Resumen de correlaciones para transferencia de calor por convecci´ on 12 de enero de 2014 ´ Indice 1. N´ umeros adimensionales importantes 1 2. Convecci´on forzada, flujo externo 2 2.1. Flujo externo sobre objetos aislados ............................................. 2 2.2. Flujo externo en bancos de tubos ............................................... 3 3. Convecci´on forzada, flujo interno 5 3.1. Flujo interno desarrollado en conductos circulares lisos ................................... 5 3.2. Flujo interno desarrollado en conductos no circulares .................................... 5 4. Convecci´on natural 6 4.1. Correlaciones generales ..................................................... 6 4.2. Correlaciones simplificadas para aire ............................................. 7 5. Historial de cambios 7 Ap´ endice: Propiedades de fluidos 8 Tabla extendida de propiedades del aire .............................................. 8 Tabla extendida de propiedades del agua .............................................. 15 Tablas de propiedades del libro ItoTSE .............................................. 17 1. N´ umeros adimensionales importantes Tabla 17.1 ItoTSE. N´ umeros adimensionales importantes en transferencia de calor por convecci´ on Table 17.1 Important Dimensionless Groups in Convection Heat Transfer Group a Definition a Interpretation/Application Nusselt number, Nu L Reynolds number, Re L Prandtl number, Pr Grashof number, Gr L Rayleigh number, Ra L Dimensionless temperature gradient at the surface. Measure of the convection heat transfer coefficient. Ratio of the inertia and viscous forces. Characterizes forced convection flows. Ratio of the momentum and thermal diffusivities. Property of the fluid. Ratio of buoyancy to viscous forces. Characterizes free con- vection flows. Product of Grashof and Prandtl numbers, Gr Pr. Character- izes free convection flows. (17.9) (17.12) (17.13) (17.16) (17.19) g1 T s T 2 L 3 g1 T s T 2 L 3 2 c p k VL hL k a The subscript L represents the characteristic length on the surface of interest. 1
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Resumen de correlaciones para transferencia de calor por conveccion
Tabla 17.1 ItoTSE. Numeros adimensionales importantes en transferencia de calor por conveccion410 Chapter 17. Heat Transfer by Convection
Table 17.1 Important Dimensionless Groups in Convection Heat Transfer
Groupa Definitiona Interpretation/Application
Nusselt number, NuL
Reynolds number, ReL
Prandtl number, Pr
Grashof number, GrL
Rayleigh number, RaL
Dimensionless temperature gradient at the surface. Measureof the convection heat transfer coefficient.
Ratio of the inertia and viscous forces. Characterizes forcedconvection flows.
Ratio of the momentum and thermal diffusivities. Property ofthe fluid.
Ratio of buoyancy to viscous forces. Characterizes free con-vection flows.
Product of Grashof and Prandtl numbers, Gr Pr. Character-izes free convection flows.
(17.9)
(17.12)
(17.13)
(17.16)
(17.19)g�1Ts � T�2L3
��
g�1Ts � T�2L3
�2
cp�
k�
�
�
VL
�
hL
k
aThe subscript L represents the characteristic length on the surface of interest.
where the subscript x has been added to emphasize our interest in conditions at a particularlocation on the surface identified by the dimensionless distance x*. The overbar indicates anaverage over the surface from x* � 0 to the location of interest.
The Reynolds number, ReL, is the ratio of the inertia to viscous forces, and is used tocharacterize boundary layer flows (Sec. 13.5)
(17.12)
where V represents the reference velocity of the fluid, L is the characteristic length of thesurface, and � is the kinematic viscosity of the fluid.
The Prandtl number, Pr, is a transport property of the fluid and provides a measure ofthe relative effectiveness of momentum and energy transport in the hydrodynamic and ther-mal boundary layers, respectively
(17.13)
where � is the dynamic viscosity and � is the thermal diffusivity of the fluid (Eq. 16.5).From Table HT-3, we see that the Prandtl number for gases is near unity, in which case
momentum and energy transport are comparable. In contrast, for oils and some liquids withPr � 1 (Tables HT-4, 5), momentum transport is more significant, and the effects extend fur-ther into the free stream. From this interpretation, it follows that the value of Pr stronglyinfluences the relative growth of the velocity and thermal boundary layers. In fact, for alaminar boundary layer, it has been shown that
(17.14)
where n is a positive constant, typically n � 1�3. Hence for a gas, �t � �; for an oil �t � �.However, for all fluids in the turbulent region, because of extensive mixing, we expect �t � �.
