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Heat Transfer Handbook part 20

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Figure 3.7 Radial conduction through a hollow cylinder.. (3.71) and the heat flow. ln (r 2 /r 1 ) (3.72). 3.4.3 Hollow Sphere. The description pertaining to the hollow cylinder also applies to the hollow sphere ofFig. Figure 3.8 Radial conduction through a hollow sphere.. T s,2 (3.74) The expressions for the temperature distribution and heat flow are. (3.75) q...

Heat Transfer Handbook part 21

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Normal Page. ln(r 2 /r Ifthe inside and outside surfaces are cooled by convection, the inside with fluid at T ∞,1 with heat transfer coefficient h 2 , the overall energy balance gives. (3.111) and for the case of T s,1 = T s,2 , eq. 192 CONDUCTION HEAT TRANSFER. Normal Page PgEnds: TEX dT. T s (3.114) The temperature...

Heat Transfer Handbook part 22

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(3.170) and (3.171), the last terms can be evaluated using eqs. and (3.123), respectively.. (3.170) and (3.171) require a numerical approach for their solutions, it is convenient to recast them in dimensionless form as. N 1 = hL/k for the plane wall, N 1 = hr 0 /k for the cylinder and sphere, N 2 = σT ∞ 3 L/k...

Heat Transfer Handbook part 23

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3.19a and let the fin radiate to free space at 0 K. The differential equation governing the temperature in the fin is. where B and B u are complete and incomplete beta functions discussed in Section 3.3.3, u = (T t /T ) 5 and T t is the unknown tip temperature. (3.212) and (3.213) when the surface heat dissipation...

Heat Transfer Handbook part 24

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Each subanaly- sis can then be solved using the method ofseparation ofthe variables, and the sum of the solutions to the two subanalyses will provide the solution to the overall problem.. 3.32, and the two solutions can be obtained from eq. (3.248) with appropriate adjustment to account for the definition of θ and the coordinates, x and y . 3.7.5...

Heat Transfer Handbook part 25

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Figure 3.37 Semi-infinite solid with (a) specified surface temperature, (b) specified surface heat flux, and (c) surface convection.. 3.8.2 Semi-infinite Solid Model. 3.37, the semi-infinite solid model envisions a solid with one identifiable surface and extending to infinity in all other directions. The parabolic partial differential equation describing the one-dimensional transient conduction is. 0 the surface at x = 0...

Heat Transfer Handbook part 26

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and the steady periodic temperature distribution is given by. TABLE 3.13 Values of the Amplitude Decay Function, φ as a Function of x/L and σ = (ω/2α) 1 / 2 L. T i + a cos ωt (3.340) where T i is the initial temperature ofthe cylinder. 3.10.1 One-Region Neumann Problem. The one-region Neumann problem deals with a semi-infinite region...

Heat Transfer Handbook part 27

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(3.377) and (3.378) strictly apply only when St = 0, Huang and Shih (1975) used them as zero-order solutions in a regular perturbation series in St and generated two additional terms. (3.377) and (3.378).. 252 CONDUCTION HEAT TRANSFER. Equations (3.373) and (3.374) also give the quasi-steady-state solutions in this case. with heat transfer coefficient h, the quasi-steady-state solutions for T...

Heat Transfer Handbook part 28

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Thermal Spreading and Contact Resistances. 4.2.1 Spreading and constriction resistances in a half-space. 4.2.2 Spreading and constriction resistances in flux tubes and channels 4.3 Spreading and constriction resistances in an isotropic half-space. 4.3.2 Circular area on a half-space Isothermal circular source Isoflux circular source. 4.3.3 Spreading resistance ofan isothermal elliptical source area on a half-space 4.3.4 Dimensionless spreading resistance ofan...

Heat Transfer Handbook part 29

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Figure 4.2 Heat flow lines and isotherms for steady conduction from a finite heat source into a half-space. The free surface of the half- space is adiabatic except for the source area. If heat enters the half-space, the flux lines spread apart as the heat is conducted away from the small source area (Fig. then the thermal resistance is called...

