A long iron rod (r = 7870 kg/m3, cp = 447 J/kg·K,k = 80.2 W/m·K, and a = 23.1 * 10–6 m2/s) with diameter of25 mm is initially heated to a uniform temperature of 700°C.The iron rod is then quenched in a large water bath that is maintained at constant temperature of 50°C and convection heat transfer coefficient of 128 W/m2·K. Determine the time required for the iron rod surface temperature to cool to 200°C. Solve this problem using analytical one-term approximation method (not the Heisler charts).

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Chapter1: Units, Trigonometry. And Vectors
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A long iron rod (r = 7870 kg/m3, cp = 447 J/kg·K,
k = 80.2 W/m·K, and a = 23.1 * 10–6 m2/s) with diameter of
25 mm is initially heated to a uniform temperature of 700°C.
The iron rod is then quenched in a large water bath that is maintained at constant temperature of 50°C and convection
heat transfer coefficient of 128 W/m2·K. Determine the
time required for the iron rod surface temperature to cool to
200°C. Solve this problem using analytical one-term approximation
method (not the Heisler charts).

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