In the heat treating process in a sheet-metal manufacturing plant, brass plates are annealed by first heating them in an industrial furnace oven the inside of which is maintained at a constant uniform temperature of 550°C. If the surface of the brass plate, which has a thickness of 2.5 cm, is initially at a uniform temperature of 25°C, determine the time required for heating the plate surface to 300°C after the plate has been placed inside the oven. Consider that heat transfer from the oven gases to the plate is by convection and that 135 ch = W/m2 K.

Question

GIVEN

• Brass plate of thickness L=2.5 cm=0.025 m

• Initial temperature of the plate (To) = 25°C

• Heat treating oven temperature (T?) = 550°C

• Convective heat transfer coefficient ( ch ) = 135 W/(m2 K)

FIND

• The time required for the plate to reach temperature of 3000C.

ASSUMPTIONS

• Constant thermal conductivity

• End effects are negligible

SKETCH



PROPERTIES AND CONSTANTS

As per the information provided:

Thermal conductivity (k) = 50 W/(m K) Specific heat (c) = 460 J/(kg K) Density (?) = 7865 kg/m3

Answer 1

For a flat plate we have Lc=L/2= 0.0125 m

Biot number(Bi)= ch Lc/k=45*0.0125/50=0.0135 which is << 0.1

Thus the flat plate can be considered as lumped capacitance. Therefore, the internal resistance of the rod is negligible.

The temperature-time history of the rod,