(a) Let the ends of a copper rod 100 cm long be maintained at 0°C. Suppose that the center of the bar is heated to 75°C by an ex- ternal heat source and that this situation is maintained until a steady-state results. Find this steady-state temperature distri- bution. (b) At a time t = 0 (after the steady-state of part a has been reached), let the heat source be removed. At the same instant, let the end x = 0 be placed in thermal contact with a reservoir at 10°C, while the other end remains at 0°C. Find the temperature as a function of position and time. (c) Plot u versus x for several values of t. Also plot u versus t for several values of x. (d) What limiting value does the temperature at the center of the rod approach after a long time? How much time must elapse before the center of the rod cools to within 1°C of its limiting value?
(a) Let the ends of a copper rod 100 cm long be maintained at 0°C. Suppose that the center of the bar is heated to 75°C by an ex- ternal heat source and that this situation is maintained until a steady-state results. Find this steady-state temperature distri- bution. (b) At a time t = 0 (after the steady-state of part a has been reached), let the heat source be removed. At the same instant, let the end x = 0 be placed in thermal contact with a reservoir at 10°C, while the other end remains at 0°C. Find the temperature as a function of position and time. (c) Plot u versus x for several values of t. Also plot u versus t for several values of x. (d) What limiting value does the temperature at the center of the rod approach after a long time? How much time must elapse before the center of the rod cools to within 1°C of its limiting value?
Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)
8th Edition
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Chapter3: Transient Heat Conduction
Section: Chapter Questions
Problem 3.36P
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![4. (a) Let the ends of a copper rod 100 cm long be maintained at 0°C.
Suppose that the center of the bar is heated to 75°C by an ex-
ternal heat source and that this situation is maintained until a
steady-state results. Find this steady-state temperature distri-
bution.
(b) At a time t
0 (after the steady-state of part a has been reached),
let the heat source be removed. At the same instant, let the end
= 0 be placed in thermal contact with a reservoir at 10°C, while
the other end remains at 0°C. Find the temperature as a function
of position and time.
X =
=
(c) Plot u versus x for several values of t. Also plot u versus t for
several values of x.
(d) What limiting value does the temperature at the center of the rod
approach after a long time? How much time must elapse before
the center of the rod cools to within 1°C of its limiting value?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1720cd77-2294-45a6-8b70-43447dc02920%2Fcda89bf8-a60a-4da4-9fb9-4b19e4395c9d%2Ft9ovcpo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:4. (a) Let the ends of a copper rod 100 cm long be maintained at 0°C.
Suppose that the center of the bar is heated to 75°C by an ex-
ternal heat source and that this situation is maintained until a
steady-state results. Find this steady-state temperature distri-
bution.
(b) At a time t
0 (after the steady-state of part a has been reached),
let the heat source be removed. At the same instant, let the end
= 0 be placed in thermal contact with a reservoir at 10°C, while
the other end remains at 0°C. Find the temperature as a function
of position and time.
X =
=
(c) Plot u versus x for several values of t. Also plot u versus t for
several values of x.
(d) What limiting value does the temperature at the center of the rod
approach after a long time? How much time must elapse before
the center of the rod cools to within 1°C of its limiting value?
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