The temperature of an electrically heated pipe varies in the radial direction and is defined by the following differential equation: d?T 1 dT dr2 +dr +S = 0 Where T is the temperature, r is the radial coordinate and S is the internal heat source. For a pipe with an inner radius of rinner = 0.04 [m), an outer radius of router = 0.1 (m] and an internal heat source of S = 200,000 ("C/m²), determine the temperature at r = 0.04, 0.06 and 0.08 (m). Solve this as a boundary value problem with = 12,000 ["C/m] at r = 0.04 [m] and T = 40 (C] at r = 0.1 [m). Use centered difference approximations of O(h?) on the derivative terms in the differential equation provided and use backward difference approximation of 0(h) on the Neumann boundary condition. Solve the matrix for temperatures using any method (MATLAB is also acceptable).

The temperature of an electrically heated pipe varies in the radial direction and is defined by the following differential equation: d?T 1 dT dr2 +dr +S = 0 Where T is the temperature, r is the radial coordinate and S is the internal heat source. For a pipe with an inner radius of rinner = 0.04 [m), an outer radius of router = 0.1 (m] and an internal heat source of S = 200,000 ("C/m²), determine the temperature at r = 0.04, 0.06 and 0.08 (m). Solve this as a boundary value problem with = 12,000 ["C/m] at r = 0.04 [m] and T = 40 (C] at r = 0.1 [m). Use centered difference approximations of O(h?) on the derivative terms in the differential equation provided and use backward difference approximation of 0(h) on the Neumann boundary condition. Solve the matrix for temperatures using any method (MATLAB is also acceptable).

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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