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 =

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ISBN: 9781524916817

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

Publisher: Kendall Hunt Publishing

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

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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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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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Chapter 13 Solutions