Rohsenow W., Hartnett J., Young Cho. Handbook of Heat Transfer (776121), страница 60
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4.25 and 4.26): K, °Ftemperature of the central region in a cavity (Fig. 4.26)" K, °Ffilm temperature (Too+ Tw)/2, unless specifically given another meaning insection of interest: K, °Ftemperature of hot plate in enclosure (Figs.
4.25 and 4.26): K, °Finitial temperature of quiescent fluid before transient is initiated: K, °F(Th + T~)/2: K, °Ftemperature of solid surface of body or wall: K, °Fmean value of Tw taken over surface of body: K, °Ftemperature of inside of tube wall (Fig. 4.49): K, °Fmean wall temperature halfway up the rectangular open cavity (Fig. 4.21): K, °Ffluid temperature far from solid surface or wall at a given elevation z: K, °Fmean value of Tootaken over vertical height of bodytime: stime period over which the fluid near a wall subjected to a step change intemperature or heat flux behaves like a stationary fluid (Figs. 4.37 and 4.39)" sNATURAL CONVECTIONt*UEvvVoWWXX*xlyy*ZZ[ZiZrefZ*4.85time after the initiation of a transient at which the purely conductive heattransfer solution matches the steady-state convective heat transfer (Figs.
4.37and 4.39): svalue of to when Nu at to is equal to Nu at t~ (Fig. 4.39): stime after the initiation of a transient at which the heat transfer at the wall isessentially the steady-state value (Fig. 4.37): sdimensionless time, tvo/Lfluid velocity in the x direction: m/s, ft/sfluid velocity and mean fluid velocity in tube: m/s, ft/sfluid velocity in the y direction: m/s, ft/sreference velocity, V'g~ATL(1 + Pr): m/s, ft/swidth of plate (Fig.
4.6), of cavity (Figs. 4.25 and 4.33), or of open cavity (Fig.4.23): m, ftfluid velocity in the z direction: m/s, ft/sspatial coordinate (Fig. 4.1); distance measured along a surface streamlinestarting from the beginning of the streamline (Fig. 4.3): m, ftx/Lvalue of x at trailing edge of body: m, ftspatial coordinate (Fig.
4.1); coordinate measured normal to surface of bodyand into the fluid (Fig. 4.3): m, fty/Lspatial coordinate (Fig. 4.1): m, ft; elevation of a point above reference level(Fig. 4.3c): m, ftelevation of end of streamline passing through a particular point on a bodyelevation of start of streamline passing through a particular point on a body:m, ftz at reference level: m, ftz/LGreek SymbolsO~m0~*~0Y71,Y2Aca~zxhthermal diffusivity evaluated at TI (or at Tm for enclosure problems) unless2 ft/s2specifically otherwise directed: m/s,thermal diffusivity at porous medium (Eq. 4.145): m2/s, ft2/saspect ratio, S/W in Fig. 4.23acoefficient of thermal expansion; evaluate 13at Ti for liquids and T**for gases,except for enclosure problems, where [3 is evaluated at Tm (unless otherwisespecifically directed): K -1, °R-1[3 evaluated at Ti: K -i, °R-1equals [30for liquids and [3o.for gases13evaluated at To.: K -1, °R 4pressure coefficient of expansion: Pa -~, ft2/lbfconstants in the Bejan-Tien correlation equation (Eq.
4.98)conduction layer thickness on the cold plate (Fig. 4.26): m, ftlocal turbulent conduction layer thickness on cold plate: m, ftconduction layer thickness on hot plate (Fig. 4.26): m, ft4.86CHAPTERFOURlocal conduction layer thickness for a laminar or turbulent boundary layer;Ax = k( T w - Too)/q": m, ftATAATZXTmzXT0Ax5~c~hfiw00c~.l.bVPP0p..(pc~)~(oC,)w(Y(Y"g, "gD, 'gO, 'goowtemperature difference ITw - TooI, ITh - Tc I, ITi - To I, and so on: K or °C, °Faverage conduction layer thickness around body (Eq. 4.16)area-weighted average value of ITw- Tool over the surface (or part of thesurface) of body (Eq. 4.35): K, °FAT evaluated at the mid-height of a plate, cylinder, or spherereference temperature difference, defined separately for each problem: K, °Fsegment of length in x direction: m, ftthickness of tube wall (Fig. 4.49): m, ftemissivity of cold plate in enclosure problem (Fig.
4.25)emissivity of hot plate in enclosure problem (Fig. 4.25)emissivity of wall in enclosure problem (Fig. 4.25)d/D (Fig. 4.23f)local surface angle (Fig. 4.5)parameter that accounts for transverse curvature of vertical cylinder (Eq.4.44)angle of inclination from horizontal (Figs. 4.9, 4.16, and 4.25): rad, degfor enclosure problem, the crossover value of 0 defined so that for 0 < 0c, Eq.4.107 applies and for 0c < 0 < 90 °, Eq. 4.108 applies: rad, degdimensionless temperature, ( T - Too)/(Tw - Too)dynamic viscosity, evaluated at Tf (or Tm for enclosure problems) unlessspecifically directed otherwise: Pa.s, lbm/(S'ft)viscosity of fluid evaluated at bulk temperature: Pa.s, lbm/(S'ft)kinematic viscosity, evaluated at Tf (or Tm for enclosure problems) unlessspecifically directed otherwise: m2/s, ft2/slocal density of fluid: kg/m 3, lbm/ft3reference density, evaluated at film temperature Ty and Pref: kg/m 3, lbm/ft3density of fluid at T = Too,P = P~ef: kg/m 3, lbm/ft3heat capacity per unit volume for fluid: kJ/(m3.K), Btu/(ft 3-°F)heat capacity per unit volume for wall adjacent to fluid: kJ/(m3.K), Btu/(ft 3.°F)Stefan-Boltzman constant: W/mZK4, Btu/(h.ft 2.°R 4)heat capacitance ratio for a porous medium (Eq.