The forms of the functions associated with Eqs. 17.10 and 17.11 are most commonly de-termined from extensive sets of experimental measurements performed on specific surfacegeometries and types of flows. Such functions are termed empirical correlations and are al-ways accompanied by specifications regarding surface geometry and flow conditions. ForExample… the most general correlation for forced convection external flow over flat platesand other immersed geometries has the form
(17.15)Nux � C Remx Pr n
�
�t
� Prn
Pr �cp�
k�
�
�
ReL �VL
�Reynolds number
Prandtl number
empirical correlations
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1
2. Conveccion forzada, flujo externo
2.1. Flujo externo sobre objetos aislados
Tabla 17.3 ItoTSE.Resumen de correlaciones de transferencia de calor por conveccion en flujo externo forzado.17.3 Internal Flow 423
17.2.4 Guide for Selection of External Flow Correlations
In this section you have been introduced to empirical correlations to estimate the convection co-efficients for forced convection flow over flat plates, cylinders, and spheres. For your conveniencein selecting appropriate correlations for your problems, the recommended correlations have beensummarized in Table 17.3. While specific conditions are associated with each of the correlations,you are reminded to follow the rules for performing convection calculations outlined in Sec. 17.1.3.
Internal FlowIn the previous section you saw that an external flow, such as for the flat plate, is one forwhich boundary layer development on a surface continues without external constraints. Incontrast, for internal flow in a pipe or tube, the fluid is constrained by a surface, and henceeventually the boundary layer development will be constrained. In Chap. 14 you learned thatwhen flow enters a tube, a hydrodynamic boundary layer forms in the entrance region,growing in thickness to eventually fill the tube. Beyond this location, referred to as the fullydeveloped region, the velocity profile no longer changes in the flow direction.
We begin by considering thermal boundary layer formation in the entrance and fullydeveloped regions, and how the convection coefficient is determined from the resultingtemperature profile. We will introduce empirical correlations to estimate convectioncoefficients for laminar and turbulent flows in the fully developed region, deferring consid-eration of correlations for the entrance region to a more advanced course in heat transfer.
17.3
Table 17.3 Summary of Convection Heat Transfer Correlations for External Flow
Flow Coefficient Correlationa Range of Applicability
aThermophysical properties are evaluated at the film temperature, Tf � (T� � Ts)�2, for all the correlations except Eq. 17.36. For that correlation,properties are evaluated at the free stream temperature T� or at the surface temperature Ts if designated with the subscript s.bFor the cylinder with noncircular cross section, use Eq. 17.34 with the constants listed in Table 17.2.
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Tabla 17.2 ItoTSE.Constantes utilizadas en la correlacion de Hilpert para flujo externo cruzado.17.2 External Flow 419
with the Nusselt number as a function of the Reynolds and Prandtl numbers. The Hilpertcorrelation is one of the most widely used and has the form
(17.34)
where the cylinder diameter D is the characteristic length for the Nusselt number. The con-stants C and m, which are dependent upon the Reynolds number range, are listed in Table 17.2.All properties are evaluated at the film temperature, Tf, Eq. 17.20.
The Hilpert correlation, Eq. 17.34, may also be used for gas flow over cylinders of noncircularcross section, with the characteristic length D and the constants obtained from Table 17.2.
The Churchill-Bernstein correlation is a single comprehensive equation that covers a widerange of Reynolds and Prandtl numbers. The equation is recommended for all ReD Pr � 0.2and has the form
(17.35)
where all properties are evaluated at the film temperature. This correlation is normally pre-ferred, unless the simplicity of the Hilpert equation is advantageous.
