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 asteady-state results. Find this steady-state temperature distri-bution.(b) At a time t0 (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, whilethe other end remains at 0°C. Find the temperature as a functionof position and time.X ==(c) Plot u versus x for several values of t. Also plot u versus t forseveral values of x.(d) What limiting value does the temperature at the center of the rodapproach after a long time? How much time must elapse beforethe center of the rod cools to within 1°C of its limiting value?

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(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?

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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