The left end of a rod of length I is held at temperature 130, and there is heat transfer from the right end into the surrounding medium at temperature zero. The initial temperature at any point is given by f(a). Select the partial differential equation that can be used to model this scenario. 8²u daª J²u Ju Ja J²u 2²u 02:² Ət² Select ALL boundary/initial conditions that apply to this scenario 8²u O A. a² OB.k O c. + It' ¹ 0 0 0 0 = 0, 0 0 A. (L, t) = 0, CB.«(2,0) = 0, c. u(x, 130) = f(x), 00 0 0 t> 0 t> 0

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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The left end of a rod of length I is held at temperature 130, and there is heat transfer from the right end into the surrounding medium at temperature zero. The initial temperature at any point is given by f(a).
Select the partial differential equation that can be used to model this scenario.
8²u
daª
J²u Ju
Ja
J²u 2²u
02:² Ət²
Select ALL boundary/initial conditions that apply to this scenario
8²u
O A. a²
OB.k
O c. +
It'
¹ 0<x<L₂t> 0
0<x<L,t> 0
= 0, 0<x<L,t> 0
A. (L, t) = 0,
CB.«(2,0) = 0,
c. u(x, 130) = f(x), 0<x<L
] D. u(x, L) = f(x), 0<x<L
t>0
0<a<L
E. (,0) 130, 0<x<L
OF. u(a,0) = f(x),
0<x<L
G. (0,t) = L,
OH. u(0, t) = 0,
1. (0, t) 130,
t> 0
t> 0
t> 0
Transcribed Image Text:The left end of a rod of length I is held at temperature 130, and there is heat transfer from the right end into the surrounding medium at temperature zero. The initial temperature at any point is given by f(a). Select the partial differential equation that can be used to model this scenario. 8²u daª J²u Ju Ja J²u 2²u 02:² Ət² Select ALL boundary/initial conditions that apply to this scenario 8²u O A. a² OB.k O c. + It' ¹ 0<x<L₂t> 0 0<x<L,t> 0 = 0, 0<x<L,t> 0 A. (L, t) = 0, CB.«(2,0) = 0, c. u(x, 130) = f(x), 0<x<L ] D. u(x, L) = f(x), 0<x<L t>0 0<a<L E. (,0) 130, 0<x<L OF. u(a,0) = f(x), 0<x<L G. (0,t) = L, OH. u(0, t) = 0, 1. (0, t) 130, t> 0 t> 0 t> 0
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Follow-up Question
At least one of the answers above is NOT correct.
²u
ər²
8²u du
O A. a²
ⒸB.k=
əz²
0²u
0x²
O C.
8²u
Ət²¹
Entered
The left end of a rod of length L is held at temperature 130, and there is heat transfer from the right end into the surrounding medium at temperature zero. The initial temperature at any point is given by f(x).
Select the partial differential equation that can be used to model this scenario.
B
Ət
AEF
0<x<L,t> 0
0 < a <L,t> 0
8²u
at² = 0, 0<x<L,t> 0
B. u(x, 0) = 0, 0<x<L
Select ALL boundary/initial conditions that apply to this scenario
A. u(L, t) = 0, t> 0
P
Oc. u(x, 130) = f(x), 0<x<L
OD. u(x, L) = f(x), 0<x<L
E. u(x, 0) = 130, 0<x<L
✔F. u(x, 0) = f(x), 0<x<L
t> 0
£>0
G. u(0, t) = L,
H. u(0, t) = 0,
1. u(0, t) = 130, £>0
Answer Preview
B
AEF
Result
correct
incorrect
Transcribed Image Text:At least one of the answers above is NOT correct. ²u ər² 8²u du O A. a² ⒸB.k= əz² 0²u 0x² O C. 8²u Ət²¹ Entered The left end of a rod of length L is held at temperature 130, and there is heat transfer from the right end into the surrounding medium at temperature zero. The initial temperature at any point is given by f(x). Select the partial differential equation that can be used to model this scenario. B Ət AEF 0<x<L,t> 0 0 < a <L,t> 0 8²u at² = 0, 0<x<L,t> 0 B. u(x, 0) = 0, 0<x<L Select ALL boundary/initial conditions that apply to this scenario A. u(L, t) = 0, t> 0 P Oc. u(x, 130) = f(x), 0<x<L OD. u(x, L) = f(x), 0<x<L E. u(x, 0) = 130, 0<x<L ✔F. u(x, 0) = f(x), 0<x<L t> 0 £>0 G. u(0, t) = L, H. u(0, t) = 0, 1. u(0, t) = 130, £>0 Answer Preview B AEF Result correct incorrect
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