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Consider a uniform rod of length L with an initial temperature given by u(x,0) = sin(Tx/L), 0 ≤x≤ L. Assume that both ends of the bar are insulated. (a) Find the temperature u(x, t). (b) What is the steady-state temperature as t→ ∞? (c) Let a² = 4 and L = 20. Plot u versus x for several values of t. Also plot u versus t for several values of x.

Consider a uniform rod of length L with an initial temperature given by u(x,0) = sin(Tx/L), 0 ≤x≤ L. Assume that both ends of the bar are insulated. (a) Find the temperature u(x, t). (b) What is the steady-state temperature as t→ ∞? (c) Let a² = 4 and L = 20. Plot u versus x for several values of t. Also plot u versus t for several values of x.

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)
Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)
8th Edition
ISBN:9781305387102
Author:Kreith, Frank; Manglik, Raj M.
Publisher:Kreith, Frank; Manglik, Raj M.
Chapter3: Transient Heat Conduction
Section: Chapter Questions
Problem 3.4P
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5. Consider a uniform rod of length L with an initial temperature given by u(x,0)= sin(7x/L), 0 ≤ x ≤ L. Assume that both ends of the bar are insulated. (a) Find the temperature u(x, t). (b) What is the steady-state temperature as t→ ∞? (c) Let a² 4 and L = 20. Plot u versus x for several values of t. Also plot u versus t for several values of x. = (d) Describe briefly how the temperature in the rod changes as time progresses.
Transcribed Image Text:5. Consider a uniform rod of length L with an initial temperature given by u(x,0)= sin(7x/L), 0 ≤ x ≤ L. Assume that both ends of the bar are insulated. (a) Find the temperature u(x, t). (b) What is the steady-state temperature as t→ ∞? (c) Let a² 4 and L = 20. Plot u versus x for several values of t. Also plot u versus t for several values of x. = (d) Describe briefly how the temperature in the rod changes as time progresses.
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