The CRC Handbook of Mechanical Engineering. Chapter 4. Heat and Mass Transfer (776127), страница 6
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For the calculated value of Nu = 1.01,convection must play little role. For standard glass, the heat loss by radiation would be roughly doublethe natural convection value just calculated.Special NomenclatureNote that nomenclature for each geometry considered is provided in the figures that are referred to inthe text.C,CtVCtHCtDT=====function of Prandtl number, Equation (4.2.3)function of Prandtl number, Equation (4.2.4)function of Prandtl number, Equation (4.2.5)surface averaged value of Ct, page 4–38surface averaged value of Tw – T¥ReferencesChurchill, S.W.
1983. Heat Exchanger Design Handbook, Sections 2.5.7 to 2.5.10, E.V. Schlinder, Ed.,Hemisphere Publishing, New York.Churchill S.W. and Usagi, R. 1972. A general expression for the correlation of rates of transfer and otherphenomena, AIChE J., 18, 1121–1128.Clemes, S.B., Hollands, K.G.T., and Brunger, A.P. 1994. Natural convection heat transfer from horizontalisothermal cylinders, J. Heat Transfer, 116, 96–104.© 1999 by CRC Press LLCHeat and Mass Transfer4-25Edwards, J.A. and Chaddock, J.B. 1963.
An experimental investigation of the radiation and freeconvection heat transfer from a cylindrical disk extended surface, Trans., ASHRAE, 69, 313–322.Elenbaas, W. 1942a. The dissipation of heat by free convection: the inner surface of vertical tubes ofdifferent shapes of cross-section, Physica, 9(8), 865–874.Elenbaas, W. 1942b. Heat dissipation of parallel plates by free convection, Physica, 9(1), 2–28.Fujii, T.
and Fujii, M. 1976. The dependence of local Nusselt number on Prandtl number in the case offree convection along a vertical surface with uniform heat flux, Int. J. Heat Mass Transfer, 19,121–122.Fujii, T., Honda, H., and Morioka, I. 1973. A theoretical study of natural convection heat transfer fromdownward-facing horizontal surface with uniform heat flux, Int. J. Heat Mass Transfer, 16,611–627.Goldstein, R.J., Sparrow, E.M., and Jones, D.C. 1973. Natural convection mass transfer adjacent tohorizontal plates, Int. J.
Heat Mass Transfer, 16, 1025–1035.Hollands, K.G.T. 1984. Multi-Prandtl number correlations equations for natural convection in layers andenclosures, Int. J. Heat Mass Transfer, 27, 466–468.Hollands, K.G.T., Unny, T.E., Raithby, G.D., and Konicek, K. 1976. Free convection heat transfer acrossinclined air layers, J. Heat Transfer, 98, 189–193.Incropera, F.P. and DeWitt, D.P. 1990. Fundamentals of Heat and Mass Transfer, 3rd ed., John Wiley& Sons, New York.Karagiozis, A.
1991. An Investigation of Laminar Free Convection Heat Transfer from Isothermal FinnedSurfaces, Ph.D. Thesis, Department of Mechanical Engineering, University of Waterloo.Karagiozis, A., Raithby, G.D., and Hollands, K.G.T. 1994. Natural convection heat transfer from arraysof isothermal triangular fins in air, J. Heat Transfer, 116, 105–111.Kreith, F. and Bohn, M.S. 1993. Principles of Heat Transfer. West Publishing, New York.Raithby, G.D. and Hollands, K.G.T. 1975. A general method of obtaining approximate solutions tolaminar and turbulent free convection problems, in Advances in Heat Transfer, Irvine, T.F.
andHartnett, J.P., Eds., Vol. 11, Academic Press, New York, 266–315.Raithby, G.D. and Hollands, K.G.T. 1985. Handbook Heat Transfer, Chap. 6: Natural Convection,Rohsenow, W.M., Hartnett, J.P., and Ganic, E.H., Eds., McGraw-Hill, New York.Seki, N., Fukusako, S., and Inaba, H.
1978. Heat transfer of natural convection in a rectangular cavitywith vertical walls of different temperatures, Bull. JSME., 21(152), 246–253.Shewan, E., Hollands, K.G.T., and Raithby, G.D. 1996. Heat transfer by natural convection across avertical air cavity of large aspect ratio, J. Heat Transfer, 118, 993–995.Further InformationThere are several excellent heat transfer textbooks that provide fundamental information and correlationsfor natural convection heat transfer (e.g., Kreith and Bohn, 1993; Incropera and DeWitt, 1990). Thecorrelations in this section closely follow the recommendations of Raithby and Hollands (1985), but thatreference considers many more problems.
