A thin copper rod, 6 m in length, is heated at its midpoint and the ends are held at a constant temperature of 0°. When the temperature reaches equilibrium, the temperature profile is given by T(x) = 60x(6-x), where 0≤x≤6 m is the position along the rod. The heat flux at a point on the rod equals -kT'(x), where k is a constant. If the heat flux is positive at a point, heat moves in the positive x-direction at that point, and if the heat flux is negative, heat moves in the negative x-direction. a. With k = 1, what is the heat flux at x = 1? Atx=5? b. For what values of x is the heat flux negative? Positive? c. Explain the statement that heat flows out of the rod at its ends.
A thin copper rod, 6 m in length, is heated at its midpoint and the ends are held at a constant temperature of 0°. When the temperature reaches equilibrium, the temperature profile is given by T(x) = 60x(6-x), where 0≤x≤6 m is the position along the rod. The heat flux at a point on the rod equals -kT'(x), where k is a constant. If the heat flux is positive at a point, heat moves in the positive x-direction at that point, and if the heat flux is negative, heat moves in the negative x-direction. a. With k = 1, what is the heat flux at x = 1? Atx=5? b. For what values of x is the heat flux negative? Positive? c. Explain the statement that heat flows out of the rod at its ends.
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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Transcribed Image Text:A thin copper rod, 6 m in length, is heated at its midpoint and the ends are held at a constant temperature of 0°. When the temperature reaches equilibrium, the temperature profile is given by T(x) = 60x(6-x), where
0≤x≤6 m is the position along the rod. The heat flux at a point on the rod equals - KT'(x), where k is a constant. If the heat flux is positive at a point, heat moves in the positive x-direction at that point, and if the heat
flux is negative, heat moves in the negative x-direction.
a. With k = 1, what is the heat flux at x = 1? At x = 5?
b. For what values of x is the heat flux negative? Positive?
c. Explain the statement that heat flows out of the rod at its ends.
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