Explanation Rate of heat flow across a surface S within the solid given by − K ∫ I s ∇ w . d s → assuming this as 1 st equation. In this problem, w ( x , y , z ) = 20 − 5 ( x 2 + y 2 + z 2 ) e o Observing the spherical symmetry of the problem let us change to spherical polar co-ordinates ( ρ , θ , φ ) In this co-ordinate system x 2 + y 2 + z 2 = ρ 2 (Where ρ is the distance from the origin) ∴ w ( ρ ) = 20 − 5 ( ρ 2 ) e o Let us take the gradient of w ( r ) in spherical-polar coordinate. ∴ ∇ w= ∂ w ∂ r ρ ¯ + 1 ρ ∂ w ∂ θ θ ¯ + 1 ρsinθ ∂ w ∂ φ φ ¯ = ∂ ∂ ρ (20-5ρ 2 ) ρ ¯ +0+0 ∇ w = -10ρ ρ ¯ This be the second equation Now, the surface of this problem is a sphere of radius 1m...

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ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 17.5, Problem 34E

To determine

To find the rate of heat flow out the sphere of radius 1 meter inside a large cube of copper.

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Chapter 17.5, Problem 33E

Chapter 17.5, Problem 35E

Chapter 17 Solutions

CALCULUS (CLOTH)

Ch. 17.1 - Prob. 1PQ Ch. 17.1 - Prob. 2PQ Ch. 17.1 - Prob. 3PQ Ch. 17.1 - Prob. 4PQ Ch. 17.1 - Prob. 1E Ch. 17.1 - Prob. 2E Ch. 17.1 - Prob. 3E Ch. 17.1 - Prob. 4E Ch. 17.1 - Prob. 5E Ch. 17.1 - Prob. 6E

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01 - What Is an Integral in Calculus? Learn Calculus Integration and how to Solve Integrals.; Author: Math and Science;https://www.youtube.com/watch?v=BHRWArTFgTs;License: Standard YouTube License, CC-BY

To find the rate of heat flow out the sphere of radius 1 meter inside a large cube of copper.

Solution Summary: The author explains how to determine the rate of heat flow across a surface S within the solid.

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To find the rate of heat flow out the sphere of radius 1 meter inside a large cube of copper.

Want to see the full answer?

Chapter 17 Solutions