NuD � 0.3 �0.62 Re1�2
D Pr1�3
31 � 10.4�Pr22�3 4 1�4 c1 � a ReD
282,000b5�8 d 4�5
3ReD Pr 7 0.2 4
NuD �hD
k� C Rem
D Pr1�3 3Pr � 0.7 4
Experiments have been conducted to measure the convection coefficient on a polished metallic cylinder 12.7 mm in diameterand 94 mm long (Fig. E17.4a). The cylinder is heated internally by an electrical resistance heater and is subjected to a crossflow of air in a low-speed wind tunnel. Under a specific set of operating conditions for which the free stream air velocity andtemperature were maintained at u� � 10 m/s and 26.2�C, respectively, the heater power dissipation was measured to be Pe �46 W, while the average cylinder surface temperature was determined to be Ts � 128.4�C. It is estimated that 15% of thepower dissipation is lost by conduction through the endpieces.
Example 17.4 Cylindrical Test Section: Measurement of the Convection Coefficient
Table 17.2 Constants for the Hilpert Correlation, Eq. 17.34, for Circular (Pr � 0.7) and Noncircular (Gases only) Cylinders inCross Flow
The maximum velocity is determined from the conservation of mass re-quirement for steady incompressible flow. For in-line arrangement, the maxi-mum velocity occurs at the minimum flow area between the tubes, and theconservation of mass can be expressed as (see Fig. 7-26a) � � A1 � � �maxAT
or �ST � �max(ST � D). Then the maximum velocity becomes
� (7-40)
In staggered arrangement, the fluid approaching through area A1 in Fig-ure 7–26b passes through area AT and then through area 2AD as it wrapsaround the pipe in the next row. If 2AD � AT, maximum velocity will still oc-cur at AT between the tubes, and thus the �max relation Eq. 7-40 can also beused for staggered tube banks. But if 2AD � �� [or, if 2(SD � D) � (ST � D)],maximum velocity will occur at the diagonal cross sections, and the maximumvelocity in this case becomes
Staggered and SD � (ST � D)/2: � (7-41)
since � �A1 � ��max(2AD) or �ST � 2�max(SD � D).The nature of flow around a tube in the first row resembles flow over a sin-
gle tube discussed in section 7–3, especially when the tubes are not too closeto each other. Therefore, each tube in a tube bank that consists of a singletransverse row can be treated as a single tube in cross-flow. The nature of flowaround a tube in the second and subsequent rows is very different, however,because of wakes formed and the turbulence caused by the tubes upstream.The level of turbulence, and thus the heat transfer coefficient, increases withrow number because of the combined effects of upstream rows. But there is nosignificant change in turbulence level after the first few rows, and thus theheat transfer coefficient remains constant.
Flow through tube banks is studied experimentally since it is too complexto be treated analytically. We are primarily interested in the average heat trans-fer coefficient for the entire tube bank, which depends on the number of tuberows along the flow as well as the arrangement and the size of the tubes.
Several correlations, all based on experimental data, have been proposed forthe average Nusselt number for cross flow over tube banks. More recently,Zukauskas has proposed correlations whose general form is
(7-42)
where the values of the constants C, m, and n depend on value Reynolds num-ber. Such correlations are given in Table 7–2 explicitly for 0.7 � Pr � 500 and0 � ReD � 2 106. The uncertainty in the values of Nusselt number obtainedfrom these relations is �15 percent. Note that all properties except Prs are tobe evaluated at the arithmetic mean temperature of the fluid determined from
(7-43)
where Ti and Te are the fluid temperatures at the inlet and the exit of the tubebank, respectively.
Tm �Ti � Te
2
NuD �hDk
� C RemD Pr n(Pr/Prs)0.25
�max �ST
2(SD � D)
�max �ST
ST � D
390HEAT TRANSFER
D
D
SL
ST
A1 AT
1st row 2nd row
(a) In-line
3rd row
A1 = ST LAT = (ST �D)LAD = (SD �D)L
, T1�
SL
ST
A1 AT
AD
SD
AD
(b) Staggered
, T1�
FIGURE 7–26Arrangement of the tubes in in-lineand staggered tube banks (A1, AT, andAD are flow areas at indicatedlocations, and L is the length of thetubes).
