Adrian Bejan(Editor), Allan D. Kraus (Editor). Heat transfer Handbok (776115), страница 51
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The joint was formed by Ni 200 surfaces (one flat and lapped and the secondflat and glass bead blasted). The data were obtained by subtracting the theoreticalvalue of hc from the measured values of hj to get the values of hg that appear on theplots. The agreement between the data and the predicted curves is very good.BOOKCOMP, Inc. — John Wiley & Sons / Page 359 / 2nd Proofs / Heat Transfer Handbook / BejanLines: 3952 to 3997———4.09605pt PgVar———Short PagePgEnds: TEX[359], (99)360105ExperimentHeArN2VacuumTheory104Stainless Steel 304 = 4.83 mRp = 14.7 mY/ = 3.02P/He = 1.6 ⫻ 10⫺4HeArN2Vacuumhj (W/m2 .
K)123456789101112131415161718192021222324252627282930313233343536373839404142434445THERMAL SPREADING AND CONTACT RESISTANCES[360], (100)Lines: 3997 to 4013———0.36307pt PgVar103———Normal PagePgEnds: TEX[360], (100)102100101Pg (torr)102103Figure 4.27 Joint conductance model and data for conforming rough stainless steel 304surfaces. (From Song, 1988.)Figure 4.29 shows the experimental data for argon, nitrogen, and helium and thedimensionless theoretical curve for the gap model recast as (Song et al., 1993b)G = 1 + M∗(4.294)whereG=kghg YandM∗ =MαβΛ=YY(4.295)There is excellent agreement between the model and the data over the entire rangeof the gas–gap parameter M ∗ . The joint was formed by very rough conforming NiBOOKCOMP, Inc.
— John Wiley & Sons / Page 360 / 2nd Proofs / Heat Transfer Handbook / BejanJOINT CONDUCTANCE ENHANCEMENT METHODS105ExperimentHeN2Theory104Nickel 200 = 2.32 mP = 0.52 MPaP/He = 1.7 ⫻ 10⫺4(Y/)YDH = 3.6HeN2hg (W/m2 . K)123456789101112131415161718192021222324252627282930313233343536373839404142434445361[361], (101)Lines: 4013 to 4018———0.097pt PgVar103———Normal PagePgEnds: TEX[361], (101)102100101Pg (torr)102103Figure 4.28 Gap conductance model and data for conforming rough Ni 200 surfaces. (FromSong, 1988.)200 surfaces.
The plastic deformation model was used to calculate Y . The points forM ∗ < 0.01 correspond to the high-gas-pressure tests (near 1 atm), and the points forM ∗ > 2 correspond to the low-gas-pressure tests.4.17JOINT CONDUCTANCE ENHANCEMENT METHODSIn many electronics packages the thermal joint conductance across a particular jointmust be improved for the thermal design to meet its performance objectives. If thejoint cannot be made permanent because of servicing or other considerations, the jointBOOKCOMP, Inc. — John Wiley & Sons / Page 361 / 2nd Proofs / Heat Transfer Handbook / Bejan362123456789101112131415161718192021222324252627282930313233343536373839404142434445THERMAL SPREADING AND CONTACT RESISTANCES[362], (102)Lines: 4018 to 4029———4.097pt PgVar———Long PagePgEnds: TEX[362], (102)Figure 4.29 Dimensionless gap conductance model and data for conforming rough Ni 200surfaces.
(From Song, 1988.)conductance must be “enhanced”; that is, it must be improved above the bare jointsituation utilizing one of several known techniques, such as application of thermalinterface materials (TIMs): for example, thermal grease, grease filled with particles(also called paste), oils, and phase-change materials (PCMs). Enhancement of thejoint conductance has also been achieved by the insertion of soft metallic foils into thejoint, or by the use of a relatively soft metallic coating on one or both surfaces. Morerecently, soft nonmetallic materials such as polymers and rubber have been used.One may consult review articles by Fletcher (1972, 1990), Madhusudana andFletcher (1986), Madhusudana (1996), Marotta and Fletcher (1996), Prasher (2001),Savija et al.
