The temperature distribution of a long, thin aluminium rod with a length of 12 cm can be determined by solving the one dimensional heat conduction equation (per picture) where k is the diffusivity constant. Given the values of k = 0.835 cm^2/s, Δx = 2cm, and Δt = 0.1 seconds subject to the following initial and boundary conditions, u(x,0) = 0 ℃ , 0 < x < 12 u(0,t) = 100 ℃, t ≥ 0 u(12,t) = 50 ℃, t ≥ 0 Use the explicit finite-difference method formula to: i. Determine the constant value, ii. Sketch the grid of temperature distribution graph. iii. Evaluate each interior node values for the temperature distribution. u(x, t) at t = 0.1 and 0.2 seconds
The temperature distribution of a long, thin aluminium rod with a length of 12 cm can be determined by solving the one dimensional heat conduction equation (per picture) where k is the diffusivity constant. Given the values of k = 0.835 cm^2/s, Δx = 2cm, and Δt = 0.1 seconds subject to the following initial and boundary conditions, u(x,0) = 0 ℃ , 0 < x < 12 u(0,t) = 100 ℃, t ≥ 0 u(12,t) = 50 ℃, t ≥ 0 Use the explicit finite-difference method formula to: i. Determine the constant value, ii. Sketch the grid of temperature distribution graph. iii. Evaluate each interior node values for the temperature distribution. u(x, t) at t = 0.1 and 0.2 seconds
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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The temperature distribution of a long, thin aluminium rod with a length of 12 cm can be determined by solving the one dimensional heat conduction equation (per picture)
where k is the diffusivity constant. Given the values of k = 0.835 cm^2/s, Δx = 2cm, and Δt = 0.1 seconds subject to the following initial and boundary
conditions,
u(x,0) = 0 ℃ , 0 < x < 12
u(0,t) = 100 ℃, t ≥ 0
u(12,t) = 50 ℃, t ≥ 0
Use the explicit finite-difference method formula to:
i. Determine the constant value,
ii. Sketch the grid of temperature distribution graph.
iii. Evaluate each interior node values for the temperature distribution.
u(x, t) at t = 0.1 and 0.2 seconds.
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