A10-cm-thick aluminum plate (α = 97.1 × 10−6 m2/s) is being heated in liquid with temperature of 475°c. the aluminum plate has a uniform initial temperature of 25°c. if the surface temperature of the aluminum plate is approximately the liquid temperature, determine the temperature at the center plane of the aluminum plate after 15 s of heating. solve this problem using the analytical one-term approximation method.

Explanation:

Given data:

Thickness of aluminium sheet 10 cm

initial temperature = 25 degree celcius

Assumption

Thermal properties remain constant, transfer of heat by radiation is negligible.

from the information given in the question we have

T_S ≈T_∞ , it implies we have h → ∞

from table 4.2 Biot number → ∞ the value of

The fourier number is

Temperature at center after 15 second of heating

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