Rohsenow W., Hartnett J., Young Cho. Handbook of Heat Transfer (776121), страница 59
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From Metais and Eckert [190].that the Nusselt number at these locations does not deviate by more than 10 percent from thevalues for pure natural convection and pure forced convection.ACKNOWLEDGMENTSThe authors are grateful to the Natural Science and Engineering Research Council of Canadafor financial support of the research required to prepare this chapter. Thanks to AndrewWoronko and Skye Legon for digitizing and analyzing data, and to Anita Fonn for typing themanuscript.NOMENCLATURESymbol, Definition, SI Units, English UnitsAheat transfer surface area of body: m 2, ft 2Ararea over which fluid contacts each plate in enclosure problem (Fig.
4.25): m 2, ft 2Ahflat horizontal heated area that faces downward (or cooled horizontal areathat faces upward on a cold body): m 2, ft 2Awarea over which wall contacts each plate in enclosure problem (Fig. 4.25): m 2, ft 2aproportionality constant in Morgan's law (Eq. 4.163) for forced convectionheat transfer from cylinders (see Table 4.14)constant in stratified medium (Eqs. 4.42, 4.46, and 4.50)wall thickness (Fig.
4.25): m, ftabNATURAL CONVECTIONbbbCC1C1C2C~C,cCarmCtc,C,Cccp, CpoDDaOiDoEcfRefGGrGriGzgHH~H~4.81constant in stratified medium (Eqs. 4.42, 4.46, and 4.50)function of Pr given in Table 4.12 and used in Fig. 4.38unit vector in direction of buoyancy force (Fig. 4.5)minor axis of elliptical cylinder or spheroid (Tables 4.2 and 4.3a): m, ftconstant (Eq. 4.20)constant, defined separately for different problemsfunctions of C/L for elliptic cylinders and spheroids, tabulated in Tables 4.2and 4.3aconstant (e.g., Eqs. 4.34c and 4.38)wall admittance parameter for circular cylinder enclosures, given by Eq.
4.83.wall admittance parameter for rectangular parallelepiped enclosures, given byEq. 4.82 for opaque fluids and (approximately) by Eq. 4.86 for transparentfluidsfunction of Pr (Eq. 4.13 and Table 4.1)function of Pr and ~, given by Eq. 4.28average value of C, over a body, defined by Eq. 4.23 (see Tables 4.2 and 4.3 forC, for various body shapes)function of Pr given by Eq.
4.25; see Table 4.1function of Pr given by Eq. 4.24; see Table 4.1constant, defined separately for each problemconstant in stratified medium equations (Eqs. 4.42, 4.46, and 4.50)specific heat of fluid evaluated at T;: J/(kg.K), Btu/(lbm" °F)diameter of sphere, cylinder, or disk: m, ftDarcy number (Eq. 4.146)for a pair of eccentric or concentric spheres or cylinders, the diameter of theinner one (Fig. 4.36): m, ftfor a pair of eccentric or concentric spheres or cylinders, the diameter of theouter one (Fig.
4.36): m, fttube diameter (Fig. 4.23): m, ftaverage particle diameter in porous medium: m, ftperpendicular distance between axes of eccentric cylinders, or distancebetween centers of eccentric spheres (Fig. 4.36): m, ftEckert number, VZo/(CpAT)friction factor-Reynolds number product for forced flow in a duct (Table 4.4)quantity defined by Eq. 4.45bgeometry-dependent constant (Eqs. 4.11, 4.14, and 4.37a and Tables 4.2 and 4.3)Grashof number, Ra/PrGrashof number at which NUF = NuuGraetz number, defined in Fig. 4.49acceleration of gravity: m/s 2, ft/s 2height, defined by Figs.
4.21--4.23 and 4.25: m, ftfunction of Prandtl number (Eq. 4.34a)height of partition extending up from the floor of a cavity: m, ft4.82CHAPTERFOURnuheight of partition hanging down from the ceiling of a cavity: m, flHI.function of Prandtl number (Eq. 4.36a, Table 4.1)partition height: m, ftHMIN, HMAX minimum and maximum, respectively, of Hu and HL: m, ftiflow index: i = 0 for 2D flow problems and i = 1 for axisymmetric flowproblemsthermal conductivity of fluid, evaluated at Tr for external and open cavityproblems and at Tm for enclosure problems (unless otherwise specificallydirected): W/(m.K), Btu/h.ft.°Fkl, k2kmconstants in Hollands equation (Eq. 4.78); given by Eqs.
4.80-4.81 and Table 4.7k:thermal conductivity of fluid in a porous medium: W/mK, Btu/hr ft.°Fkskwthermal conductivity of solid in a porous medium: W/mK, Btu/hr ft-°Fthermal conductivity of wall: W/(m.K), Btu/h.ft-°Fkwtequivalent enclosure wall thermal conductivity, given by Eq. 4.84: W/(m.K),Btu/h.ft.°Fk*,special wall conductivity, equal to kw for enclosures with finlike walls andopaque fluids, and given by Eq.
