6. A thin homogeneous metal bar of length 20cm. and made of material with thermal diffusivity 5cm/s has insulated ends and lateral sides. The bar has initial temperature in (Cº) given by u(x, 0) = 10 + 4x 0 < x< 10 u(x,0) = 90 – 4x 10 < x< 20 %3D (a) Model an initial-boundary value problem [IBVP] of the heat equation from the above statement. (b) Use separation of variables to find the solution of the IBVP obtained in part (a) (c) What is lim t → ∞ u(x, 1)?Explain it physically.
6. A thin homogeneous metal bar of length 20cm. and made of material with thermal diffusivity 5cm/s has insulated ends and lateral sides. The bar has initial temperature in (Cº) given by u(x, 0) = 10 + 4x 0 < x< 10 u(x,0) = 90 – 4x 10 < x< 20 %3D (a) Model an initial-boundary value problem [IBVP] of the heat equation from the above statement. (b) Use separation of variables to find the solution of the IBVP obtained in part (a) (c) What is lim t → ∞ u(x, 1)?Explain it physically.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![6. A thin homogeneous metal bar of length 20cm. and made of material with
thermal diffusivity 5cm/s has insulated ends and lateral sides. The bar has
initial temperature in (C) given by
u(x, 0) = 10 +4x 0 < x< 10
u(x,0) = 90 – 4x
10 < x< 20
(a) Model an initial-boundary value problem [IBVP] of the heat equation
from the above statement.
(b) Use separation of variables to find the solution of the IBVP obtained in
part (a)
(c) What is lim t → o u(x, 1)?Explain it physically.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd1d4c710-065e-42f1-8793-c74434785eff%2F0379e284-27c7-444e-a5ec-c45bc56b0eab%2Frv4fuw_processed.jpeg&w=3840&q=75)
Transcribed Image Text:6. A thin homogeneous metal bar of length 20cm. and made of material with
thermal diffusivity 5cm/s has insulated ends and lateral sides. The bar has
initial temperature in (C) given by
u(x, 0) = 10 +4x 0 < x< 10
u(x,0) = 90 – 4x
10 < x< 20
(a) Model an initial-boundary value problem [IBVP] of the heat equation
from the above statement.
(b) Use separation of variables to find the solution of the IBVP obtained in
part (a)
(c) What is lim t → o u(x, 1)?Explain it physically.
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