Answered: A cylindrical tube has an inner…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

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 $\to D_{i} = 2 C m = 0.02 m$

So the inner radius of the tube is $\to r_{i} = \frac{D_{i}}{2} = \frac{0.02}{2} = 0.01 m$

Thickness of the wall $\to t = 1 C m = 0.01 m$

So the outer radius of the tube is $\to r_{o} = r_{i} + t = 0.01 + 0.01 = 0.02 m$

Thermal conductivity of the tube $\to k = 2 W / m K$

Temperature of the water is 298 K

Convective heat transfer coefficient $\to h = 100 W / m^{2} K$

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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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