131.9 Concept of continuum
in highly rarefied flows. In radiation, for example, the continuum breaks down in the
atmosphere beyond 50 km from the mean sea level.
Problems
1.1. Consider the heat transfer from an evacuated filament bulb. List all the perti-
nent heat transfer processes associated with the bulb.
1.2. A widely used method to determine the thermal conductivity of solid material
is to make a thin sheet out of it, thereby reducing the heat transfer across the
material to be one-dimensional. A smart way of measuring the thermal con-
ductivity would be to use a foil heater and sandwich it between two identical
samples of the material, as shown in Fig. 1.7. The four sides (left, right, front,
and back) are insulated to reduce heat losses.
Consider an experiment where two 6 mm plates of the material whose thermal
conductivity is to be estimated are used. The sides of the plates are 20 cm by
20 cm. The heater is energized, and temperatures
TTTT,,,and
1234
are recorded.
After some time, steady-state is reached and the following temperatures are
recorded (see Table 1.3).
Assuming that the thermal conductivity of the material is invariant with respect
to temperature, determine the thermal conductivity of the material when the
electric power used is 40 W.
1.3. Consider a typical freezer compartment that is 1.65 m high, 0.75 m wide, and
0.75 m deep. The freezer is insulated with the help of polyurethane foam with
a thermal conductivity of 0.028 W/m/K. Consider insulation with this material
with a thickness of 200 mm all around the freezer except on the bottom side. If
the outside and inside of the insulation are at 40 and −12 °C, what is the heat
leak into the freezer?
T1,T2,T3, and T4
FIGURE 1.7 Foil heater and sample arrangement.
Table 1.3 Recorded temperature data for problem 1.2.
S. No. Quantity Temperature (°C)
1 T190.4
2 T290.5
3 T381.6
4 T481.7
