Starting from first principles, show that the general equation for conduction in a solid in Cartesian coordinates is a d 9₂ + ax (K. OT) + (K, OT) + O₂(K, 07). k where symbols have their usual meaning. at at =pcp²
Starting from first principles, show that the general equation for conduction in a solid in Cartesian coordinates is a d 9₂ + ax (K. OT) + (K, OT) + O₂(K, 07). k where symbols have their usual meaning. at at =pcp²
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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
Transcribed Image Text:(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
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
In case of Steady State Heat Conduction Equation, the temperature function is independent of time.
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