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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 timet is modelled by the partial differential equation (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(rx/l) 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 timet is modelled by the partial differential equation (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(rx/l) 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.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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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 Uų = aUzz (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/l) 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.
Transcribed Image Text: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 Uų = aUzz (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/l) 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.
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