Question

A convection space heater sold at Bass Pro Shop advertises 9000 BTU/hr of heating power. The heater works by forcing 40 ft³/min of ambient air past the heating coils, then emitting the heated air to the room, where it mixes with the cold air in the room.

Part A) You decide to buy this space heater for your screened porch, and begin using it on a night where the temperature is 54°F and the barometric pressure is 100 kPa. If the heat loss from the heating unit is 200 W, what is the temperature of the exit air?

Part B) You move the space heater to an enclosed 100 ft³ room that is initially 64°F. As you let the heater operate, the heated outlet air mixes with the cooler air in the room, which raises the room temperature. Consequently, the inlet air temperature becomes greater as time passes, which further increases the temperature of the outlet air in a positive-feedback loop.

If you leave the room and forget to turn off the heater, will the temperature of the room continue to rise indefinitely, or is there a temperature at which steady-state is achieved? If there is a steady-state temperature, calculate it.

Part C) Given the result of part B, are there any safety features that you would consider incorporating into the heating unit?

A convection space heater sold at Bass Pro Shop advertises 9000 BTU/hr of heating power. The heater works by forcing 40 ft³/min of ambient air past the heating coils, then emitting the heated air to the room, where it mixes with the cold air in the room.

T = 118°C

Part A) You decide to buy this space heater for your screened porch, and begin using it on a night where the temperature is 54°F and the barometric pressure is 100 kPa. If the heat loss from the heating unit is 200 W, what is the temperature of the exit air?

Part B) You move the space heater to an enclosed 100 ft³ room that is initially 64°F. As you let the heater operate, the heated outlet air mixes with the cooler air in the room, which raises the room temperature. Consequently, the inlet air temperature becomes greater as time passes, which further increases the temperature of the outlet air in a positive-feedback loop.

The temperature will keep rising indefinitly

If you leave the room and forget to turn off the heater, will the temperature of the room continue to rise indefinitely, or is there a temperature at which steady-state is achieved? If there is a steady-state temperature, calculate it.

Part C) Given the result of part B, are there any safety features that you would consider incorporating into the heating unit?

Answer 1

solution : The space heates for your screened posich, and being beyin using it on night where the temperature The barometric pressusie is 100 kPa. It The heat loss from the heating units is 2oow. ) heat loss from the heates) Q = 2006 - 2003) ais flow in the heaten = 40 cu.ft/min = 0.0189 cu.m)s mass of air flowing = 0.0189 * 1.23 = 0.023 kg/s heat capacity of air Cp = 1010 J/kg-K. Q = cp* m* AT AT = 200/0.023*100 = 553 K = 15:35 F Tempasatuse of the ais - 54.0 + 15:35 = 69.35 F b) Temp. in the room increases with time. The room will loose some heat to the outside environment. The loss of heat from the room depends on the out side temp. and the room insulation. We need to know these parameters to know the heat loss from the room. The temp. in the room reaches a steady state when the heat given out by the heater is equal to the heat loss from the room. c) The heating unit shall have a temparature controle such that it will shut down when the desired temp is reached in the sunsounding) The indet temparature.