Answered: On a multi-layered square wall, the…

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

On a multi-layered square wall, the thermal resistance of the first layer is 0.005 ° C / W, the resistance of the second layer is 0.3 ° C / W, and the third layer is 0.1 ° C / W. The overall temperature gradient in the wall is multilayered from one side. to the other side is 50 ° C. a. Determine the heat flux through the walls. = Answer watts / m2. b. If the thermal resistance of the second layer is changed to 0.1 ° C / W, what is the effect in% on heat flux, assuming the temperature gradient remains the same? = AnswerAnswer %.

Expert Solution

Given Data

The thermal resistance of first layer is $R_{1} = 0.005 ° C / W$ .

The thermal resistance of second layer is $R_{2} = 0.3 ° C / W$ .

The thermal resistance of third layer is $R_{2} = 0.1 ° C / W$ .

The temperature gradient is $∆ T = 50 ° C$ .

Step 1

(a)

The expression for the total resistance of composite wall is given as,

$R_{t h} = R_{1} + R_{2} + R_{3}$

Substitute the values,

$\begin{array}{rcl} R_{t h} & = & 0.005 ° C / W + 0.3 ° C / W + 0.1 ° C / W \\ R_{t h} & = & 0.405 ° C / W \end{array}$

The expression for the heat flux can be given as,

$Q = \frac{∆ T}{R_{t h}}$

Substitute the values,

$Q = \frac{70 ° C}{0.405 ° C / W} Q = 172.83 W$

Thus, the heat flux through the walls is $172.83 W$ .

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