Rohsenow W., Hartnett J., Young Cho. Handbook of Heat Transfer (776121), страница 38
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J. Whitehouse and J. E Archard, "The Properties of Random Surfaces of Significance in TheirContact," Proc. Roy. Soc. Lond. A (316): 97-121, 1970.126. M. L. Wiedmann and P. R. Trumpler, "Thermal Accommodation Coefficients," Trans. ASME, Vol.68, pp. 57-64, 1946.127. D. A. Wesley and M. M. Yovanovich, "A New Gaseous Gap Conductance Relationship," NuclearTechnology, Vol. 72, pp. 70-74, 1986.128. E C. Yip, "Thermal Contact Constriction Resistance," PhD thesis, Department of Mechanical Engineering, University of Calgary, Calgary, Alberta, Canada, 1969.129.
E C. Yip, "Effect of Oxide Films on Thermal Contact Resistance," in Progress in Astronautics andAeronautics, Heat Transfer With Thermal Control M. M. Yovanovich ed., Vol. 39, pp. 45-64, MITPress, Cambridge, MA, 1974.130. M. M. Yovanovich, "A General Expression for Predicting Conduction Shape Factors," in Thermophysics and Spacecraft Thermal Control AIAA Progress in Astronautics and Aeronautics, Vol. 35,pp.
265-291, MIT Press, Cambridge, MA, 1974.131. M. M. Yovanovich, "General Thermal Constriction Resistance Parameter for Annular Contacts onCircular Flux Tubes," AIAA Journal (14/6): 822-824, 1976.3.72CHAPTER THREE132. M. M. Yovanovich, "General Expressions for Constriction Resistances of Arbitrary Flux Distributions," in Radiative Transfer and Thermal Control, AIAA Progress in Astronautics and Aeronautics,Vol. 49, pp.
381-396, New York, 1976.133. M. M. Yovanovich, "Thermal Constriction of Contacts on a Half-Space: Integral Formulation," inRadiative Transfer and Thermal Control, Vol. 49, pp. 397-418, AIAA, New York, 1976.134. M. M. Yovanovich and S. S. Burde, "Centroidal and Area Average Resistances of Nonsymmetric,Singly Connected Contacts," AIAA Journal (15/10): 1523-1525, 1977.135. M. M. Yovanovich and G.
E. Schneider, "Thermal Constriction Resistance Due to a Circular Annular Contact," AIAA Progress in Astronautics and Aeronautics, Vol. 56, pp. 141-154, 1977.136. M. M. Yovanovich, "General Conduction Resistance for Spheroids, Cavities, Disks, Spheroidal andCylindrical Shells," AIAA 77-742, AIAA 12th Thermophysics Conference, Albuquerque, New Mexico, June 27-29, 1977.137.
M. M. Yovanovich, S. S. Burde, and J. C. Thompson, "Thermal Constriction Resistance of ArbitraryPlanar Contacts With Constant Flux," Thermophysics of Spacecraft And Outer Planet Entry Probes,A I A A Progress in Astronautics and Aeronautics, Vol. 56, pp. 127-139, 1977.138.
M. M. Yovanovich, C. H. Tien, and G. E. Schneider, "General Solution of Constriction ResistanceWithin a Compound Disk," Heat Transfer, Thermal Control, and Heat Pipes, AIAA Progress inAstronautics and Aeronautics, Vol. 70, pp. 47-62, 1980.139. M. M. Yovanovich, "Thermal Contact Correlations," in Progress in Astronautics and Aeronautics,Spacecraft Radiative Transfer and Temperature Control, Thomas E.
Horton ed., Vol. 83, New York,1982.140. M. M. Yovanovich, A. A. Hegazy, and J. DeVaal, "Surface Hardness Distribution Effects Upon Contact, Gap and Joint Conductances," AIAA-82-0887, AIAA/ASME 3rd Joint Thermophysics, Fluids,Plasma and Heat Transfer Conference, St.
Louis, MO, June 7-11, 1982.141. M. M. Yovanovich, J. DeVaal, and A. A. Hegazy, "A Statistical Model to Predict Thermal Gap Conductance Between Conforming Rough Surfaces," AIAA-82-0888, AIAA/ASME Third Joint Thermophysics, Fluids, Plasma and Heat Transfer Conference, St. Louis, MO, June 1982.142. M.
