Solutions to Practical Problems
1. Greenhouse – The greenhouse works due to selective transmissivity of glass.
Short wave radiation from sun is transmitted through the glass; long wave
radiation from plants is blocked. Internal temperature rises until heat gain by
radiation balances shell heat loss.
2. Insulation – Insulation inhibits air movement, which eliminates convection.
Hence, heat transfer occurs by conduction through air/glass fiber blend and by
radiation between fibers. For radiation, color matters. But pink and yellow have
about the same emissivity, so little difference could be detected.
3. Parallel plates on heaters – Plates act as fins, which increase the area for
convection from the heater to the surrounding air. Q = h A ∆T. For a Q set by
heater power, as A↑ the ∆T↓ for the same h value. Reducing ∆T lowers the
operating temperature of the heating element (increases useful life) and reduces
surface temperature of all parts (safety).
4. Thermos bottle – The thermos bottle flask is a sealed, double wall container. Air
is evacuated between the two walls, so only radiation can transmit thermal energy,
which greatly inhibits heat loss. Coating the surfaces with a shiny layer (silver)
reduces the emissivity to reduce radiation losses further.
5. Chill factor – The human body internally generates thermal energy which is lost
continuously by convection at the surface (as well as respiration and perspiration).
The heat loss in still air can be calculated by Q = h A ∆T, where ∆T = Tsurface - T∞.
When the wind blows, the convective heat transfer coefficient hwind is much
larger, so the heat loss is the same as it would be for still air with the original h
but a much lower temperature Twind chill.
Q = h A (Tsurface - Twind chill) = hwind A (Tsurface - T∞)
6. Thermal touch – When objects initially at a temperature lower than that of the
skin surface is touched, heat will be lost to that object. The initial rate of heat lost
affects the sensation of “warm” or “cool”. That rate is predicted by factor
p
Ck
ρ
for the material being touched: the larger this factor, the cooler an object
will feel. (See section 5.7 of Incropera and DeWitt).
7. Car roof frost – A car’s roof will reach an equilibrium temperature which
balances the convection from surrounding air and radiation loss to the clear sky.
Since deep space is approximately -40ºF, the roof’s surface can cool to below the
freezing point. During day, indirect radiation changes the balance. The side of
the car does not freeze because of reduced shape factor with the cold sky.
