Question

An electric heater whose total area is 2 ft? and whose volume is 1/12 ft3 is dissipating elec- trical energy at the rate of 5000 watts-17,000 Btu/hr in the steady state while suspended in a room where the air is at 80 F and the average surface coefficient of heat transfer is 30 Btu/hr ft °F. Suddenly, the heater falls (but remains plugged in) on to a rug on the floor which effectively insulates half the heater. For the heater, k 25 Btu/hr ft F, p-500 lbm/ft', and c 0.1 Btu/lbm °R. (a) Calculate the initial steady-state temperature of the heater. (b) If the ignition point of the rug is 500 °F, calculate the time needed for it to reaclh the ignition temperature. 3.65

Answer 1

Let the initial steady state temperature of heater is T

hA ( T -To ) = 17000Btu/hr

=>30×2×( T - 80 )=17000

=> T = 363.33 ^o F

When the heater is fallen it is insulated half,so now the convection heat transfer will occur through half of the area

E× t= h×(A/2)×( Tf-To ) + m c_p ( Tf - T )

Here Tf= 500

=> 17000× t = 30×1×( 500-80) + 500×(1/12)×0.1×(500-366.33)

=>. t=0.7739 Hr