M. Yovanovich, K. J. Negus, and J. C. Thompson, "Transient Temperature Rise of Arbitrary Contacts with Uniform Flux by Surface Element Methods," AIAA-84-0397, A I A A 22nd Aerospace Sciences Meeting, Reno, NV, January 9-12, 1984.143. M. M. Yovanovich, "Recent Developments in Thermal Contact, Gap and Joint Conductance Theories and Experiments," Eighth Int. Heat Transfer Conference, San Francisco, CA, Vol. 1, pp. 35-45,1986.144. M. M. Yovanovich, "New Nusselt and Sherwood Numbers for Arbitrary Isopotential Geometries atNear Zero Peclet and Rayleigh Numbers," AIAA-87-1643, AIAA 22nd Thermophysics Conference,Honolulu, HI, 1987.145.
M. M. Yovanovich, "Natural Convection from Isothermal Spheroids in the Conductive to LaminarFlow Regimes," AIAA-87-1587, AIAA 22nd Thermophysics Conference, Honolulu, HI, 1987.146. M. M. Yovanovich, "On the Effect of Shape, Aspect Ratio and Orientation Upon Natural Convection from Isothermal Bodies of Complex Shape," ASME HTD (82): 121-129, 1987.147. M. M. Yovanovich and V. W. Antonetti, "Application of Thermal Contact Resistance Theory toElectronic Packages," in Advances in Thermal Modeling of Electronic Components and Systems, A.Bar-Cohen and A. D.
Kraus eds., Vol. 1, Chap. 2, pp. 79-128, Hemisphere Publishing, New York,1988.148. M. M. Yovanovich, "Theory and Applications of Constriction and Spreading Resistance ConceptsFor Microelectronic Thermal Management," in Cooling Techniques For Computers, W. Aung ed.,pp. 277-332, Hemisphere Publishing Corp., New York, 1991.149. M. M. Yovanovich, P. Teertstra, and J.
R. Culham, "Modeling Transient Conduction From Isothermal Convex Bodies of Arbitrary Shape," Journal of Thermophysics and Heat Transfer (9/3):385-390, 1995.150. M. M. Yovanovich, "Dimensionless Shape Factors and Diffusion Lengths of Three-DimensionalBodies," ASME/JSME Thermal Engineering Joint Conference (1): 103-114, 1995.151. M.
M. Yovanovich, "Simple Explicit Expressions for Calculation of the Heisler-Grober Charts,"AIAA-96-3968, 1996 National Heat Transfer Conference, Houston, TX, August 3-6, 1996.CONDUCTION AND THERMAL CONTACT RESISTANCES (CONDUCTANCES)3.73152. M. M. Yovanovich, "Transient Spreading Resistance of Arbitrary Isoflux Contact Areas: Development of a Universal Time Function," AIAA-97-2458, AIAA 32nd Thermophysics Conference,Atlanta, GA, June 23-25, 1997.153. Mathematica, Wolfram Research Inc., Champaign, IL, 1996.154. K.A. Martin, "Thermal Constriction Resistance of Arbitrary Contacts With the Boundary Condition of the Third Kind," M.A.Sc. Thesis, Department of Mechanical Engineering, University ofWaterloo, Waterloo, Ontario, Canada, 1980.155.
S.S. Sadhal, "Exact Solutions for the Steady and Unsteady Diffusion Problems for a RectangularPrism: Cases of Complex Neumann Conditions," ASME 84-HT-83, 22nd Heat Transfer Conference,Niagara Falls, NY, Aug. 6-8, 1984.156. S. Song, S. Lee, and V. Au, "Closed-Form Equation for Thermal Constriction/Spreading ResistancesWith Variable Resistance Boundary Condition," Proc. IEPS Conference, Atlanta, GA, pp. 111-121,1994.157. S. Lee, S.
Song, V. Au, and K. P. Moran, "Constriction/Spreading Resistance Model for ElectronicsPackaging," Proc. 4th ASME/JSME Thermal Engineering Joint Conference, Maui, HI, pp. 199-206,March 19-24, 1995.158. D. J. Nelson and W. A. Sayers, "A Comparison of Two-Dimensional Planar, Axisymmetric andThree-Dimensional Spreading Resistances," Proc. 8th IEEE SEMI-THERM Symposium on Semiconductor, Thermal Measurements, and Management, Austin, TX, pp.
