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 0sxs6 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 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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Chapter1: Units, Trigonometry. And Vectors
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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.
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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