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Figura 7-26a Cengel, configuracion en lınea (in-line or aligned)
The maximum velocity is determined from the conservation of mass re-quirement for steady incompressible flow. For in-line arrangement, the maxi-mum velocity occurs at the minimum flow area between the tubes, and theconservation of mass can be expressed as (see Fig. 7-26a) � � A1 � � �maxAT
or �ST � �max(ST � D). Then the maximum velocity becomes
� (7-40)
In staggered arrangement, the fluid approaching through area A1 in Fig-ure 7–26b passes through area AT and then through area 2AD as it wrapsaround the pipe in the next row. If 2AD � AT, maximum velocity will still oc-cur at AT between the tubes, and thus the �max relation Eq. 7-40 can also beused for staggered tube banks. But if 2AD � �� [or, if 2(SD � D) � (ST � D)],maximum velocity will occur at the diagonal cross sections, and the maximumvelocity in this case becomes
Staggered and SD � (ST � D)/2: � (7-41)
since � �A1 � ��max(2AD) or �ST � 2�max(SD � D).The nature of flow around a tube in the first row resembles flow over a sin-
gle tube discussed in section 7–3, especially when the tubes are not too closeto each other. Therefore, each tube in a tube bank that consists of a singletransverse row can be treated as a single tube in cross-flow. The nature of flowaround a tube in the second and subsequent rows is very different, however,because of wakes formed and the turbulence caused by the tubes upstream.The level of turbulence, and thus the heat transfer coefficient, increases withrow number because of the combined effects of upstream rows. But there is nosignificant change in turbulence level after the first few rows, and thus theheat transfer coefficient remains constant.
Flow through tube banks is studied experimentally since it is too complexto be treated analytically. We are primarily interested in the average heat trans-fer coefficient for the entire tube bank, which depends on the number of tuberows along the flow as well as the arrangement and the size of the tubes.
Several correlations, all based on experimental data, have been proposed forthe average Nusselt number for cross flow over tube banks. More recently,Zukauskas has proposed correlations whose general form is
(7-42)
where the values of the constants C, m, and n depend on value Reynolds num-ber. Such correlations are given in Table 7–2 explicitly for 0.7 � Pr � 500 and0 � ReD � 2 106. The uncertainty in the values of Nusselt number obtainedfrom these relations is �15 percent. Note that all properties except Prs are tobe evaluated at the arithmetic mean temperature of the fluid determined from
(7-43)
where Ti and Te are the fluid temperatures at the inlet and the exit of the tubebank, respectively.
Tm �Ti � Te
2
NuD �hDk
� C RemD Pr n(Pr/Prs)0.25
�max �ST
2(SD � D)
�max �ST
ST � D
390HEAT TRANSFER
D
D
SL
ST
A1 AT
1st row 2nd row
(a) In-line
3rd row
A1 = ST LAT = (ST �D)LAD = (SD �D)L
, T1�
SL
ST
A1 AT
AD
SD
AD
(b) Staggered
, T1�
FIGURE 7–26Arrangement of the tubes in in-lineand staggered tube banks (A1, AT, andAD are flow areas at indicatedlocations, and L is the length of thetubes).
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Figura 7-26b Cengel, configuracion al tresbolillo (staggered)
Velocidad maxima, se calcula a partir de la velocidad de aproximacion del fluido V. En el caso de la configuracion enlınea,ecuacion Cengel 7-40:
Vmax =ST
ST −DV
En el caso de la configuracion al tresbolillo, se tienen dos situaciones. Si SD > (ST +D) /2, el maximo estrechamientotiene lugar en el area transversal y se utiliza la misma expresion que en la configuracion en lınea. Por el contrario,siSD 6 (ST +D) /2 entonces el maximo estrechamiento tiene lugar en el area diagonal y se utilizarıa la ecuacion Cengel7-41:
Vmax =ST
2 (SD −D)V
Calculo de Nusselt: correlacion de Zukauskas, ecuacion Cengel 7-42. Ver tabla Cengel 7-2 para los diferentes casos:
NuD =hD
k= C RemD Prn(Pr /Prs)
0,25
donde ReD = VmaxDν
y todas las propiedades se deben evaluar a la temperatura media aritmetica del fluido entre laentrada y salida del banco de tubos, excepto Prs que se evalua a la temperatura de pared del tubo.
