An electric heating blanket is subjected to an acceptance test. It is to dissipate 400 W on the high setting when hanging in air at 20°C. (a) If the blanket is 1.3-m-wide: what is the length required if its average temperature at the high setting is to be 40°C, (b) If the average temperature at the low setting is to be 30°C, what rate of dissipation is possible?

Question

GIVEN

• An electric blanket hanging in air

• Heat dissipation rate (qh) = 400 W

• Air temperature (T?) = 20°C

• Blanket width (w) = 1.3 m

• Average temperatures ? High (Tsh) = 40°C

? Low (Ts1) = 30°C

FIND

(a) The length of the blanket (L) (b) Heat dissipation rate on the low setting (q1) ASSUMPTIONS

• Air is still

• Moisture in the air has a negligible effect

• Blanket is hung vertically with its 1.3 m sides vertical

SKETCH



PROPERTIES AND CONSTANTS

for dry air at the mean temperatures for the two settings

Answer 1

(a) On the high setting, the Grashof number for the blanket is



Therefore, the boundary layer is turbulent and the natural convection heat transfer coefficient



The rate of heat transfer from both sides of the blanket is



Solving for the length of the blanket



(b) The Grashof number for the blanket on the low setting is



This is still turbulent, therefore



The heat dissipation rate possible is equal to the rate of convection from both sides