A large billet of steel initially at 260°C is placed in a radiant furnace where the surface temperature is held at 1200°C. Assuming the billet to be infinite in extent, compute the temperature at point P shown in the accompanying sketch after 25 min have elapsed. The average properties of steel are: k = 28 W/(m K), p = 7360 kg/m3, and c = 500 J/(kg K).
GIVEN
A large billet of steel is placed in a radiant furnace
Initial temperature (To) = 260°C
Surface temperature of billet in the oven (Ts) = 1200°C
Lapse time (t) = 25 min = 1500 s
Thermal conductivity (k) = 28 W/(m K)
Density (p) = 7360 kg/m3
Specific heat (c) = 500 J/(kg K)
FIND
The temperature at point P shown in the accompanying sketch
ASSUMPTIONS
The billet infinite in extent
SKETCH
the solution for a one quarter infinite solid is
Where S(x) and S(y) are solutions for a semi-infinite solid, which are given for a constant surface temperature
by
for the error functional values
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