(a)
q w = constant
T i
(b)
Temp
T i
T w
q ″ w
T w
T(r)
T b
x
X f,t
Thermally fully developed
(c)

15

hD

k

hD
4.3 = Nu =
k
x
""
q =
q w = h(T w − T b )
(8.15)
w
A s
""
q =
q w = h(T w − T b )
(8.16)
w
'-v'
A s
' -v '
const.
const.
Bulk mean temperature
From energy balance,
""
q =
w
""
q =
w
�
0
R ρuT · 2πr dr
T b =
(8.17)
�
0
R ρu · 2πr dr
q w = ˙
(8.18)
mC p (T b,o − T b,i )/A s
A s
˙
dT b
dT b
mC p
⇒
= const
(8.19)
πD dx
dx
173
Internal Forced Convection
FIGURE 8.5
Laminar flow in a circular tube with uniform surface heat flux condition. (a) Thermal boundary
layer; (b) temperature; and (c) heat transfer coefficient.