A 1200-W iron is left on the iron board with its base exposed to ambient air at 26°C. The base plate of the iron has a thickness of L = 0.5 cm, base area of A = 150 cm2 , and thermal conductivity of k = 18 W/m·K. The inner surface of the base plate is subjected to uniform heat flux generated by the resistance heaters inside. The outer surface of the base plate whose emissivity is ε = 0.7, loses heat by convection to ambient air with an average heat transfer coefficient of h = 30 W/m2 ·K as well as by radiation to the surrounding surfaces at an average temperature of Tsurr = 295 K. Disregarding any heat loss through the upper part of the iron,

(a) express the differential equation and the boundary conditions for steady one-dimensional heat conduction through the plate,

(b) obtain a relation for the temperature of the outer surface of the plate by solving the differential equation, and

(c) evaluate the outer surface temperature.

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Explanation:

Given that;

A 1200-W iron is left on the iron board with its base exposed to ambient air at 26°C. The base plate of the iron has a thickness of L = 0.5 cm, base area of A = 150 cm2 , and thermal conductivity of k = 18 W/m·K. The inner surface of the base plate is subjected to uniform heat flux generated by the resistance heaters inside. The outer surface of the base plate whose emissivity is ε = 0.7, loses heat by convection to ambient air with an average heat transfer coefficient of h = 30 W/m2 ·K as well as by radiation to the surrounding surfaces at an average temperature of Tsurr = 295 K. Disregarding any heat loss through the upper part of the iron,

(a) express the differential equation and the boundary conditions for steady one-dimensional heat conduction through the plate,

(b) obtain a relation for the temperature of the outer surface of the plate by solving the differential equation, and

(c) evaluate the outer surface temperature.

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