Document zMjMZrrmQ78DEjrwED60GK3n
CHAPTER 5
perature difference ((, -- t,) which is the temperature of the surface less * that of the fluid. The particular fluid temperature to use for a given " system will be noted under the discussion of that system. The-propor tionality factor is termed the unit thermal convective conductance (sometimes called the film coefficient for convection), hc, Btu per (hour) (square foot) (Fahrenheit degree). Fig. 1 shows the conditions associated with con- H vection.
The heat transmission by free or natural convection for objects sur rounded by air can be conveniently expressed as in Equation 2a:
it. - tiY "
(2a)
where
-- = heat transmission by convection, Btu per (square foot) (hour). A
C = a constant depending upon the shape of the surface.
D = diameter of pipe or circular duct or height of vertical wall, inches. 1
(Effect of diameter or height becomes constant at 24 in.).
7'av = average of wall surface and surrounding air temperature, Fahrenheit ,
degrees absolute.
>
-- tf -- temperature excess between wall surface and surrounding air, Fahren-
heit degrees.
For horizontal cylinders, the value of C = 1.02 has been well estab lished by various investigations. For vertical plates, the value of C = 1.39 has been fairly well established. Suggested values2 of C for hori zontal plates warmer than the surrounding air are 1.79 when facing upward, and 0.89 when facing downward.
Problems in either forced convection or natural convection may be solved by the simple first-power equation if the convection coefficient is expressed as a unit conductance:
q = fc0 A (fx - is)
(2b):
where
q = heat transmission by convection, Btu per hour.
A = surface area, square feet.
fi -- f = temperature difference between the surface and the fluid, Fahrenheit
degrees.
= unit convective conductance, from Table 2, Btu per (square foot)),
(hour) (Fahrenheit degree temperature difference).
irf,
Thermal Radiation Equation
)
The relation given by Equation 3 is applicable to systems in which |
radiant exchange takes place between the surfaces of solids, as schemati- V
q, = vA.FaFe (TV - 7V)
(3) i
cally shown in Fig. 3. Gaseous and luminous radiation are not considered.;) in this discussion. Equation 3 states that the net radiation per unit trans-1 fer area of surface 1, gJA Btu per (hour)' (square foot), which sees surface 2 through a non-absorbing medium, is proportional to the difference of the ;
Heat Transfer t**" 2-
93 "* **
Expressed in Convenient Empirical Form
Cas e r
1
System
Heat Transfer Equation* and its Limits of Appt.tp attov
J* obced Convection
General Equation
TT -
09" (%9"
Longitudinal flow in a circular cylinder6. 2 Same as Case l.6
where * > 4.4Z) and (f) > 2200
Equation for Air
3 Same as Case l.b
4 Flow normal to a sinrfa ovlinHov
5 Same as Case 4. 6 Same as Case 4.
Ac -- 5.4 X lO^fTf)'" * Z)o.i where * > 4:4D
and > 2200
Equation for Liquid Water (32-400 F) '
K = 13.5(1,)*
where * > 4.4D and (i--) > 2200
General Equation
(v)M W - o-26
where 1000 < -- < 50.000 a
Equation for Air
Ac(*verace) =* 0.211(7V)* Z>9
where 1000 < -- < 50.000 M
Equation for Liquid Water (32-400 F)
Ac (average) = 34.0(lf)- V - > * .
where 1000 < -- < 50,000
M
General Equation (Turbulent Flow) !f- <TM (frc-rr
Refer3 3
3
4 4 4 3
Flow along a flat plate. Same as Case 7.
Where
> 500,000 and
Ac = 1.25Acz
Equation for Air (Turbulent Flow)
Age = QSl
(i)>
where (??) > 500,000
Ae,average) -- 1.25Acx
3