(a)Starting from first principles, show that the general equation for conduction in asolid in Cartesian coordinates is107 ) + 2 (K₂)ƏT д ƏT+ k,Əzдуəzwhere symbols have their usual meaning.9gəƏxkxpcpatôt

Answered: Starting from first principles, show…

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)
Starting from first principles, show that the general equation for conduction in a
solid in Cartesian coordinates is
107 ) + 2 (K₂)
ƏT д ƏT
+ k,
Əz
ду
əz
where symbols have their usual meaning.
9g
ə
Əx
kx
pcp
at
ôt

Expert Solution

Step 1 Introduction of Steady State Heat Conduction Equation.

In the case of steady-state heat conduction, the temperature ceases to be a function of time as well as space coordinates. Hence, steady state conduction can be expressed as

$T = f (x, y, z, t)$

Under many practical situations, heat conduction is significant only in one direction of the coordinate axis. The heat conduction is termed as One-Dimensional Heat Conduction equation and temperature becomes

$T = f (x, t)$

In case of Steady State Heat Conduction Equation, the temperature function is independent of time.

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