Adrian Bejan(Editor), Allan D. Kraus (Editor). Heat transfer Handbok (776115), страница 78
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— John Wiley & Sons / Page 511 / 2nd Proofs / Heat Transfer Handbook / Bejan———Normal PagePgEnds: TEX[511], (73)α−0.02In the turbulent range (Re ≤ Re∗ + 1000),−0.364.71225pt PgVar(6.170)(6.171)512123456789101112131415161718192021222324252627282930313233343536373839404142434445FORCED CONVECTION: EXTERNAL FLOWS1.328(Re )1/2b=t+Re =(6.172)Uc ν(6.173)The parameter α is the aspect ratio. α = s/W , where W is the strip width.• Flush-mounted heat sources (Section 6.6.1):Nu = 0.486Pe0.53sesx0.71 kskf0.057(6.174)For the rectangular patch,0.63 2sP s 0.180.480.60Pec2xs + s2ANu =0.70 2sP s 0.07 0.43Pe0.52c2xs + s2Aksub=1kfksub= 10kf[512], (74)(6.175)(6.176)———Normal PagePgEnds: TEXU0 (sx + se )αA/P is the source surface area/perimeter ratio.
The foregoing correlations arevalid for103 ≤ Pec ≤ 1055≤xs + s /2≤ 150s0.2 ≤ws≤5sIn the foregoing, ws is the heat source height, P its length, and Pw its width. Thechannel width is W = 12 mm and the height H can vary from 7 to 30 mm. Theheat source dimensions covered in the experiments are P = 12 mm, Ph = 4, 8,and 12 mm, H − Ph = 3, 8, and 12 mm, and Ps = 12 mm.• Isolated blocks (Section 6.6.3):Nu = 0.150Re0.612 (A∗ )−0.455HP0.727(6.178)where Nu = h̄P /k, h̄ is the average heat transfer coefficient, and As is the heattransfer area,As = 2Ph Pw + P Pw + 2Ph PT̄s is the average surface temperature and T∞ is the stream temperature. TheReynolds number is defined as Re = UDh /ν, where U is the average channelBOOKCOMP, Inc. — John Wiley & Sons / Page 512 / 2nd Proofs / Heat Transfer Handbook / Bejan———0.49246pt PgVarHere Nu is as defined for the two-dimensional strip,Pec =Lines: 3190 to 3241[512], (74)SUMMARY OF HEAT TRANSFER CORRELATIONS123456789101112131415161718192021222324252627282930313233343536373839404142434445513velocity upstream of the heat source, DH is the channel hydraulic diameter ata section unobstructed by the heat source, and ν is the fluid (air) kinematicviscosity.
The fraction of the channel open to flow isA∗ = 1 −Pw /WPh /HEquation (6.178) is valid for1500 ≤ Re ≤ 1040.12 ≤0.33 ≤Pw≤ 1.00WPh≤ 1.00P0.583 ≤H≤ 2.50P[513], (75)A realistic error bound is 5%.• Block array (Section 6.6.4):NuP = 0.348Re0.6P(6.182)———where the characteristic length for both Nu and Re is the streamwise length ofthe block, P .• Pin fin heat sinks (Section 6.6.6): Two correlations are given:0.574Nu = 7.12 × 10−4 C∆p a 0.223 p 1.72LLines: 3241 to 3305d0.65236pt PgVar———Normal Page* PgEnds: Eject(6.185)[513], (75)where inC∆p =ρL3 ∆pµ2µ is the dynamic viscosity of the air.
Equation (6.185) was derived from the datafor 5 × 106 < C∆p < 1.5 × 108 :Nu = 3.2 × 10−6 CP0.520W a −0.205 p 0.89Ld(6.186)whereCPW =ρ2 LPwµ3covers a range of 1011 to 1013 .• Single round submerged jet impinging on an isothermal target surface (Section6.7.2):NuD H,f1 (Re)=G(6.190)r DPr0.42BOOKCOMP, Inc.