62-68, February, 1992.159. Y. Ogniewicz, "Conduction in Basic Cells of Packed Beds," M.A.Sc. Thesis, Department of Mechanical Engineering, University of Waterloo, Waterloo, Ontario, Canada, 1975.CHAPTER 4NATURAL CONVECTIONG. D. Raithby and K. G. T. HollandsUniversity of WaterlooINTRODUCTIONNatural convection is the motion that results from the interaction of gravity with density differences within a fluid. The differences may result from gradients in temperature, concentration, or composition.
This chapter deals with the heat transfer associated with naturalconvection driven by temperature gradients in a newtonian fluid.The first section presents some fundamental ideas that are frequently referred to in theremainder of the chapter. The next three sections deal with the major topics in natural convection. The first of these addresses problems of heat exchange between a body and an extensive quiescent ambient fluid, such as that depicted in Fig.
4.1a. Open cavity problems, such asnatural convection in fin arrays or through cooling slots (Fig. 4.1b), are considered next. Thelast major section deals with natural convection in enclosures, such as in the annulus betweencylinders (Fig. 4.1c). The remaining sections present results for special topics including transient convection, natural convection with internal heat generation, mixed convection, andnatural convection in porous media.In response to the main needs of engineers, this chapter focuses on the average (ratherthan the local) heat transfer, and it provides correlation equations in preference to tabulateddata.
The advantage is that even complex equations are easy to program into computer codesused for design.The forms of the correlation equations are based, whenever possible, on general principlesand an approximate solution method, both briefly discussed in the section on basics. Confidence in the use of the equations will be enhanced by reading that section. Where accuracy isimportant, the underlying assumptions and experimental validation should be understood,and where accuracy is critical, no equation should be used beyond its range of experimentalvalidation.BASICSEquations of Motion and Their SimplificationIn this section the full equations of motion for the external problem sketched in Fig.
4.1a aresimplified by using approximations appropriate to natural convection, and the resulting equations are nondimensionalized to bring to light the important dimensionless groups. Although4.14.2CHAPTERFOUR(1 g(a)(b)(c)FIGURE 4.1 Natural convection on external surfaces (a), through open cavities (b), and in enclosures (c).this development is written around the external problem, similar developments may be madefor the open cavity and internal problems (Fig.
4.1b and c).Full Equations of Motion.The complete equations of motion in cartesian coordinates andfor a newtonian fluid are presented in Chap. 1. The coordinate z will be used to represent theupward vertical direction as shown in Fig. la.Simplified Equations of Motion.The local pressure in the fluid can (for convenience) bebroken into three terms:fP ~ Prer-zgp~(Z) dz + Pd(4.1)z refThe first term is the pressure at some reference point (Xref,Yref, Zref) in the ambient fluid farfrom the body; the second term is the hydrostatic pressure of this ambient fluid; and the thirdterm, Pal, is the pressure component associated with dynamics of the flow. Substituting Eq. 4.1for P into the full equations of motion, we find that Pd simply replaces P in the x and ymomentum equations. But in the z momentum equation there arises the additional termp~(z)g, representing the hydrostatic pressure gradient force.
The local gravitational bodyforce pg also appears in the z momentum equation, and the imbalance between these twoforces, represented by the difference p=(z)g- pg, is the driving force of natural convection. Byintroducing 13=-(1/p)(t)p/i)T)p and y= 1/p(i)p/i)P)r, this imbalance, called the buoyancy force,can be expressed by(p=(z) - p)g = pg[exp~-jr~ dT +~ldP - 1(4.2)where r and P (like 9) are local values at x, y, z, and T=(z) and P~(z), like p=(z), are values inthe ambient fluid at the same z.Equation 4.2 may be simplified. Because the difference between P(x, y, z) and P~(z) issmall, the term involving 7 may be dropped. Further simplifications are different for gases andliquids. For gases (assumed ideal), J3= 1/T and Eq. 4.2 reduces to(P=(Z) - o)g1=og ~( T - T=) ~- pog~=(T- T=)(4.3)where J3== 1/T= and P0 is evaluated at a mean film temperature TI: TI = 0.5(Tw + T=). [Tw andT= are Tw and T= (z) averaged over the vertical height of the body.] The replacement of P byNATURAL CONVECTION4.390 in the third term in Eq.
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