Page 339 - Bird R.B. Transport phenomena

Problems 323

Fig. 10B.4. Temperature profile in an annular wall.

10B.5. Viscous heat generation in a polymer melt. Rework the problem discussed in §10.4 for a
molten polymer, whose viscosity can be adequately described by the power law model (see
Chapter 8). Show that the temperature distribution is the same as that in Eq. 10.4-9 but with
the Brinkman number replaced by

mv" +
b
(10B.5-1)
10B.6. Insulation thickness for a furnace wall (Fig. 10B.6). A furnace wall consists of three layers:
(i) a layer of heat-resistant or refractory brick, (ii) a layer of insulating brick, and (iii) a steel
plate, 0.25 in. thick, for mechanical protection. Calculate the thickness of each layer of brick to
give minimum total wall thickness if the heat loss through the wall is to be 5000 Btu/ft 2 • hr,
assuming that the layers are in excellent thermal contact. The following information is
available:
Maximum Thermal conductivity
allowable (Btu/hr • ft • F)
Material temperature at100°F at 2000°F
Refractory brick 2600°F 1.8 3.6
Insulating brick 2000°F 0.9 1.8
Steel 26.1

Answer: Refractory brick, 0.39 ft; insulating brick, 0.51 ft.
10B.7. Forced-convection heat transfer in flow between parallel plates (Fig. 10B.7). A viscous fluid
with temperature-independent physical properties is in fully developed laminar flow be-
tween two flat surfaces placed a distance 2B apart. For z < 0 the fluid temperature is uniform
at T = 7\. For z > 0 heat is added at a constant, uniform flux q at both walls. Find the temper-
0
ature distribution T(x, z) for large z.
(a) Make a shell energy balance to obtain the differential equation for T(x, z). Then discard
the viscous dissipation term and the axial heat conduction term.

Steel plate
N

ск
м 100°F
t ьо
о •я
Refra 1

Fig. 10B.6. A composite furnace wall.