Alternative equations are provided by Churchill (1983).Forced Convection — External FlowsN.V. SuryanarayanaIntroductionIn this section we consider heat transfer between a solid surface and an adjacent fluid which is in motionrelative to the solid surface.
If the surface temperature is different from that of the fluid, heat is transferredas forced convection. If the bulk motion of the fluid results solely from the difference in temperature ofthe solid surface and the fluid, the mechanism is natural convection. The velocity and temperature ofthe fluid far away from the solid surface are the free-stream velocity and free-stream temperature. Both© 1999 by CRC Press LLC4-26Section 4are usually known or specified. We are then required to find the heat flux from or to the surface withspecified surface temperature or the surface temperature if the heat flux is specified. The specifiedtemperature or heat flux either may be uniform or may vary. The convective heat transfer coefficient his defined byq ¢¢ = h(Ts - T¥ )(4.2.29)In Equation (4.2.29) with the local heat flux, we obtain the local heat transfer coefficient, and with theaverage heat flux with a uniform surface temperature we get the average heat transfer coefficient.
For aspecified heat flux the local surface temperature is obtained by employing the local convective heattransfer coefficient.Many correlations for finding the convective heat transfer coefficient are based on experimental datawhich have some uncertainty, although the experiments are performed under carefully controlled conditions.
The causes of the uncertainty are many. Actual situations rarely conform completely to theexperimental situations for which the correlations are applicable. Hence, one should not expect the actualvalue of the heat transfer coefficient to be within better than ±10% of the predicted value.Many different correlations to determine the convective heat transfer coefficient have been developed.In this section only one or two correlations are given. For other correlations and more details, refer tothe books given in the bibliography at the end of this section.Flat PlateWith a fluid flowing parallel to a flat plate, changes in velocity and temperature of the fluid are confinedto a thin region adjacent to the solid boundary — the boundary layer.
Several cases arise:1.2.3.4.Flows without or with pressure gradientLaminar or turbulent boundary layerNegligible or significant viscous dissipation (effect of frictional heating)Pr ³ 0.7 or Pr ! 1Flows with Zero Pressure Gradient and Negligible Viscous DissipationWhen the free-stream pressure is uniform, the free-stream velocity is also uniform. Whether the boundarylayer is laminar or turbulent depends on the Reynolds number ReX (rU¥ x/m) and the shape of the solidat entrance. With a sharp edge at the leading edge (Figure 4.2.7) the boundary layer is initially laminarbut at some distance downstream there is a transition region where the boundary layer is neither totallylaminar nor totally turbulent.
Farther downstream of the transition region the boundary layer becomesturbulent. For engineering applications the existence of the transition region is usually neglected and itis assumed that the boundary layer becomes turbulent if the Reynolds number, ReX, is greater than thecritical Reynolds number, Recr . A typical value of 5 ´ 105 for the critical Reynolds number is generallyaccepted, but it can be greater if the free-stream turbulence is low and lower if the free-stream turbulenceis high, the surface is rough, or the surface does not have a sharp edge at entrance. If the entrance isblunt, the boundary layer may be turbulent from the leading edge.FIGURE 4.2.7 Flow of a fluid over a flat plate with laminar, transition, and turbulent boundary layers.© 1999 by CRC Press LLC4-27Heat and Mass TransferTemperature Boundary LayerAnalogous to the velocity boundary layer there is a temperature boundary layer adjacent to a heated (orcooled) plate.
The temperature of the fluid changes from the surface temperature at the surface to thefree-stream temperature at the edge of the temperature boundary layer (Figure 4.2.8).FIGURE 4.2.8 Temperature boundary layer thickness relative to velocity boundary layer thickness.The velocity boundary layer thickness d depends on the Reynolds number ReX. The thermal boundarylayer thickness dT depends both on ReX and PrRex < Recr:d=x5Re xPr > 0.7d= Pr 1 3dTPr ! 1d= Pr 1 2dT(4.2.30)Recr < Rex:d0.37=x Re 0x.2d » dT(4.2.31)Viscous dissipation and high-speed effects can be neglected if Pr1/2 Ec/2 ! 1.
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