3
Tabla 7-2 Cengel. Correlacion de Zukauskas para el numero de Nusselt en flujo cruzado sobre banco de tubos.
The average Nusselt number relations in Table 7–2 are for tube banks with16 or more rows. Those relations can also be used for tube banks with NL pro-vided that they are modified as
(7-44)
where F is a correction factor F whose values are given in Table 7–3. ForReD � 1000, the correction factor is independent of Reynolds number.
Once the Nusselt number and thus the average heat transfer coefficient forthe entire tube bank is known, the heat transfer rate can be determined fromNewton’s law of cooling using a suitable temperature difference �T. The firstthought that comes to mind is to use �T � Ts � Tm � Ts � (Ti � Te)/2. Butthis will, in general, over predict the heat transfer rate. We will show in thenext chapter that the proper temperature difference for internal flow (flowover tube banks is still internal flow through the shell) is the 1ogarithmicmean temperature difference �Tln defined as
(7-45)
We will also show that the exit temperature of the fluid Te can be determinedfrom
Nusselt number correlations for cross flow over tube banks for N � 16 and0.7 � Pr � 500 (from Zukauskas, Ref. 15, 1987)*
Arrangement Range of ReD Correlation
0–100
100–1000In-line
1000–2 105
2 105–2 106
0–500
500–1000Staggered
1000–2 105
2 105–2 106
*All properties except Prs are to be evaluated at the arithmetic mean of the inlet and outlet temperaturesof the fluid (Prs is to be evaluated at Ts ).
NuD � 0.031(ST /SL)0.2 Re0.8D Pr0.36(Pr/Prs)0.25
NuD � 0.35(ST /SL)0.2 Re0.6D Pr0.36(Pr/Prs)0.25
NuD � 0.71 Re0.5D Pr0.36(Pr/Prs)0.25
NuD � 1.04 Re0.4D Pr0.36(Pr/Prs)0.25
NuD � 0.033 Re0.8D Pr0.4(Pr/Prs)0.25
NuD � 0.27 Re0.63D Pr0.36(Pr/Prs)0.25
NuD � 0.52 Re0.5D Pr0.36(Pr/Prs)0.25
NuD � 0.9 Re0.4D Pr0.36(Pr/Prs)0.25
TABLE 7–3
Correction factor F to be used in , = FNuD for NL � 16 and ReD � 1000(from Zukauskas, Ref 15, 1987).
NL 1 2 3 4 5 7 10 13
In-line 0.70 0.80 0.86 0.90 0.93 0.96 0.98 0.99
Staggered 0.64 0.76 0.84 0.89 0.93 0.96 0.98 0.99
NuD, NL
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Correcion para numero de filas menor de 16: si el banco de tubos tuviese un numero de filas menor de 16 hay quecorregir el numero de Nusselt con la ecuacion Cengel 7-44:
NuD,NL = FNuD
donde el factor de correccion F se obtiene de la tabla Cengel 7-3, que es valida si ReD > 1000. A partir de este valor deReD el factor de correccion resulta independiente del numero de Reynolds.
Tabla 7-3 Cengel. Factor de correccion en caso de que el banco de tubos tenga menos de 16 filas.
The average Nusselt number relations in Table 7–2 are for tube banks with16 or more rows. Those relations can also be used for tube banks with NL pro-vided that they are modified as
(7-44)
where F is a correction factor F whose values are given in Table 7–3. ForReD � 1000, the correction factor is independent of Reynolds number.
