The steady-state temperature u ( x , t ) for the boundary-value problem ∂ 2 u ∂ x 2 + ∂ 2 u ∂ y 2 , 0 < y < 1 , x > 0 , u ( 0 , y ) = u 0 , lim x → ∞ u ( x , y ) = 0 , ∂ u ∂ y | y = 0 = 0 and ∂ u ∂ y | y = 1 = − h u ( x , 1 ) , h > 0 , x > 0 .

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Answer 1

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Chapter 12.7, Problem 4E

To determine

The steady-state temperature u(x,t) for the boundary-value problem ∂2u∂x2+∂2u∂y2, 0<y<1, x>0, u(0,y)=u0, limx→∞u(x,y)=0, ∂u∂y|y=0=0 and ∂u∂y|y=1=−hu(x,1), h>0,x>0.

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Answer 2

Question

Chapter 12.7, Problem 4E

To determine

The steady-state temperature u(x,t) for the boundary-value problem ∂2u∂x2+∂2u∂y2, 0<y<1, x>0, u(0,y)=u0, limx→∞u(x,y)=0, ∂u∂y|y=0=0 and ∂u∂y|y=1=−hu(x,1), h>0,x>0.

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Answer 3

Question

Chapter 12.7, Problem 4E

To determine

The steady-state temperature u(x,t) for the boundary-value problem ∂2u∂x2+∂2u∂y2, 0<y<1, x>0, u(0,y)=u0, limx→∞u(x,y)=0, ∂u∂y|y=0=0 and ∂u∂y|y=1=−hu(x,1), h>0,x>0.

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Answer 4

Question

Chapter 12.7, Problem 4E

To determine

The steady-state temperature u(x,t) for the boundary-value problem ∂2u∂x2+∂2u∂y2, 0<y<1, x>0, u(0,y)=u0, limx→∞u(x,y)=0, ∂u∂y|y=0=0 and ∂u∂y|y=1=−hu(x,1), h>0,x>0.

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Answer 5

Chapter 12.7, Problem 4E

To determine

The steady-state temperature u(x,t) for the boundary-value problem ∂2u∂x2+∂2u∂y2, 0<y<1, x>0, u(0,y)=u0, limx→∞u(x,y)=0, ∂u∂y|y=0=0 and ∂u∂y|y=1=−hu(x,1), h>0,x>0.

Answer 6

Chapter 12.7, Problem 4E

To determine

The steady-state temperature u(x,t) for the boundary-value problem ∂2u∂x2+∂2u∂y2, 0<y<1, x>0, u(0,y)=u0, limx→∞u(x,y)=0, ∂u∂y|y=0=0 and ∂u∂y|y=1=−hu(x,1), h>0,x>0.

Answer 7

Chapter 12.7, Problem 4E

To determine

The steady-state temperature u(x,t) for the boundary-value problem ∂2u∂x2+∂2u∂y2, 0<y<1, x>0, u(0,y)=u0, limx→∞u(x,y)=0, ∂u∂y|y=0=0 and ∂u∂y|y=1=−hu(x,1), h>0,x>0.

Answer 8

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Answer 9

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Answer 10

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Answer 11

The steady-state temperature u ( x , t ) for the boundary-value problem ∂ 2 u ∂ x 2 + ∂ 2 u ∂ y 2 , 0 < y < 1 , x > 0 , u ( 0 , y ) = u 0 , lim x → ∞ u ( x , y ) = 0 , ∂ u ∂ y | y = 0 = 0 and ∂ u ∂ y | y = 1 = − h u ( x , 1 ) , h > 0 , x > 0 .

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The steady-state temperature u(x,t) for the boundary-value problem ∂2u∂x2+∂2u∂y2, 0<y<1, x>0, u(0,y)=u0, limx→∞u(x,y)=0, ∂u∂y|y=0=0 and ∂u∂y|y=1=−hu(x,1), h>0,x>0.

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Chapter 12 Solutions

The steady-state temperature u ( x , t ) for the boundary-value problem ∂ 2 u ∂ x 2 + ∂ 2 u ∂ y 2 , 0 &lt; y &lt; 1 , x &gt; 0 , u ( 0 , y ) = u 0 , lim x → ∞ u ( x , y ) = 0 , ∂ u ∂ y | y = 0 = 0 and ∂ u ∂ y | y = 1 = − h u ( x , 1 ) , h &gt; 0 , x &gt; 0 .

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The steady-state temperature u(x,t) for the boundary-value problem ∂2u∂x2+∂2u∂y2, 0<y<1, x>0, u(0,y)=u0, limx→∞u(x,y)=0, ∂u∂y|y=0=0 and ∂u∂y|y=1=−hu(x,1), h>0,x>0.

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Chapter 12 Solutions

The steady-state temperature u ( x , t ) for the boundary-value problem ∂ 2 u ∂ x 2 + ∂ 2 u ∂ y 2 , 0 < y < 1 , x > 0 , u ( 0 , y ) = u 0 , lim x → ∞ u ( x , y ) = 0 , ∂ u ∂ y | y = 0 = 0 and ∂ u ∂ y | y = 1 = − h u ( x , 1 ) , h > 0 , x > 0 .