Consider a one-dimensional plane wall of thickness 2L that experiences uniform volumetric heat generation. The surface temperatures of the wall are maintained at T₁1 and T,2 as shown in the sketch. Verify, by direct substitution, that an expression of the form T(x) = qL² 2k x² T₁2-T₁.1 XT₁1 + T5.2 2 L 1² 2 Ist satisfies the steady-state form of the heat diffusion equation. Determine an expression for the heat flux dis- tribution, q"(x). + -L +L IS2

Consider a one-dimensional plane wall of thickness 2L that experiences uniform volumetric heat generation. The surface temperatures of the wall are maintained at T₁1 and T,2 as shown in the sketch. Verify, by direct substitution, that an expression of the form T(x) = qL² 2k x² T₁2-T₁.1 XT₁1 + T5.2 2 L 1² 2 Ist satisfies the steady-state form of the heat diffusion equation. Determine an expression for the heat flux dis- tribution, q"(x). + -L +L IS2

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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Concept explainers

Conduction and Convection

When energy travels from one object to another it is said to have undergone heat transfer. Heat transfer is nothing but the transfer of thermal energy or internal energy from one thing to another, like e.g., when a vessel with water, kept on top of a burner, heats up because of the flame underneath it.

Question

2.19 Consider a one-dimensional plane wall of thickness 2L
that experiences uniform volumetric heat generation.
The surface temperatures of the wall are maintained at
T₁1 and T2 as shown in the sketch. Verify, by direct
substitution, that an expression of the form
T(x) =
X
qL²
2k
2²/1 (1 - 2 ² )
Tsit
+
satisfies the steady-state form of the heat diffusion
equation. Determine an expression for the heat flux dis-
tribution, q"(x).
-L
T₁,2 - T₁.1 X T.1 + T.2
2 L
+
2
+L
I s.2

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