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# The temperature u(x, t) of a long, thin rod of constant cross section and homogeneous ISBN: 9780534392000 331

## Solution for problem 12.2.18 Chapter 12-2

Numerical Analysis (Available Titles CengageNOW) | 8th Edition

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Problem 12.2.18

The temperature u(x, t) of a long, thin rod of constant cross section and homogeneous conducting material is governed by the one-dimensional heat equation. If heat is generated in the material, for example, by resistance to current or nuclear reaction, the heat equation becomes 2u x 2 + Kr C = K u t , 0 < x < l, 0 < t, where l is the length, is the density, C is the specific heat, and K is the thermal diffusivity of the rod. The function r = r(x, t, u) represents the heat generated per unit volume. Suppose that l = 1.5 cm, K = 1.04 cal/cm deg s, = 10.6 g/cm3 , C = 0.056 cal/g deg, and r(x,t, u) = 5.0 cal/cm3 s. If the ends of the rod are kept at 0C, then u(0, t) = u(l, t) = 0, t > 0. Suppose the initial temperature distribution is given by u(x, 0) = sin x l , 0 x l. Use the results of Exercise 15 to approximate the temperature distribution with h = 0.15 and k = 0.0225.

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##### ISBN: 9780534392000

Numerical Analysis (Available Titles CengageNOW) was written by and is associated to the ISBN: 9780534392000. Since the solution to 12.2.18 from 12-2 chapter was answered, more than 218 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: Numerical Analysis (Available Titles CengageNOW) , edition: 8. This full solution covers the following key subjects: . This expansive textbook survival guide covers 69 chapters, and 1072 solutions. The answer to “The temperature u(x, t) of a long, thin rod of constant cross section and homogeneous conducting material is governed by the one-dimensional heat equation. If heat is generated in the material, for example, by resistance to current or nuclear reaction, the heat equation becomes 2u x 2 + Kr C = K u t , 0 < x < l, 0 < t, where l is the length, is the density, C is the specific heat, and K is the thermal diffusivity of the rod. The function r = r(x, t, u) represents the heat generated per unit volume. Suppose that l = 1.5 cm, K = 1.04 cal/cm deg s, = 10.6 g/cm3 , C = 0.056 cal/g deg, and r(x,t, u) = 5.0 cal/cm3 s. If the ends of the rod are kept at 0C, then u(0, t) = u(l, t) = 0, t > 0. Suppose the initial temperature distribution is given by u(x, 0) = sin x l , 0 x l. Use the results of Exercise 15 to approximate the temperature distribution with h = 0.15 and k = 0.0225.” is broken down into a number of easy to follow steps, and 185 words. The full step-by-step solution to problem: 12.2.18 from chapter: 12-2 was answered by , our top Calculus solution expert on 03/05/18, 08:28PM.

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