Page 337 - Bird R.B. Transport phenomena

Problems 321

"T = 61 °F I Surface temperatures
2
- T} = 69°F J °f plastic panel
= V
1 3
Wall
^ Plastic panel has
thermal conductivity
к = 0.075
Btu/hr • ft • °F
(average value between
T-t and T )
2
6"-
-0.502"
Fig. 10A.6. Determination of the thermal resistance of
a wall.

10A.6. Insulating power of a wall (Fig. 10A.6). The "insulating power" of a wall can be measured
by means of the arrangement shown in the figure. One places a plastic panel against the wall.
In the panel two thermocouples are mounted flush with the panel surfaces. The thermal con-
ductivity and thickness of the plastic panel are known. From the measured steady-state tem-
peratures shown in the figure, calculate:
(a) The steady-state heat flux through the wall (and panel).
(b) The "thermal resistance" (wall thickness divided by thermal conductivity).
2
Answers: (a) 14.4 Btu/hr • ft ; (b) 4.24 ft 2 • hr • F/Btu
10A.7. Viscous heating in a ball-point pen. You are asked to decide whether the apparent decrease
in viscosity in ball-point pen inks during writing results from "shear thinning" (decrease in
viscosity because of non-Newtonian effects) or "temperature thinning" (decrease in viscosity
because of temperature rise caused by viscous heating). If the temperature rise is less than IK,
then "temperature thinning" will not be important. Estimate the temperature rise using Eq.
10.4-9 and the following estimated data:

Clearance between ball and holding cavity 5 X 1(Г in.
Э
Diameter of ball 1 mm
Viscosity of ink 10 cp
4
Speed of writing 100 in./min
4
Thermal conductivity of ink (rough guess) 5 X 10~ cal/s-cm-C
10A.8. Temperature rise in an electrical wire.
(a) A copper wire, 5 mm in diameter and 15 ft long, has a voltage drop of 0.6 volts. Find the
maximum temperature in the wire if the ambient air temperature is 25°C and the heat transfer
coefficient h is 5.7 Btu/hr • ft 2 • F.
(b) Compare the temperature drops across the wire and the surrounding air film.

10B.1. Heat conduction from a sphere to a stagnant fluid. A heated sphere of radius R is sus-
pended in a large, motionless body of fluid. It is desired to study the heat conduction in the
fluid surrounding the sphere in the absence of convection.
(a) Set up the differential equation describing the temperature T in the surrounding fluid as a
function of r, the distance from the center of the sphere. The thermal conductivity к of the
fluid is considered constant.
(b) Integrate the differential equation and use these boundary conditions to determine the in-
tegration constants: at r = R, T = T ; and at r = °°, T = T .
K
R