Consider a uniform rod of length L with an initial temperature given by u(x,0) = sin(Tx/L), 0 ≤x≤ L. Assume that both ends of the bar are insulated. (a) Find the temperature u(x, t). (b) What is the steady-state temperature as t→ ∞? (c) Let a² = 4 and L = 20. Plot u versus x for several values of t. Also plot u versus t for several values of x.

Consider a uniform rod of length L with an initial temperature given by u(x,0) = sin(Tx/L), 0 ≤x≤ L. Assume that both ends of the bar are insulated. (a) Find the temperature u(x, t). (b) What is the steady-state temperature as t→ ∞? (c) Let a² = 4 and L = 20. Plot u versus x for several values of t. Also plot u versus t for several values of x.

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

Axial Load

When a bar of the uniform cross-section is acted by a load, such that the load acts along the longitudinal axis of the bar, such kinds of loadings are known as axial loadings. In general terms, a load is an external force acting on a component. An axial load acts perpendicular to the geometric cross-section of the component. Based on the direction of the application of the load, an axial load can be tensile or compressive. The analysis of bodies under the action of axial loads is generally studied under the branch of mechanics, known as statics.

Question

5. Consider a uniform rod of length L with an initial temperature given
by u(x,0)= sin(7x/L), 0 ≤ x ≤ L. Assume that both ends of the bar
are insulated.
(a) Find the temperature u(x, t).
(b) What is the steady-state temperature as t→ ∞?
(c) Let a²
4 and L = 20. Plot u versus x for several values of t.
Also plot u versus t for several values of x.
=
(d) Describe briefly how the temperature in the rod changes as time
progresses.

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