4.145)dimensionless time, 4o~t/D 2, 40ffD/D 2, 4~to/D 2, 4o~too/D2, respectivelyvolume fraction occupied by fluid for a porous mediumfunction of cz*, given by Eq. 4.61bangle of opening of V-corrugated surface (Fig. 4.23c): rad, degForscheimer coefficient (Eq. 4.141)Special Brackets[]"I XX2, 1• • • ,, Xn]min[Xl, X2 .
. . . .Xn]maxindicates that only positive values of quantities in brackets are to betaken: [X]" = (IX] + X)/2indicates that the minimum member of set {xi} is to be takenindicates that the maximum member of the set {xi} is to be takenNATURAL CONVECTION4.87OperatorsDXbXDt*-t)t*- + u* ~x* + v* ~)y, + w* ~3z,~X~2XbXb2XV*zX = ~+~9x.2 ~bXb2X+~9z.2REFERENCES1.
T. Aihara, "Natural Convective Heat Transfer in Vertical Parallel Fins of Rectangular Profile," Jpn.Soc. Mech. Eng. (34): 915-926, 1968.2. T. Aihara, Y. Yamada, and S. Endo, "Free Convection Along a Downward-Facing Surface of aHeated Horizontal Plate," Int. J. Heat Mass Transfer (15): 2535-2549, 1972.3. M.
AI-Arabi and M. M. EI-Rafaee, "Heat Transfer by Natural Convection From Corrugated Platesto Air," Int. J. Heat Mass Transfer (21): 357-359, 1978.4. M. AI-Arabi and M. K. E1-Riedy, "Natural Convection Heat Transfer From Isothermal HorizontalPlates of Different Shapes," Int.
J. Heat Mass Transfer (19): 1399-1404, 1976.5. M. A1-Arabi and B. Sakr, "Natural Convection Heat Transfer From Inclined Isothermal Plates," Int.J. Heat Mass Transfer (31): 559-566, 1988.6. M. AI-Arabi and Y. K. Salman, "Laminar Natural Convection Heat Transfer from an Inclined Cylinder," Int. J. Heat Mass Transfer (23): 45-51, 1980.7. J. N. Arnold, P. N. Bonaparte, I. Catton, and D. K.
Edwards, "Experimental Investigation of NaturalConvection in a Finite Rectangular Region Inclined at Various Angles from 0 ° to 180°,'' Proc. 1974Heat Transfer Fluid Mech. Inst., Corvallis, Ore., Stanford University Press, Stanford, CA, pp. 321329, 1974.8. J. N. Arnold, I. Catton, and D. K. Edwards, "Experimental Investigation of Natural Convection inInclined Rectangular Regions of Differing Aspect Ratios," J. Heat Transfer (98): 67-71, 1976.9. J. N.
Arnold, D. K. Edwards, and I. Catton, "Effect of Tilt and Horizontal Aspect Ratio on NaturalConvection in Rectangular Honeycombs," J. Heat Transfer (99): 120-122, 1977.10. Y. Asako, H. Nakamura, and M. Faghri, "Three-Dimensional Laminar Natural Convection in a Vertical Air Slot With Hexagonal Honeycomb Core," J. Heat Transfer (112): 130-136, 1990.11. W. Aung, "Fully Developed Laminar Free Convection Between Vertical Plates Heated Asymmetrically," Int. J. Heat Mass Transfer (15): 1577-1580, 1972.12.
W. Aung, L. S. Fletcher, and V. Sernas, "Developing Laminar Free Convection Between Vertical FlatPlates With Asymmetric Heating," Int. J. Heat Mass Transfer (15): 2293-2308, 1972.13. L. Baker, R. E. Faw, and E A. Kulacki, "Post-Accident Heat Removal, Part I, Heat Transfer Withinan Internally Heated Nonboiling Liquid Layer," Nucl. Sci. Eng.
(61): 222-230, 1976.14. A. Bar-Cohen and W. M. Rohsenow, "Thermally Optimum Spacing of Vertical, Natural ConvectionCooled, Parallel Plates," J. Heat Transfer (106): 116-123, 1984.15. A. Bejan, "On the Boundary Layer Regime in a Vertical Enclosure Filled with a Porous Medium,"Letters Heat Mass Transfer (6): 93-102, 1979.16. A. Bejan and C. L. Tien, "Laminar Natural Convection Heat Transfer in a Horizontal Cavity withDifferent End Temperatures," J. Heat Transfer (100): 641--647, 1978.17. R.
E Bergholz, "Instability of Steady Natural Convection in a Vertical Fluid Layer," J. Fluid Mech.(84/4): 743-768, 1978.18. R. E Bergholz, "Natural Convection of a Heat Generating Fluid in a Closed Cavity," J. Heat Transfer (102): 242-247, 1980.19. A.E. Bergles and R. R. Simonds, "Combined Forced and Free Convection for Laminar Flow in Horizontal Tubes with Uniform Heat Flux," Int. J. Heat Mass Transfer (14): 1989-2000, 1971.4.88CHAPTER FOUR20.
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