A room is to be heated by a coal-burning stove, which is a cylindrical cavity
with an outer diameter of \(32 \mathrm{~cm}\) and a height of \(70 \mathrm{~cm}\).
The rate of heat loss from the room is estimated to be \(1.5 \mathrm{~kW}\) when
the air temperature in the room is maintained constant at \(24^{\circ}
\mathrm{C}\). The emissivity of the stove surface is \(0.85\), and the average
temperature of the surrounding wall surfaces is \(14^{\circ} \mathrm{C}\).
Determine the surface temperature of the stove. Neglect the heat transfer from
the bottom surface and take the heat transfer coefficient at the top surface
to be the same as that on the side surface.
The heating value of the coal is \(30,000 \mathrm{~kJ} / \mathrm{kg}\), and the
combustion efficiency is 65 percent. Determine the amount of coal burned a day
if the stove operates \(14 \mathrm{~h}\) a day. Evaluate air properties at a
film temperature of \(77^{\circ} \mathrm{C}\) and \(1 \mathrm{~atm}\) pressure. Is
this a good assumption?