— John Wiley & Sons / Page 513 / 2nd Proofs / Heat Transfer Handbook / Bejan514123456789101112131415161718192021222324252627282930313233343536373839404142434445FORCED CONVECTION: EXTERNAL FLOWSwheref1 (Re) = 2Re1/2 (1 + 0.005Re0.55 )1/2G=(6.191a)D1 − 1.1(D/r)r 1 + 0.1[(H /D) − 6](D/r)(6.191b)The range of applicability of the foregoing is2000 ≤ Re ≤ 4 × 1052≤H≤ 12D2.5 ≤r≤ 7.5D0.004 ≤ Ar ≤ 0.04• Single submerged slot jet impinging on an isothermal target surface (Section6.7.2):[514], (76)mNu3.06Re=0.42(x/W ) + (H /W ) + 2.78Pr(6.193)Lines: 3305 to 3360———where x H 1.33m = 0.695 −+ 3.06+2W2W1.58235pt PgVar−1(6.194)———Normal Page* PgEnds: EjectThe range of applicability is3000 ≤ Re ≤ 9 × 1044≤H≤ 20W4≤[514], (76)x≤ 50W• Array of round submerged jets impinging on an isothermal target surface (Section 6.7.2):NuHH=KA,,,GAf2 (Re)rrDDPr0.42(6.195)wheref2 (Re) = 0.5Re2/3K = 1 +(6.196a) −0.056H /D1/20.6/Ar(6.196b)and G is given by eq.
(1.191b). The range of validity of the foregoing is2000 ≤ Re ≤ 1052≤H≤ 12DBOOKCOMP, Inc. — John Wiley & Sons / Page 514 / 2nd Proofs / Heat Transfer Handbook / Bejan2.5 ≤r≤ 7.5D0.004 ≤ Ar ≤ 0.04NOMENCLATURE123456789101112131415161718192021222324252627282930313233343536373839404142434445515• Array of submerged slot jets impinging on an isothermal target surface (Section6.7.2):Nu2 3/4= Ar,03Pr0.422ReAr /Ar,0 + Ar,0 /Ar2/3(6.197)whereAr,0h= 60 + 4−22W2 −1/2(6.198)with a range of validity of1500 ≤ Re ≤ 4 × 1042≤H≤ 80W[515], (77)0.008 ≤ Ar ≤ 2.5Ar,0• Single round free surface jet impinging on a square isothermal target surface(Section 6.7.2):NuLhLh= C1 · RemAr + C2 · RenL∗ ∗ (1 − Ar )Di0.4DiLPr(6.202)Ar =Roman Letter SymbolsAconstant or correlation constant, dimensionlessPrandtl number–dependent constant, dimensionlesssource surface area, m2Assurface area, m2ATtotal heat sink surface area, m2∗Afraction of channel cross section open to flow, m2flow area (aligned tube arrangement), m2A1BOOKCOMP, Inc.
— John Wiley & Sons / Page 515 / 2nd Proofs / Heat Transfer Handbook / Bejan———Normal PagePgEnds: TEX[515], (77)(6.201)These data have been found to be best correlated in the range 1000 ≤ ReDn ≤51,000 for C1 = 0.516, C2 = 0.491, and n = 0.532, where the fluid propertiesare evaluated at the mean of the surface and ambient fluid temperature.NOMENCLATURE———0.43257pt PgVarwhereπDi24L2h√0.5( 2 Lh − Di ) + 0.5(Lh − Di )∗L =2Lines: 3360 to 3613516123456789101112131415161718192021222324252627282930313233343536373839404142434445A2aBbb(x)CC∆pCPwC̄Cfc(x)cpDDhDHdd(x)dhEcFF̄ff (η)GHhh̄hadhavhLhTii(i,j )jFORCED CONVECTION: EXTERNAL FLOWSflow area (staggered tube arrangement), m2sphere radius, mfin height, mcorrelation constant, dimensionlessparameter defined by eq.
(6.172), dimensionlesssimilarity function, dimensionlessratio of eddy to turbulent diffusivity, dimensionlessconstant or correlation constant, dimensionlesscoefficient in eq. (6.185), dimensionlesscoefficient in eq. (6.186), dimensionlesscoefficient in free stream velocity definition, dimensionlessfriction coefficient, dimensionlesssimilarity function, dimensionlessspecific heat, J/kg · Ksubstantial derivative, dimensionlesscylinder or sphere diameter, mround jet diameter, mhydraulic diameter, mchannel hydraulic diameter, mpin diameter, mtube diameter, msimilarity function, dimensionlesshydraulic diameter, mEckert number, dimensionlessfunction, dimensionlessPrandtl number, dimensionlessfriction factor, dimensionlessstream function, dimensionlessparameter defined by eq.