Once the Nusselt number and thus the average heat transfer coefficient forthe entire tube bank is known, the heat transfer rate can be determined fromNewton’s law of cooling using a suitable temperature difference �T. The firstthought that comes to mind is to use �T � Ts � Tm � Ts � (Ti � Te)/2. Butthis will, in general, over predict the heat transfer rate. We will show in thenext chapter that the proper temperature difference for internal flow (flowover tube banks is still internal flow through the shell) is the 1ogarithmicmean temperature difference �Tln defined as
(7-45)
We will also show that the exit temperature of the fluid Te can be determinedfrom
Nusselt number correlations for cross flow over tube banks for N � 16 and0.7 � Pr � 500 (from Zukauskas, Ref. 15, 1987)*
Arrangement Range of ReD Correlation
0–100
100–1000In-line
1000–2 105
2 105–2 106
0–500
500–1000Staggered
1000–2 105
2 105–2 106
*All properties except Prs are to be evaluated at the arithmetic mean of the inlet and outlet temperaturesof the fluid (Prs is to be evaluated at Ts ).
NuD � 0.031(ST /SL)0.2 Re0.8D Pr0.36(Pr/Prs)0.25
NuD � 0.35(ST /SL)0.2 Re0.6D Pr0.36(Pr/Prs)0.25
NuD � 0.71 Re0.5D Pr0.36(Pr/Prs)0.25
NuD � 1.04 Re0.4D Pr0.36(Pr/Prs)0.25
NuD � 0.033 Re0.8D Pr0.4(Pr/Prs)0.25
NuD � 0.27 Re0.63D Pr0.36(Pr/Prs)0.25
NuD � 0.52 Re0.5D Pr0.36(Pr/Prs)0.25
NuD � 0.9 Re0.4D Pr0.36(Pr/Prs)0.25
TABLE 7–3
Correction factor F to be used in , = FNuD for NL � 16 and ReD � 1000(from Zukauskas, Ref 15, 1987).
NL 1 2 3 4 5 7 10 13
In-line 0.70 0.80 0.86 0.90 0.93 0.96 0.98 0.99
Staggered 0.64 0.76 0.84 0.89 0.93 0.96 0.98 0.99
NuD, NL
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4
3. Conveccion forzada, flujo interno
3.1. Flujo interno desarrollado en conductos circulares lisos
Tabla 17.5 ItoTSE. Correlaciones de transferencia de calor en flujo interno forzado en conductos circulares lisos.438 Chapter 17. Heat Transfer by Convection
Table 17.5 Summary of Forced Convection Heat Transfer Correlations for Internal Flow in Smooth Circular Tubesc
Flow/Surface Thermal Conditions Correlationa,b Restrictions on Applicability
Constant or Ts (Dittus-Boelter) (17.64) 0.6 � Pr � 160, ReD � 10,000,n � 0.4 for Ts � Tm and n � 0.3for Ts Tm
Constant or Ts (Sieder-Tate) (17.65) 0.7 � Pr � 16,700, ReD � 10,000
aThermophysical properties in Eqs. 17.61, 17.62, and 17.64 are based upon the mean temperature, Tm. If the correlations are used to estimate theaverage Nusselt number over the entire tube length, the properties should be based upon the average of the mean temperatures, � (Tm,i � Tm,o)�2.bThermophysical properties in Eq. 17.65 should be evaluated at Tm or , except for �s, which is evaluated at the tube wall temperature Ts or cFor tubes of noncircular cross section, use the hydraulic diameter, Dh, Eq. 17.63, as the characteristic length for the Reynolds and Nusseltnumbers. Results for fully developed laminar flow are provided in Table 17.4. For turbulent flow, Eq. 17.64 may be used as a first approximation.
Ts.Tm
Tm
NuD � 0.027 Re4�5D Pr1�3 a �
�sb0.14
q–s
NuD � 0.023 Re4�D
5 Prnq–s
q–s
Free Convection
Free ConvectionIn the preceding sections of this chapter, we considered convection heat transfer in fluid flowsthat originate from an external forcing condition. Now we consider situations for which thereis no forced motion, but heat transfer occurs because of convection currents that are inducedby buoyancy forces, which arise from density differences caused by temperature variationsin the fluid. Heat transfer by this means is referred to as free (or natural) convection.
