Question

Air at 25C blows over a hot plate maintained at 300C. The hot plate has dimensions of 50cm width and 75cm lenghth. after small investigation.it has been found that heat transfer is 3.5kW. Provide all assumptions used.

1.Draw a picture to represent the scenario

2.calculate convective heat transfer

3.Assuming that the hot plate is made of carbon steel (1%C) 2cm thick and that an additional 450kW is lost from the plate surface through radiation, calculate inside plate temperature

Answer 1

Assumptions

All heat transfer occurs at steady state conditions

Thermal conductivity is constant over the temperature range within the plate.

No heat is lost during the process

Given data

Air temperature Ta = 25 °C

Hot surface temperature T2 = 300 °C

Area of plate = length x width = 50 cm x 75 cm

= 3750 cm2 x (1m/100cm)²

= 0.375 m2

Thermal conductivity of carbon steel (1%C) k = 41 W/m-K

Thickness L = 2 cm x 1m/100cm = 0.02 m

Part a

Heat transfer by convection q = 3.5 kW x 1000W/kW = 3500 W

q = h x A x (T2 - Ta)

3500 = h x 0.375 x (300 - 25)K

Convective heat transfer coefficient

h = 33.94 W/m2-K

Part b

Heat transfer by conduction = Heat transfer by convection + heat transfer by radiation

kA(T1 - T2)/L = 3500 + 450 x 1000

41 x 0.375 x (T1 - 300)/0.02 = 453500

T1 - 300 = 590

Inside plate temperature T1 = 890 °C