(2002a, b), and other pertinent references may be found in these reviews.This section is limited to a few examples where models and data are available.BOOKCOMP, Inc. — John Wiley & Sons / Page 362 / 2nd Proofs / Heat Transfer Handbook / BejanJOINT CONDUCTANCE ENHANCEMENT METHODS1234567891011121314151617181920212223242526272829303132333435363738394041424344454.17.1363Metallic Coatings and FoilsAn effective method for enhancement of joint conductance consists of vapor deposition of a very thin soft metallic layer on the surface of the substrate. The layerthickness is often less than 100 µm; it is in “perfect” thermal and mechanical contactwith the substrate, and its bulk resistance is negligibly small relative to the contactresistance. The thermal resistance at the layer–substrate interface is also negligible.A comprehensive treatment of the theoretical development and experimental verification of the thermomechanical model can be found in Antonetti (1983) and Antonetti and Yovanovich (1983, 1985).
In the following discussion, therefore, onlythose portions of the theory needed to apply the model to a thermal design problemare presented. The general expression for the contact conductance of the coated jointoperating in a vacuum ishc= hcHSH0.93k1 + k 2Ck1 + k2[363], (103)(W/m2 · K)(4.296)where hc is the uncoated contact conductance, HS the microhardness of the softersubstrate, H the effective microhardness of the layer–substrate combination, C aspreading–constriction parameter correction factor that accounts for the heat spreading in the coated substrate, and k1 and k2 the thermal conductivities of the two substrates, respectively.The coated contact conductance relationship consists of the product of three quantities: the uncoated contact conductance hc , the mechanical modification factor (HS /H )0.93 , and the thermal modification factor.
The uncoated (bare) contact conductancemay be determined by means of the conforming, rough surface correlation equationbased on plastic deformation: m 2k k P 0.951 2hc = 1.25σ k1 + k 2 H S(W/m2 · K)(4.297)where HS is the flow pressure (microhardness) of the softer substrate, m the combinedaverage absolute asperity slope, and σ the combined rms surface roughness of thejoint.For a given joint, the only unknowns are the effective microhardness H and thespreading–constriction parameter correction factor C.
Thus, the key to solving coatedcontact problems is the determination of these two quantities.Mechanical Model The substrate microhardness can be obtained from the following approximate relationship (Hegazy, 1985):HS = (12.2 − 3.54HB ) σ −0.26m(GPa)(4.298)which requires the combined surface roughness parameters σ and m and the bulkhardness of the substrate HB . In the correlation equation the units of the joint roughness parameter σ/m are micrometers. For Ni 200 substrates, HB = 1.67 GPa.BOOKCOMP, Inc.
— John Wiley & Sons / Page 363 / 2nd Proofs / Heat Transfer Handbook / BejanLines: 4029 to 4060———2.33809pt PgVar———Long PagePgEnds: TEX[363], (103)364123456789101112131415161718192021222324252627282930313233343536373839404142434445THERMAL SPREADING AND CONTACT RESISTANCESThe effective microhardness must be obtained empirically for the particular layer(coating)–substrate combination under consideration. This requires a series of Vickers microhardness measurements which will result in an effective microhardness plotsimilar to that shown in Fig. 4.30 (e.g., a silver layer on a Ni 200 substrate).The effective Vickers microhardness measurements, denoted H , are plottedagainst the relative indentation depth t/d, where t is the layer thickness and d isthe indentation depth.
The three microhardness regions were correlated asttt+ 1.81HLfor 0 ≤ < 1.0(4.299)1−HSdddtH = 1.81HL − 0.21HL t − 1for 1.0 ≤ ≤ 4.90(4.300)ddtHfor > 4.90(4.301)Ldwhere HS and HL are the substrate and layer microhardness, respectively. The Ni200 substrate microhardness is found to be HS = 2.97 GPa for the joint roughnessparameter values: σ = 4.27 µm and m = 0.236 rad. The Vickers microhardness ofthe silver layer is approximately HL = 40 kg/mm2 = 0.394 GPa.The relative indentation depth is obtained from the following approximate correlation equation (Antonetti and Yovanovich, 1983, 1985) −0.097ttP= 1.04ddHHS + H L2(GPa)For a given value of t and P , the first value of t/d can be computed.
From thethree correlation equations, one can find a new value for H : say, H2 . The newmicrohardness value, H2 , is used to find another value for t/d, which leads to anothervalue, H3 . The procedure is continued until convergence occurs. This usually occurswithin three or four iterations (Antonetti and Yovanovich, 1983, 1985).Thermal Model The spreading–constriction resistance parameter correction factor C is defined as the ratio of the spreading–constriction resistance parameter for asubstrate with a layer to a bare substrate, for the same value of the relative contactspot radius :C=Ψ( , φn )Ψ( )BOOKCOMP, Inc.
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