Page 57 - Mechanical Engineers Reference Book

1/46 Mechanical engineering principles

3 Surface 2
/

2
5
a
1

0 1 2 3 4 5 6
Dl Y

Figure 1.74 The geometric factor chart
emissivity is encountered. In new situations it will be necessary
to determine emissivity by experiment before proceeding. No
account has been taken of intervening media for which
transmissivity is not unity. Gas absorption and radiation needs
j;r AiFiz j; further information. For gases such as oxygen, nitrogen and
hydrogen with symmetric, diatomic molecules the above work
is adequate, but asymmetric molecular structures cause pro-
blems. In particular, hydrocarbon fuel combustion products
(H,O), C02, CO, SO2) are important in engineering calcula-
tions and account must be taken of their radiation properties.
Solar radiation problems also need special consideration.
1.7.3.4 Finned surfaces
In many heat exchange problems involving the determination
of a U-value it is found that the surface heat transfer coeffi-
cient on one side of the solid interface is much smaller than
that on the other. The smaller coefficient will dictate the heat
transfer rate achieved, and in order to overcome this problem
fins may be added to this poor convection surface to increase
the area for heat transfer. This problem will occur in liquid to
gas exchangers on the gas side. The addition of fins will alter
the flow pattern so that a new coefficient should if possible be
Figure 1.75 The electrical analogy for grey-body radiation problems
determined. It is also possible that there may be variation of
coefficient over the fin surface.
and any required heat flux can be found. In the three-body Simple fin theory in which conduction along the fin is
problem, for example, the heat transfer from 1 to 2 balanced with convection from the surface can be used to
3-x determine the temperature distribution and heat transfer rate
= 1/AIF,* of the fin. For example, when a long fin of constant cross-
sectional area is examined (Figure 1.76) it is found that the
or the total heat transfer from body 1 is temperature distribution is
& - p, _- cosh(m(Z - x))
0
-
00 cosh(ml)
PllAlel
Special cases are:
1. If N 7 1 bqdies are in large surroundings then for this Nth
body J" = E{;
2. An insulated or refractory surface has no black body
potential but contributes to the heat transfer by.taking up
an equilibrium temperature T given by mp = J";
3. Radiation shield problems will show six resistances in
series rather than the series-parallel circuits used pre-
viously.
P =2(w+r)
In all the discussion on radiation above no account has been A =WT
taken of the selective emitter for which emissivity is not eo = T,., - T,
constant. Additional techniques are required to solve these
real problems and care should be exercised if widely varying Figure 1.76 Simple rectangular fin nomenclature