Chapter 16.7, Problem 47E

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8th Edition

James Stewart

ISBN: 9781285741550

Textbook Problem

The temperature at the point (*x, y, z*) in a substance with conductivity *K* = 6.5 is *u*(*x*, y, *z*) *=* 2*y*^{2} + 2*z*^{2}. Find the rate of heat flow inward across the cylindrical surface *y*^{2}* + z*^{2} *-* 6, 0 ≤ *x* ≤ 4.

To determine

**To find:** The rate of heat flow inward across the cylindrical surface

Explanation

**Given:**

**Formula used:**

Let

Find

Substitute

Find

Modify equation (2).

Substitute

Find

Modify equation (2).

Substitute

Find

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