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The temperature u(x, t) of a metal bar of length (= 2 at a distance r from one end and at time t is modelled by the partial differential equation (0 < r < l, t> 0) U = augr It is given that the metal has diffusivity a = 2.25, that the two ends of the bar are kept at temperature u = 0 and that the initial temperature distribution is u(x, 0) = f(x) = sin(Tx/e) Use the explicit difference parabolic method with Ax = 0.5 and At = 0.05 to approximate u(x, t) at t = 0.05 and t 0.10.

The temperature u(x, t) of a metal bar of length (= 2 at a distance r from one end and at time t is modelled by the partial differential equation (0 < r < l, t> 0) U = augr It is given that the metal has diffusivity a = 2.25, that the two ends of the bar are kept at temperature u = 0 and that the initial temperature distribution is u(x, 0) = f(x) = sin(Tx/e) Use the explicit difference parabolic method with Ax = 0.5 and At = 0.05 to approximate u(x, t) at t = 0.05 and t 0.10.

Advanced Engineering Mathematics
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 u(x, t) of a metal bar of length e = 2 at a distance r from one end and at time t is modelled by the partial differential equation Ut = aurr (0 < x < l, t> 0) It is given that the metal has diffusivity a = 2.25, that the two ends of the bar are kept at temperature u = 0 and that the initial temperature distribution is u(x,0) = f(x) = sin(Tx/0) Use the explicit difference parabolic method with Ar = 0.5 and At 0.05 to approximate u(x, t) at t= 0.05 and t= 0.10.
Transcribed Image Text:The temperature u(x, t) of a metal bar of length e = 2 at a distance r from one end and at time t is modelled by the partial differential equation Ut = aurr (0 < x < l, t> 0) It is given that the metal has diffusivity a = 2.25, that the two ends of the bar are kept at temperature u = 0 and that the initial temperature distribution is u(x,0) = f(x) = sin(Tx/0) Use the explicit difference parabolic method with Ar = 0.5 and At 0.05 to approximate u(x, t) at t= 0.05 and t= 0.10.
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