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

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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Concept explainers

Engineering Drawing

Technical drawing has been around since ancient times. As in the ancient Renaissance, complicated drawings were created, including Leonardo da Vinci's drawing. Modern engineering drawing, including its specific orthographic projection with scale conventions, began in Europe (France) during the early stages of Industrialization. L.T. C. Rolt also made some of Marc's drawings for its block-making machinery (in 1799) that also may have contributed significantly to British engineering technology. Since he learned the art of presenting three-dimensional(3D) items in a two-dimensional(2D) plane, as we now term mechanical drawing. 

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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.

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