c) What is the temperature of the iron heating element at x=30mm (in ∘C)? Use the origin defined in the given diagram. d) At which position x (in mm) does the iron heating element experience its highest temperature? e) In this scenario outlined in this question (constant heat generation under steady-state, 1-D conditions), can the temperature distribution in the iron ever be linear? Yes or No? Justify your reasoning.

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Chapter3: Transient Heat Conduction
Section: Chapter Questions
Problem 3.7P
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c) What is the temperature of the iron heating element at x=30mm (in ∘C)? Use the origin defined in the given diagram.

d) At which position x (in mm) does the iron heating element experience its highest temperature?

e) In this scenario outlined in this question (constant heat generation under steady-state, 1-D conditions), can the temperature distribution in the iron ever be linear? Yes or No? Justify your reasoning.

The heating element of a clothes iron is 30mm thick, and has a thermal conductivity of 40W/mK.
You can assume that the iron is at steady state. You are asked to assume that the volumetric heat
generation rate in the iron is constant (but non-zero) because it is tumed on. Consider a 1-D
scenario of the heat diffusion equation and assume that the iron is one dimensional (its temperature
varies only in the x direction). The side of the iron at x = 0mm is maintained at a constant
temperature of 200°C and is perfectly insulated. The side of the iron at x = 30mm is in contact
with cool air at a temperature of 20° C and experiences convection. The heat transfer coefficient
between the side of the iron at = 30mm and ambient air is 40W/m²K. Don't forget to draw a
"translated" version of this geometry on your written work submission, with each known condition
and location clearly labeled.
30mm
Transcribed Image Text:The heating element of a clothes iron is 30mm thick, and has a thermal conductivity of 40W/mK. You can assume that the iron is at steady state. You are asked to assume that the volumetric heat generation rate in the iron is constant (but non-zero) because it is tumed on. Consider a 1-D scenario of the heat diffusion equation and assume that the iron is one dimensional (its temperature varies only in the x direction). The side of the iron at x = 0mm is maintained at a constant temperature of 200°C and is perfectly insulated. The side of the iron at x = 30mm is in contact with cool air at a temperature of 20° C and experiences convection. The heat transfer coefficient between the side of the iron at = 30mm and ambient air is 40W/m²K. Don't forget to draw a "translated" version of this geometry on your written work submission, with each known condition and location clearly labeled. 30mm
Expert Solution
Step 1

(c)

Write the given data.

Thickness of heating element, t=30 mmThermal conductivity, k=40 W/mKTat x=0=200 °CT=20 °CHeat transfer coefficient for ambient air, h=40 W/m2K

 

 

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