Problem 25 Consider the following heat Problem in dimunionless variables 0o Ц = Ихх - вх tro U (0,₁t) = 0, a(t) = Derive the steady-state solution, (or stationery solution). 16 = (x (1-x²) Us
Problem 25 Consider the following heat Problem in dimunionless variables 0o Ц = Ихх - вх tro U (0,₁t) = 0, a(t) = Derive the steady-state solution, (or stationery solution). 16 = (x (1-x²) Us
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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025
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![**Problem 25**
Consider the following heat problem in dimensionless variables:
\( 0 < x < 1, \quad t > 0 \)
\[ u_t = u_{xx} - bx \]
\[ u(0, t) = 0, \quad u(1, t) = 0 \quad t > 0 \]
Derive the steady-state solution (or stationary solution).
\[ u_s = \frac{b}{6} x (1 - x^2) \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9c55fd55-ae67-4b97-a36c-91359ff73a6f%2Fb6d9b6e2-7bf9-4dd0-a494-e0ee0dc456a1%2F5do4iz7_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 25**
Consider the following heat problem in dimensionless variables:
\( 0 < x < 1, \quad t > 0 \)
\[ u_t = u_{xx} - bx \]
\[ u(0, t) = 0, \quad u(1, t) = 0 \quad t > 0 \]
Derive the steady-state solution (or stationary solution).
\[ u_s = \frac{b}{6} x (1 - x^2) \]
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