4: A rod of length L. coincides with the interval [0, L] on the x-axis. Let u(x, t) be the temperature. Consider the following conditions. (A) The left end is held at temperature 0°. (B) The right end is insulated. (C) There is heat transfer from the lateral surface of the rod into the surrounding medium, which is held at temperature 0° (D) The left end is insulated. (E) The initial temperature is 0° throughout. (F) The right end is held at temperature 0°. (G) There is heat transfer from the right end into the surrounding medium, which is held at a constant temperature of 0°. (H) There is heat transfer from the left end into the surrounding medium, which is held at a constant temperature of 0°. In each part below, determine which of the above conditions corresponds to the given initial or boundary condition for the heat equation. (a) u(x, 0) = 0 (b) u(0, 1) = 0 (c) ou Oxx-L (d) du axx=0 = --hu(L, 1) hu(0, 1)

4: A rod of length L. coincides with the interval [0, L] on the x-axis. Let u(x, t) be the temperature. Consider the following conditions. (A) The left end is held at temperature 0°. (B) The right end is insulated. (C) There is heat transfer from the lateral surface of the rod into the surrounding medium, which is held at temperature 0° (D) The left end is insulated. (E) The initial temperature is 0° throughout. (F) The right end is held at temperature 0°. (G) There is heat transfer from the right end into the surrounding medium, which is held at a constant temperature of 0°. (H) There is heat transfer from the left end into the surrounding medium, which is held at a constant temperature of 0°. In each part below, determine which of the above conditions corresponds to the given initial or boundary condition for the heat equation. (a) u(x, 0) = 0 (b) u(0, 1) = 0 (c) ou Oxx-L (d) du axx=0 = --hu(L, 1) hu(0, 1)

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

Center of Gravity and Centroid

The term center of gravity indicates the position or location of a point about which the whole weight of a body or system is supposed to be concentrated, which means the whole weight of the body or system works through this point. It is closely related to mass distribution. For all positions of the body, the center of gravity would be a single point.

Question

#4: A rod of length L. coincides with the interval [0, L] on the x-axis. Let u(x, t) be the
temperature. Consider the following conditions.
(A) The left end is held at temperature 0°.
(B) The right end is insulated.
(C) There is heat transfer from the lateral surface of the rod into the
surrounding medium, which is held at temperature 0°
(D) The left end is insulated.
(E) The initial temperature is 0° throughout.
(F) The right end is held at temperature 0°.
(G) There is heat transfer from the right end into the surrounding medium,
which is held at a constant temperature of 0°.
(H) There is heat transfer from the left end into the surrounding medium,
which is held at a constant temperature of 0°.
In each part below, determine which of the above conditions corresponds to the
given initial or boundary condition for the heat equation.
(a) u(x, 0) = 0
(b) u(0, 1) = 0
(c) du
(d) ou
x=L
ox|x=0
= -hu(L, 1)
= hu(0, 1)

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