pores far from the conducting post. Also there are some unchangedgeometric parameters such as pore diameter and number of pores in a unit cell becausethese parameters are strongly related to this problem and we avoid to discuss in thispaper. In future, these things will be discussed in detail.AKNOWLEDGEMENTSThe authors would like to acknowledge funding for this project supplied by the NASACommercial Space Center, Center for Space Power within the Texas EngineeringExperimental Station at Texas A&M University.NOMENCLATUREAHamaker constant (J)bwidth of conducting post (m)CpP/dCbb/wdpore diameter (m)Dl , Dv pipe diameter in transport line between evaporator and condenserffriction factorhheight of conducting wall (m)
h fglatent heat (J/kg)hvvapor enthalpy (J/kg)kBoltzmann constant (molecule K / J)klthermal conductivity for working liquid (W/mK)k wallthermal conductivity (W/mK)lslit length (m)Mmolecular weight (kg)nnumber of pores per unit cellNtotal number of pores in an evaporatorNAAvogadro’s number (1/mol)Ppitch between pores or slits (m)Plbulk liquid pressure (P a)P liliquid pressure at interface (Pa)PVbulk vapor pressure (Pa)P Viq ′evapvapor pressure at interface (Pa)evaporation rate per unit horizontal pore area (W/ m2)qtataltotal thermal energy from the heat source (W)q ′sourcethermal density of heat source (W/m2)Qpartial evaporation rate (W)Q totaltotal evaporation rate per pore or slit (W/pore )R gasUniversal gas constant (J/kg mol K)R porepore radius or half length of slit width (m)Senthoropy (J/kgT)T litemperature at the interface of liquid side (K)Twwall temperature (K)TVvapor temperature (K)T Vivlvapor temperature at interface (K)specific volume of liquid (m 3/kg)Vvelocity (m/s)wlength per unit cell (m)yradial coordinate (m)zaxial coordinate (m)
Γmass flow rate (kg/m)δfilm Thickness (m) PPressure Drop (Pa) TTemperature Difference (K) zdistance between nodes for axial directionµlliquid chemical potential (J/kg/molecule) or liquid viscosity (Pa s)µvvapor chemical potential (J/kg/molecule) or vapor viscosity (Pa s)νkinematic viscosity (m2/s)Πdisjoining pressure (Pa)σsurface tension (N/m )θcontact angle (Degree)Superscriptionskindex of z positionlinetransport line between evaporator and condenserwickwickSubscriptionscellunit celll or liqliquidliliquid interfacep or pore poresatsaturation conditionsource heat sourcev or vap vaporvivapor interfacew or wall wall saturation condition for flat interface
REFERENCES1. Faghri, A, Heat Pipe Science and Technology, Washington, Taylor & Francis,(1995).2. Potash, M., Jr. and Wayner, P. C., Jr., “Evaporation from a Two-DimensionalExtended Meniscus”, International Journal of Heat and Mass Transfer 15,1851-1863 (1972).3. DasGupta, S., Schonberg, J. A., Kim, I. Y. and Wayner, P. C., Jr., “Use of theAugmented Young-Laplace Equation to Model Equilibrium and EvaporatingExtended Menisci”, Journal of Colloid and Interface Science 157 , 332-342 (1993).4. Ward, C. A., Fang G., “Expression for predicting liquid evaporation flux: Statisticalrate theory approach”, Physical Review E 59, 429-440 (1999).5. Carey, P. V., Statistical Thermodynamics and Mircoscale Thermophysics,Cambridge(U.K.), Cambridge University Press, (1999).6. White, M. F., Viscous Fluid Flow, New York, McGraw-Hill, Inc, (1991) .
the phase change is normally 10-1000 times larger than typical heat transfer methods such as heat conduction, forced vapor or liquid convection. Even though a heat pipe has a big potential to remove the thermal energy from a high heat flux source, the heat removal performance of heat pipes cannot be predicted well since a first principles of
Design.4 PE Pipe Systems PE Pipe Systems PE Pipe Systems PE Pipe Systems PE Pipe Systems PE Pipe Systems PE Pipe Systems design Pipe Dimensions Table 4.2 PE Pipe Dimensions AS/NZS 4130 Nominal Size DN SDR 41 SDR 33 SDR 26 SDR 21 SDR 17 SDR 13.6 SDR 11 SDR 9 SDR 7.4 Min. Wall Thickness (mm) Mean I.D. (mm) Min. Wall Thickness (mm) Mean I.D. (mm)
Road crossing with casing pipe Carbon Steel and FRP, carrier pipe pre-insulated Carbon Steel and FRP. TECHNICAL DESCRIPTION Carrier Pipe: Carbon Steel, FRP Size of Carrier Pipe: DN 1200mm CS pipe - DN 750mm FRP pipe (pre-insulated) Casing Pipe: FRP Size of Casing Pipe: FRP casing pipe I.D. 1520mm, FRP casing pipe size I.D.
1. CUT THE PIPE Cut the pipe using a pipe cutter, making a perpendicular cut and cleaning the pipe end from grease and pipe chips. Fit the plastic ring on the pipe and make sure the pipe is flushed with the upper edge of the ring. 2. PLACE THE RING OVER THE PIPE Insert the pipe into the ring until the pipe reaches the safety stop which exists
2.12 Two-shells pass and two-tubes pass heat exchanger 14 2.13 Spiral tube heat exchanger 15 2.14 Compact heat exchanger (unmixed) 16 2.15 Compact heat exchanger (mixed) 16 2.16 Flat plate heat exchanger 17 2.17 Hairpin heat exchanger 18 2.18 Heat transfer of double pipe heat exchanger 19 3.1 Project Flow 25 3.2 Double pipe heat exchanger .
Direct transfer type heat exchanger :- In direct type heat exchanger both the fluids could not come into contact with each other but the transfer of heat occurs through the pipe wall of separation. Examples:- 1. Concentric type heat exchanger 2. Economiser 3. Super heater 4. Double pipe heat exchanger 5. Pipe in pipe heat exchanger cold2 fluid h 1
British Standard BS3897 Parts I, II and III Pipe Supports. 2. Definitions To help with the understanding of pipe supports, below are some definitions. (1) Pipe Clamp: A bolted pipe attachment which clamps around the pipe to connect the pipe to the remainder of a pipe hanger assembly. (2) 3 Bolt Pipe
HEAT PIPE A very popular and efficient style of heat pipes applied to air conditioning and dehumidifiers is the wrap around configuration to be mounted around the DX or chill water cooling coil. HEAT PIPE DEHUMIDIFICATION FIGURE 5. WRAP AROUND HEAT PIPE The heat pipes can be
ALBERT WOODFOX . CIVIL ACTION NO. 06-789-JJB-RLB . VERSUS . BURL CAIN, WARDEN OF THE LOUISIANA . STATE PENITENTIARY, ET AL. RULING . Before this Court is the pending Motion (doc. 279) for Rule 23(c) release of Petitioner, Albert Woodfox. Briefs were filed in response to this motion and were considered by this Court. Subsequently, a motion hearing on this matter was held before this Court on .
