113.2 Viscous heating in laminar tube ﬂow (asymptOtic solutions)
a. From the energy equation we have
60 (avz)z
ppzaz rar ar “ar
Into this we substitute the expression for the velocity distribution of a
Newtonian ﬂuid in a circular tube: 02 = vzimax[1 —
12A.1 Unsteady-state heat conduction in an iron sphere
a. The thermal diffusivity of the sphere is given by Eq. 9.1-8:
k 30
a: A =———=0.573 ftz /hr
,ocp (436)(0.12)
b. The center temperature is to be 128°F; hence
TH—TO _ 128—70
C
_ = 0.29
T1 — To 270 —
10A.8 Temperature rise in an electrical wire
(a) The maximum temperature in the wire occurs at the centerline. Equation 10.2-23 gives
this value as
Tmax Tair
Se R 2 Se R
4k
2h
in which
I 2 ke E 1 E 2 ke
Se
ke L ke L2
2
The Wiedemann-Franz-Lorenz relat
9A.3 Estimation of the thermal conductivity of a dense gas.
a. Table 13.1 gives the following critical constants for methane (CH4): T c =
191.1 K, p6 = 45.8 atm, and he 2 158 X 10‘6 cal/cm-s-K. The reduced conditions
for the prediction are then T, = (459.
10A.2 Heat loss from a rectangular ﬁn.
From Eq. 10.7—14 we obtain the heat loss expression
Q = 2WLh(Tw — Ta) - 77
in which 77 is given by Eq. 10.7—16:
2
= tanhN with N = hL
” N 7973‘
For the conditions of this problem,
hL2 (120 Btu/hr-ftz-F).(0.2 ft)2
=