Since free convection flow velocities are generally much smaller than those associated withforced convection, the corresponding heat transfer rates are also smaller. However, in manythermal systems, free convection may provide the largest resistance to heat transfer and there-fore plays an important role in the design or performance of the system. Free convection is of-ten the preferred mode of convection heat transfer, especially in electronic systems, for reasonsof space limitations, maintenance-free operation, and reduced operating costs. Free convectionstrongly influences heat transfer from pipes, transmission lines, transformers, baseboard heaters,as well as appliances such as your stereo, television and laptop computer. It is also relevant tothe environmental sciences, where it is responsible for oceanic and atmospheric motions.
We begin by considering the physical origins and nature of buoyancy-driven flows, andintroduce empirical correlations to estimate convection coefficients for common geometries.
17.4.1 Flow and Thermal Considerations
To illustrate the nature of the boundary layer development in free convection flows, considerthe heated vertical plate (Fig. 17.20a) that is immersed in a cooler extensive, quiescent fluid.An extensive medium is, in principle, an infinite one; a quiescent fluid is one that is other-wise at rest, except in the vicinity of the surface.
Since the plate is hotter than the fluid, Ts � T�, the fluid close to the plate is less densethan fluid in the quiescent region. The fluid density gradient and the gravitational field cre-ate the buoyancy force that induces the free convection boundary layer flow in which theheated fluid rises. The boundary layer grows as more fluid from the quiescent region is
17.4
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3.2. Flujo interno desarrollado en conductos no circulares
Tabla 17.4 ItoTSE. Numero de Nusselt para flujo laminar completamente desarrollado en el interior de conductos nocirculares.
17.3.3 Convection Correlations for Tubes: Fully Developed Region
To use many of the foregoing results for internal flow, the convection coefficients must beknown. In this section we present correlations for estimating the coefficients for fullydeveloped laminar and turbulent flows in circular and noncircular tubes. The correlationsfor internal flow are summarized in Table 17.5 (page 438) along with guidelines to facilitatetheir selection for your application.
Laminar FlowThe problem of laminar flow (ReD 2300) in tubes has been treated theoretically, and theresults can be used to determine the convection coefficients. For flow in a circular tubecharacterized by uniform surface heat flux and laminar, fully developed conditions, the Nusseltnumber is a constant, independent of ReD, Pr, and axial location
(17.61)
When the thermal surface condition is characterized by a constant surface temperature, theresults are of similar form, but with a smaller value for the Nusselt number
(17.62)
In using these equations to determine h, the thermal conductivity should be evaluated at Tm.
NuD �hD
k� 3.66 3Ts � constant 4
NuD �hD
k� 4.36 3q–s � constant 4
Table 17.4 Nusselt Numbers for Fully Developed Laminar Flow in Noncircular Tubes forConstant Ts and qs Surface Thermal Conditionsa
Cross Section Constant qs Constant Ts
— 4.36 3.66
1.0 3.61 2.98
1.43 3.73 3.08
2.0 4.12 3.39
3.0 4.79 3.96
4.0 5.33 4.44
8.0 6.49 5.60
� 8.23 7.54
� 5.39 4.86
— 3.11 2.47
aThe characteristic length is the hydraulic diameter, Dh, Eq. 17.63.
b
a
NuD �hDh
k
ba
a
a
a
a
a
b
b
b
b
b
Insulated
Heated
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Para flujo turbulento usar la ecuacion 17.64 con el diametro hidraulico: Dh ≡ 4AcP
, ecuacion ItoTSE 17.63, donde Aces el area transversal de paso y P es el perımetro mojado.
5
4. Conveccion natural
4.1. Correlaciones generales
Tabla 17.6 ItoTSE. Correlaciones de transferencia de calor por conveccion natural en geometrıas sumergidas.446 Chapter 17. Heat Transfer by Convection
Table 17.6 Summary of Free Convection Correlations for Immersed Geometries
Geometry Recommended Correlation Restrictions
(17.74) RaL 1013
(17.78) 105 RaL 1010
(17.79) 104 RaL 107
(17.80) 107 RaL 1011
(17.84) RaD 1012
(17.85)
aThe correlation may be applied to a vertical cylinder if (D�L) � (35� ).bThe characteristic length is defined as L � As�P, Eq. 17.77.
