Page 140 - Mechanical Engineer's Data Handbook

THERMODYNAMICS AND HEAT TRANSFER 129

1 Conduction through composite cylinder fluid to
U= fluid
1
x
-+-+- 1
ha hb
A typical example is a lagged pipe.
4=UA(ta-tb)
l l x q=-
R =- +- +-= R, + R, + R R
h,A h,A kA
Conduction through composite wall
q=UA(t,-t,)
1
U=
(R,+Rl+R2+. . . R,)A
R=Ra+R,+R2+. . . R,

R’=~,A,, etc.
where: R, =A,
x2
X
k,Al

3.14.4 Heat transfer from fins

The heat flow depends on the rate of conduction along
the fin and on the surface heat-transfer coefficient. The
theory involves the use of hyperbolic functions.
cylinder wall Fin of constant cross-section with insulated tip

2nk(t, -t2)L kA, Let:
-
4= -- (t,--t,) L = fin length
r2 X
In - A =fin cross-sectional area
rl
P=perimeter of fin
Al=2nrlL; A2=2nr2L; Am=- A2-A1 k =conductivity
In ‘. h = surface heat-transfer coefficient
rl ta = air temperature
x = r2 - r,, L = Length of cylinder t, = fin root temperature
Heat flow from fin, 4= kA(t,-t,)m tanhmL

where: m=&.