(6.131), dimensionlessenvelope height, mlocation outside the boundary layer, mchannel height (plate spacing), mheight, mheat transfer coefficient, W/m2 · Kmean heat transfer coefficient, W/m2 · Kadiabatic heat transfer coefficient, W/m2 · Kaverage heat transfer coefficient, W/m2 · Kheat transfer coefficient for laminar boundary layer, W/m2 · Kheat transfer coefficient for turbulent boundary layer, W/m2 · Kunit vector in x-coordinate direction, dimensionlessstep counter, dimensionlessrow counter, dimensionlessrow and column index, dimensionlesscolumn counter, dimensionlessColburn heat transfer factor, dimensionlessBOOKCOMP, Inc. — John Wiley & Sons / Page 516 / 2nd Proofs / Heat Transfer Handbook / Bejan[516], (78)Lines: 3613 to 3613———0.87755pt PgVar———Normal PagePgEnds: TEX[516], (78)NOMENCLATURE123456789101112131415161718192021222324252627282930313233343536373839404142434445j (x)jKk∗kplatekfksksubkLLcore12smNNLNuNuNuDNuDNuLNuxnOPPhPPWPwPePec517similarity function, dimensionlessunit vector in y-coordinate direction, dimensionlessflow index, dimensionlessthermal conductivity, W/m · Kplate/fluid thermal conductivity ratio, W/m · Kfluid thermal conductivity, W/m · Kmean roughness length scale, dimensionlesssubstrate thermal conductivity, W/m · Kunit vector in z coordinate direction, dimensionlessenvelope length, mlength scale factor, mlength of heat sink, mlength in streamwise direction, mcore length, mplate length, mcylinder length, mmixing length, mspacing between plates, mleading edge to first block spacing, mlast block to trailing edge spacing, mheat source length, mexponent, dimensionlessconstant, dimensionlessexponent, dimensionlessnumber of tube rows, dimensionlessNusselt number, dimensionlessmean or average Nusselt number, dimensionlessNusselt number based on diameter, dimensionlessaverage Nusselt number based on diameter, dimensionlessNusselt number based on length, dimensionlessNusselt number based on diameter, dimensionlessexponent, dimensionlessnumber of pins, dimensionlessnumber of plates in stack, dimensionlessorder, dimensionlessperimeter, mheight of block, mheat source height, mheat source length, mlength of block, mfan power, Wwidth of block, mheat source widthPéclet number, dimensionlessPéclet number used in eqs.
(6.175) and (6.176), dimensionlessBOOKCOMP, Inc. — John Wiley & Sons / Page 517 / 2nd Proofs / Heat Transfer Handbook / Bejan[517], (79)Lines: 3613 to 3613———0.39821pt PgVar———Normal PagePgEnds: TEX[517], (79)518123456789101112131415161718192021222324252627282930313233343536373839404142434445FORCED CONVECTION: EXTERNAL FLOWSPrPrTpp+p̄p∗pmQQAQBqqAqBq qmq q(i,j )RReRe∗bReDReD,maxRekReLReRePhRePReTRexRe∗rrcr0SSDSLSTStStkPrandtl number, dimensionlessturbulent Prandtl number, dimensionlesspressure, N/m2fin pitch, mnormalized pressure, N/m2mean or average pressure, N/m2normalized pressure, N/m2motion pressure, N/m2total heat generated, Wheat sink dissipation, Wheater power input, Wdirect heat transfer component, Wconjugate heat transfer component through substrate, Wexponent, dimensionlessheat dissipation, block A, Wheat dissipation, block B, Wheat flux, W/m2mean heat flux, W/m2volumetric heat generation, W/m3rate of heat dissipation by block (i,j ) in the array, Wthermal resistance, K/WReynolds number, dimensionlessReynolds number defined by eq.
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