Gr1�4L
RaD 1011
Pr � 0.7NuD � 2 �
0.589 Ra1�4D
31 � 10.469 Pr29�16 4 4�9
NuD � e0.60 �0.387 Ra1�6
D
31 � 10.559�Pr 29�16 4 8�27 f2
NuL � 0.15 Ra1�3L
NuL � 0.54 Ra1�4L
NuL � 0.27 Ra1�4L
NuL � e0.825 �0.387 Ra1�6
L
31 � 10.492�Pr29�16 4 8�27 f2
Vertical platesa
Horizontal platesb
Case A or B:Hot surface down or cold surface up
Case C or D:Hot surface up or cold surface down
Horizontal cylinder
Sphere
17.4.5 Guide for Selection of Free Convection Correlations
In this section you have been introduced to empirical correlations to estimate the convectioncoefficients for free convection heat transfer for vertical and horizontal plates, the horizon-tal cylinder, and the sphere. For your convenience in selecting appropriate correlations foryour problems, the recommended correlations have been summarized in Table 17.6. Specificconditions are associated with each of the correlations, and you are reminded to follow therules for peforming convection calculations outlined in Sec. 17.1.3.
Convection Application: Heat Exchangers
Heat ExchangersThe process of heat exchange between two fluids that are at different temperatures andseparated by a solid wall occurs in many engineering applications. The device used toimplement this exchange is termed a heat exchanger, and specific applications can be found
17.5
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Correlacion de Morgan para cilindros largos horizontales (alternativa mas sencilla a la correlacion 17.84)
Ecuacion Rango Ecuacion ItoTSE
NuD = 0,850Ra0,188D 102 ≤ RaL ≤ 104 (17.81)
NuD = 0,480Ra0,250D 104 ≤ RaL ≤ 107 (17.82)
NuD = 0,125Ra0,333D 107 ≤ RaL ≤ 1012 (17.83)
Temperatura de referencia: En conveccion natural, las propiedades del fluido se evaluan a temperatura de pelıculaexcepto el coeficiente de expansion volumetrica β que se debe evaluar a la temperatura de fluido sin perturbar.
Longitud caracterıstica en placas horizontales: es la razon entre la superficie de la placa (una sola cara) y elperımetro, ecuacion ItoTSE 17.77:
L ≡ AsP
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4.2. Correlaciones simplificadas para aire
Tabla de correlaciones para calcular el coeficiente de pelıcula en conveccion natural no confinada (flujo externo)**solo validas para aire a temperatura ambiente**
Configuracion geometrica Ecuacion Regimen de flujo
Placa plana (o cilindro) verticalhcv = 1,42 · (∆T/L)
1/4Laminar 104 < RaL < 109
hcv = 1,31 · (∆T )1/3
Turbulento 109 < RaL < 1013
Placa plana horizontal, conveccion favorecidahcv = 1,32 · (∆T/L)
1/4Laminar 104 < RaL < 109
hcv = 1,52 · (∆T )1/3
Turbulento 109 < RaL < 1013
Placa plana horizontal, conveccion impedida hcv = 0,59 · (∆T/L)1/4
Laminar 104 < RaL < 109
Cilindro horizontalhcv = 1,32 · (∆T/D)
1/4Laminar 104 < RaD < 109
hcv = 1,24 · (∆T )1/3
Turbulento 109 < RaD < 1013
5. Historial de cambios8-dic-2012 primera version10-ene-2013 # anadida la correlacion de Morgan de conveccion natural
# aclaracion sobre la temperatura de referencia en conveccion natural# anadida la tabla extendida de propiedades del agua
12-ene-2014 # bancos de tubos, correccion de errata en formula Vmax para trebolillo, Cengel 7-41# varias aclaraciones y mejoras en la seccion de bancos de tubos# mejorada la seccion de flujo interno
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Propiedades del aire seco a presion atmosferica.EES v.9.250. 29-Nov-2012 1