A cylindrical tube has an inner diameter of 2 cm and a wall thickness of 1 cm. The tube is evacuated. In the center, there is a radiation source along its axis that sends 1e^5 W/m^2 to the inner surface of the tube. K for the tube wall is 2 W/m K. If the outer surface of the tube is cooled with water at 298 K with a convective heat transfer coefficient of 100 W/m^2 K, determine the minimum temperature rating for the tube material for safe operation.

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
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A cylindrical tube has an inner diameter of 2 cm and a wall thickness of 1 cm. The tube is
evacuated. In the center, there is a radiation source along its axis that sends 1e^5 W/m^2
to the inner surface of the tube. K for the tube wall is 2 W/m K. If the outer surface of
the tube is cooled with water at 298 K with a convective heat transfer coefficient of 100
W/m^2 K, determine the minimum temperature rating for the tube material for safe
operation.

Expert Solution
Step 1

Given:

Inner diameter of the tube is Di=2 Cm=0.02 m

So the inner radius of the tube isri=Di2=0.022=0.01 m

Thickness of the wall t=1 Cm=0.01 m

So the outer radius of the tube is ro=ri+t=0.01+0.01=0.02 m

Thermal conductivity of the tubek=2 W/mK

Temperature of the water is 298 K

Convective heat transfer coefficient h=100 W/m2K

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how did you find the equation for L in step 2 and also why isnt h mulplied by the Area when solving for the total resistance?

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