High-strength stainless steel is required for use in building structures and equipment (e.g. , cranes). It is produced by heat treating quench-hardened steel in a process called tempering that reduces brittleness and imparts toughness. In a production facility, alloy steel plates (k=50 W/(m K), c=460 J/(kg K) and ?=7865 kg/m3) of thickness 3 cm have to be tempered in a convective oven by heating them to 5500C. If the plates are initially at 400C and the air inside the heat treating oven is at 7000C with a convective heat transfer coefficient of 45 W/(m2 K), determine how long the plate has to remain in the oven.

Question

GIVEN

• Alloy steel plate of thickness L=3 cm=0.03 m

• Tempering in oven to 5500C

• Initial temperature of the plate (To) = 40°C

• Heat treating oven temperature (T?) = 700°C

• Convective heat transfer coefficient ( ch ) = 45 W/(m2 K)

FIND

• The time required for the plate to reach 5500C.

ASSUMPTIONS

• Constant thermal conductivity

• End effects are negligible

SKETCH

Answer 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, is