4.85 (approximately) for enclosures with thickwalls and transparent fluids: W/(m.K), Btu/h.ft. °Feffective thermal conductivity of porous medium: W/mK, Btu/hr ft.°Fcharacteristic length, chosen separately for each problem: m, ftspacing between isothermal surfaces (Figs. 4.25 and 4.26), or length of a plateor a cylinder (Figs. 4.6 and 4.14): m, ftvertical distance between lowest and highest points on a body: m, ftL*lmlicharacteristic length for a horizontal plate, equal to A/p (Fig. 4.10): m, ftcharacteristic dimension of body or enclosure: m, ftexponent used in the Churchill-Usagi fit (Eqs. 4.32, 4.34d, 4.36d, etc.)unit vector normal to the surface (Fig. 4.5)NuNusselt number, usually given by qL/(A ATk), but see separate definingsketch for each problemNUCONDNut:Nusselt number when fluid is stationary and transfer is by conduction onlyNusselt number for pure forced convectionNUrdNusselt number for fully developed flowNun (Ra)Nu-Ra relation which results when a given inclined cavity is rotated to thehorizontal positionNuisoNusselt number that is obtained for constant Tw and T**with Tw - T**= ATmNusselt number for a cavity with no partitionNunpNulpNutNusselt number for a cavity with full interior partitionaverage Nusselt number taken over entire body, assuming laminar flowprevails over entire bodyNUNNu,Nusselt number for pure natural convectionNu,,xlocal Nusselt number for turbulent heat transfer at location x, q"x/ATkaverage Nusselt number taken over entire body, assuming turbulent heattransfer prevails over whole bodyNATURAL CONVECTIONNuv (Ra)NulNu rNuo (Ra)nPPdP/PrefP.Pwp,,Prpp~(z)Qqq*q'q,,q,,qPlfq:q/oqrq,,oqwqw0q~AqRa4.83Nu-Ra relation that results when a given inclined cavity is rotated to thevertical positionlocal Nusselt number for a turbulent boundary layer at point xaverage "thin-layer-solution" Nusselt number for laminar flowNu-Ra relation for a cavity inclined at angle 0Churchill usage constant used to determine Nue (Eq.
4.19, Table 4.3)exponent in Eq. 4.163 for forced convection heat transfer over cylinders(Table 4.14)pressure: Pa, lbf/ft2pressure component associated with dynamics of flow (Eq. 4.1): Pa, lbf/ft 2perimeter of a cylinder at the intersection of its surface with the plane normalto its axis: m, ftreference pressure, equal to pressure at z = Zref far from solid surface: Pa, lbf/ft 2pressure at height z and far from solid surface or wall: Pa, lbf/ft 2"circumferential heat flux" dimensionless group for internal mixed convectionproblems (Fig. 4.49)rate of internal generation of energy in a wall per unit of heat transfer surfacearea of the wall: W/m 2, Btu/(h.ft 2)Prandtl number, equal to v/a, evaluated at T/(or Tm for enclosure problems)unless otherwise specifically directedperimeter of plate (Fig.
4.10b): m, fttilt parameter for long tilted cylinder (Eq. 4.47b)perimeter of body along the intersection with a horizontal plane at elevationz: m, ftaverage body perimeter, defined by Eq. 4.15dimensionless thermal capacity rate (Fig. 4.38)heat transfer rate, total heat delivered to fluid moving through an open cavity:W, Btu/hheat flux ratio for rectangular open cavity, equal to qa/q~ (Fig. 4.21)heat flow per unit length of surface: W/m, Btu (h.ft)heat flow per unit area of surface: W/m 2, Btu (h.ft a)average heat flux over surface, equals q/A: W/m 2, Btu (h-ft 2)rate of internal generation of heat within the fluid: W/m 3, Btu (h.ft 3)heat transfer from hot plate to fluid in enclosure problem: W, Btu/hvalue of q/when fluid is stationary: W, Btu/hradiative heat transfer from hot plate in enclosure problem: W, Btu/hvalue of qr when fluid is stationary: W, Btu/hheat transfer over Aw from plate to wall in enclosure problem (see Fig.
4.25 fordefinition of plate and wall): W, Btu/hvalue of q~ when fluid is stationary: W, Btu/hlocal heat flux at location x: W/m 2, Btu/(h.ft a)heat flow through area AA: W, Btu/hRayleigh number in terms of the reference temperature difference AT0,usually given by gfAAToL3/vo~ (but see separate definition sketch for eachproblem discussed)4.84CHAPTERFOURRacRaci, RacpRaxRamaxRa*Ra*ReR~Re/ReprSSSS(Z)TT7"*TbTcTcrTIThT/T~TwTwTwiTwo/2)TooT~ttocritical Rayleigh number governing the initiation of small eddy convectivemotion in a fluidcritical Rayleigh numbers for cavities with adiabatic and perfectly conductingwalls, respectivelylocal value of Ra based on local temperature difference, given by g~JATx3/vO~value of Ra at which the heat transfer per unit volume of vertical channels ismaximum for a given channel height HRayleigh number for porous medium (Eq.
4.146)Rayleigh number in terms of surface flux q", usually given by g~3q"L4/vctk (butsee separate definition sketch for each problem)local value of Ra* defined in separate definition sketch for each problem (e.g.,Fig. 4.6)Reynolds number, usually equal to Lvo/v (but see separate definition sketchfor each problem)Reynolds number when flow and heat transfer are fully developedReynolds number at which NUF = NUNReynolds number based on particle diameter in a porous mediumradius of axisymmetric body in horizontal plane measured from vertical axischaracteristic dimension (Fig.
4.3b): m, ftspacing between fins or width of open cavity (Fig. 4.21 or 4.23): m, ftaverage spacing between vertical triangular fins (Fig. 4.23d)stratification number, given by Eq. 4.41, with L - D for cylinders, spheresvertical height of plate at location X (Fig. 4.9): m, ftlocal fluid temperature: K, °Fmean fluid temperature: K, °Fwall temperature ratio for open rectangular cavity (Fig. 4.21)average of inlet and outlet bulk fluid temperatures for internal tube flow: K, °Ftemperature of cold plate of enclosure (Figs.
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