Concept explainers
A 1000-W iron is left on the ironing board with its base exposed to the air at 23°C. The convection heat transfer coefficient between the base surface and the surrounding air is 20 W/m2·°C. If the base has an emissivity of 0.4 and a surface area of 0.02 m2, determine the temperature of the base of the iron.
The temperature of the base of the iron.
Answer to Problem 101P
The temperature of the base of the iron is
Explanation of Solution
Since the 1000 W iron is left on the ironing board, so it is supplying energy to the surooundings by convection and radiation heat transfer.
Write the equation of the total rate of heat transfer.
Here, the rate of heat transfer by convection and radiation are
Calculate the rate of heat transfer by convection.
Here, change in the temperature is
Calculate the rate of heat transfer by radiation.
Here, emissivity of the base surface is
Conclusion:
Substitute 1000 W for
Substitute
Substitute
Substitute
Solve equation (V) using hit and trial method as in Table (1).
Equation (V) | |
900 | 535.72 |
1000 | 731.71 |
1100 | 982.23 |
1106 | 999.242 |
1200 | 1298.70 |
1300 | 1693.64 |
From Table (1), it is shown that at the value of 999.242, equation (V) right side is equal to the left side value of 1000 W. Therefore, the temperature at value of 999.242 is 1106 K.
Convert the unit of temperature,
Thus, the temperature of the base of the iron is
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