There is a metal plate with thickness, length, width, thermal conductivity, density, and specific heat of 10mm, 2 m, 1m, 200 W/m·°C, 2500 kg/m3, and 900 J/kg. K, respectively. It has an initial uniform temperature of 22°C and is being heated in an oven for 2 minutes. Air in the oven is maintained at 900 C with convection heat transfer coefficient of 190 W/m2.K. Determine the temperature of the plate when it is removed from the oven.\

788°C

Explanation:

Metal palte details

Thickness = t=10 mm =0.01 m.

Thermal conductivity= k =200 W/mC

Heat capacity C=900 J/kg-k.

Initial temp Ti =22 C.

Time for which it has been kept in oven =t=2 min =120 sec.

Air properties.

Temp of air in oven =Ta =900 C

Heat transfer coefficient =h =190 W/m-k.

Temp of block after 2 min= T =?

In problem, it is not given block dimension. Let us assume that Block is 1 m in legth and 1 m in width.

Volume of block =V= 1*1*0.01 =0.01 m3 .(We know thckness =0.01 m).

Surface area of block = A=2(1*1+1*0.01+0.01*1)=2.04 m2.

Biot number for this problem is 0.004656 which is less than 0.1. So Lumped capacitance method is applicable to this problem, according to formulae,

T - Tair /Ti - Tair =e(-hAt/density* C* V) .

T - 900/(22-900) = e(-190*2.04*120 /2500*900*0.01) .

T - 900/(22-900) =e-2.0672 .

T -900 = - 110.09

Temp of block after 2 min =788 °C.

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