Heat Transfer Handbook part 30

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TABLE 4.4 Dimensionless Spreading Resistance of an Isothermal Rectangular Area. Schneider (1978) presented numerical values and a correlation ofthose values for the dimensionless spreading resistance ofan isothermal rectangle for the aspect ratio range: 1 ≤ a/b ≤ 4. A comparison ofthe values for the isothermal rectangular area and the isothermal elliptical area reveals a very close relationship. It is expected...

Heat Transfer Handbook part 31

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Sons / Page 291 / 2nd Proofs / Heat Transfer Handbook / Bejan. SPREADING RESISTANCE WITHIN A COMPOUND DISK WITH CONDUCTANCE 291. The general solution for the compound disk may be used to obtain spreading re- sistances for several special cases examined previously by many researchers. The spe- cial cases fall into the following two categories: isotropic half-space, semi-infinite flux...

Heat Transfer Handbook part 32

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case of a circular contact area on a half-space. The corresponding half-space results were reported by Strong et al. Correlation Equations for Spreading Resistance Since the three series so- lutions presented above for the three heat flux distributions µ. converge slowly as → 0, correlation equations for the dimensionless spreading resistance ψ = 4kaR s for the three flux distributions...

Heat Transfer Handbook part 33

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isothermal strip provided that a/c 1, (2) µ = 0 for an isoflux distribution, and (3) µ = 1 2 , which gives a parabolic flux distribution. The three flux distributions are. The dimensionless spreading resistance relationship based on the mean source temperature is. and the three dimensionless system parameters and their ranges are. The general relationship gives the following...

Heat Transfer Handbook part 34

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Normal Page PgEnds: TEX B. The Hertz solution requires the calculation of k , the ellipticity, K(k. and E(k ) to the local geometry ofthe contacting solids through the geometric pa- rameters A and B. Table 4.15 shows how k, m, and n depend on the parameter ω over a range ofvalues that should cover most practical contact problems. The...

Heat Transfer Handbook part 35

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(From Stevanovi´c et al., 2001.). a L = 1 − c 3 exp(c 1 τ c with correlation coefficients: c c and c 3 = 1.04. The reference contact radius is a L , which corresponds to the very thick layer limit given by. The maximum difference between the correlation equation and the numerical values obtained from the model of...

Heat Transfer Handbook part 36

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y 2 (x) dx (m) (4.230) where y(x) is the distance ofpoints in the surface from the mean plane (Fig. A second very important surface roughness parameter is the absolute mean asperity slope, which is defined as (Cooper et al., 1969. and DeVaal et al. Figure 4.22 Typical joint between conforming rough surfaces. The effective rms surface roughness and the...

Heat Transfer Handbook part 37

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Short Page PgEnds: TEX λ . (4.262) Sridhar and Yovanovich (1994) reviewed the plastic and elastic deformation con- tact conductance correlation equations and compared them against vacuum data (Mi- kic and Rohsenow, 1966. Sridhar and Yovanovich (1996a) showed that the elastic deformation model was in better agreement with the vacuum data obtained for joints formed by conforming rough surfaces of...

Heat Transfer Handbook part 38

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Figure 4.28 Gap conductance model and data for conforming rough Ni 200 surfaces. 0.01 correspond to the high-gas-pressure tests (near 1 atm), and the points for M ∗ >. 4.17 JOINT CONDUCTANCE ENHANCEMENT METHODS. In many electronics packages the thermal joint conductance across a particular joint must be improved for the thermal design to meet its performance objectives. Figure 4.29...

Heat Transfer Handbook part 39

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Normal Page PgEnds: TEX the highest contact conductance, and silver with the highest microhardness has the. The thermal conductivity ofthe coating appears to play a secondary role.. The unusual shape ofthe curves is attributable to the fact that the assumed effective hardness curve shown in Fig. Moreover, because the microhardness ofsilver is much closer to aluminum than are the microhardness...