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92
CHAPTER 5
1954 Guide
perature difference (t, -- 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), h,, Btu per (hour) (square foot) (Fahrenheit degree). Fig.' 1 shows the conditions associated with con
vection.
The heat transmission by free or natural convection for objects sur rounded by. air can be conveniently expressed as in Equation 2a:
where
heat transmission by convection, Btu per (square foot) (hour).
a constant depending upon the shape of the surface, diameter of pipe or circular duct or height of vertical wall, inches. (Effect of diameter or height becomes constant at 24 in.), average of wall surface and surrounding air temperature, Fahrenheit degrees absolute. 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 = ho A. (h -- ii)
(2b)
where
q = heat transmission by convection, Btu per hour. A = surface area, square feet. <i -- <t = temperature difference between the, surface and the fluid, Fahrenheit
degrees.
K = unit convective conductance, from Table 2, Btu per (square foot)
(hour) (Fahrenheit degree temperature difference).
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-
q, = vAiFaFe (2V - 2Y)
(3)
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 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
V
Table 2.` Approximate Unit Conductances for Thermal Convection for Several Flow Svstems
Expressed in Convenient Empirical Form
Heat Tbansfeb Equation anw iTo Limits of Application
RefbbENCfc
General Equation 0.0225 (--ly*
Longitudinal flow in a circular cylinder1*. Same as Case l.b
AD > 2200 Equation for Air
Same as Case l.b
U
tFlow normal to a single cylinder. Same as Case 4. Same as Case 4.
he ~ 5A X
where * > 4.40
()and > 2200
Equation for Liquid Water (32-400 F) :
he
where * > 4.40
and (^r) > 2200
General Equation
1 mheD
k > 0.26
where 1000 < -- < 50,000
Equation for Air
*e(veie) = 0-211(rf)M DM
where 1000 < 52 < 50,000
Equation for Liquid Water (33-400 F)
)Ae(&v*ngB) = 34.0(h)0-" \ DM
where 1000 < ^2 < 50,000 -
////////Flow along a fiat plate.
General Equation (Turbulent Flow) = 0-0200_(f)"(?)"
where
> 500,000and.
* 2 1-25Acx
Equation'for Air (Turbulent Flow)
ia =. ojurmM
*
(?)"> .
where
> 500,000
^(average) = 125ha