Question

Air at 20ºc with a convection heat transfer coefficient of 25 w/m2·k blows over a horizontal steel hot plate (k = 43 w/m·k). the surface area of the plate is 0.38 m2 with a thickness of 2 cm. the plate surface is maintained at a constant temperature of ts = 350°c, and the plate loses 300 w from its surface by radiation. calculate the inside plate temperature (ti). (round your answer up to 3 decimal places.)

Answer 1

Heat transfer due to convection = Heat transfer due to conduction

Heat transfer due to convection, Q = h_c*AdT
Where,
h_c =25 W/m^2K
A = 0.38 m^2
dT = 350 - 20 = 330 K
Substituting;
Q = 25*0.38*330 = 3135 W

Heat transfer through the hot steel plate, Q = (k/s)AdT
k = 43 W/m.k
s = 2 cm = 0.02 m
dT = ti - 350

Therefore,
3135 = (43/0.02)*0.38*(ti-3500
ti-350 = 3135/[(43/0.02)*0.38] = 3.837
ti = 3.837+350 = 353.837°