Page 340 - Bird R.B. Transport phenomena

324 Chapter 10 Shell Energy Balances and Temperature Distributions in Solids and Laminar Flow

Fig. 10B.7. Laminar, incompressible flow
between parallel plates, both of which are
being heated by a uniform wall heat flux q 0
starting at z = 0.
ъ Z = 0

Fully developed vAx) Direction
slit flow at of flow
z = 0; inlet
temperature
isT,
= -B x = +B

(b) Recast the problem in terms of the dimensionless quantities
TT kz (10B.7-l,2,3)
q B/k В
0
(c) Obtain the asymptotic solution for large z:

= U + -У - W - ш (10B.7-4)
10B.8. Electrical heating of a pipe (Fig. 10B.8). In the manufacture of glass-coated steel pipes, it is
common practice first to heat the pipe to the melting range of glass and then to contact the hot
pipe surface with glass granules. These granules melt and wet the pipe surface to form a
tightly adhering nonporous coat. In one method of preheating the pipe, an electric current is
passed along the pipe, with the result that the pipe is heated (as in §10.2). For the purpose of
this problem make the following assumptions:
(i) The electrical conductivity of the pipe k is constant over the temperature range of in-
c
terest. The local rate of electrical heat production S is then uniform throughout the pipe wall.
e
(ii) The top and bottom of the pipe are capped in such a way that heat losses through
them are negligible.
(iii) Heat loss from the outer surface of the pipe to the surroundings is given by New-
ton's law of cooling: q r = h(T - T ). Here h is a suitable heat transfer coefficient.
a
x
How much electrical power is needed to maintain the inner pipe surface at some desired
temperature, T , for known k, T h, and pipe dimensions?
K
af

Fig. IOB.80 Electrical heating of a pipe.