g Steel plates (AISI 1010) of 4 cm thickness initially at a uniform temperature of 500 deg C are cooled by air at 50 deg C with a convection coefficient of 30 W-m2-K-1. Estimate the time it will take for their midplane temperature to reach 100 deg C.

Solution :

Characteristic length  = thickness / 2

                                    = 0.02 m

Thermal conductivity for steel is 42.5 W/m.K

                  = 0.014

Since the Biot number is less than 0.01, the lumped system analysis is applicable.

Where,

T = temperature after t time

= surrounding temperature

= initial temperature

t = time

We calculate B:

  = 0.000416

Thus,

t = 5281.78 second

  = 88.02 minutes

Thus the time taken for reaching 100 degree Celsius is 88.02 minutes.

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