Explanation Let S be a closed surface that bounds D . The amount of heat leaving D per unit time is ∬ S F → ⋅ N → d S . According to the divergence theorem, ∬ S F → ⋅ N → d S = ∭ D div ( − K ∇ T − T ∇ K ) d V = ∭ D ( − K ∇ ⋅ ∇ T − ∇ K ⋅ ∇ T ) d V =

Calculus: Special Edition: Chapters 1-5 (w/ WebAssign)

6th Edition

ISBN: 9781524908102

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Chapter 13.7, Problem 52PS

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To prove: Thatif K(x,y,z) is a variable, then show that the heat equation becomes K∇2T+∇K⋅∇T=σρ∂T∂t

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Chapter 13.7, Problem 51PS

Chapter 13.7, Problem 53PS

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Calculus: Special Edition: Chapters 1-5 (w/ WebAssign)

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To prove: Thatif K ( x , y , z ) is a variable, then show that the heat equation becomes K ∇ 2 T + ∇ K ⋅ ∇ T = σ ρ ∂ T ∂ t

Solution Summary: The author explains that K(x,y,z) is a variable and shows that the heat equation becomes

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To prove: Thatif K(x,y,z) is a variable, then show that the heat equation becomes K∇2T+∇K⋅∇T=σρ∂T∂t

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