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# Sagar and Payne [SP] analyze the stress-strain relationships and material properties of

ISBN: 9780534392000 331

## Solution for problem 12.2.19 Chapter 12-2

Numerical Analysis (Available Titles CengageNOW) | 8th Edition

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Problem 12.2.19

Sagar and Payne [SP] analyze the stress-strain relationships and material properties of a cylinder alternately subjected to heating and cooling and consider the equation 2T r 2 + 1 r T r = 1 4K T t , 1 2 < r < 1, 0 < T, where T = T (r,t) is the temperature, r is the radial distance from the center of the cylinder, t is time, and K is a diffusivity coefficient. a. Find approximations to T (r, 10) for a cylinder with outside radius 1, given the initial and boundary conditions: T (1, t) = 100 + 40t, T 1 2 , t = t, 0 t 10; T (r, 0) = 200(r 0.5), 0.5 r 1. Use a modification of the Backward-Difference method with K = 0.1, k = 0.5, and h = r = 0.1. b. Use the temperature distribution of part (a) to calculate the strain I by approximating the integral I = 1 0.5 T (r,t)r dr, where = 10.7 and t = 10. Use the Composite Trapezoidal method with n = 5.

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##### ISBN: 9780534392000

The answer to “Sagar and Payne [SP] analyze the stress-strain relationships and material properties of a cylinder alternately subjected to heating and cooling and consider the equation 2T r 2 + 1 r T r = 1 4K T t , 1 2 < r < 1, 0 < T, where T = T (r,t) is the temperature, r is the radial distance from the center of the cylinder, t is time, and K is a diffusivity coefficient. a. Find approximations to T (r, 10) for a cylinder with outside radius 1, given the initial and boundary conditions: T (1, t) = 100 + 40t, T 1 2 , t = t, 0 t 10; T (r, 0) = 200(r 0.5), 0.5 r 1. Use a modification of the Backward-Difference method with K = 0.1, k = 0.5, and h = r = 0.1. b. Use the temperature distribution of part (a) to calculate the strain I by approximating the integral I = 1 0.5 T (r,t)r dr, where = 10.7 and t = 10. Use the Composite Trapezoidal method with n = 5.” is broken down into a number of easy to follow steps, and 181 words. This full solution covers the following key subjects: . This expansive textbook survival guide covers 69 chapters, and 1072 solutions. Numerical Analysis (Available Titles CengageNOW) was written by and is associated to the ISBN: 9780534392000. Since the solution to 12.2.19 from 12-2 chapter was answered, more than 211 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 12.2.19 from chapter: 12-2 was answered by , our top Calculus solution expert on 03/05/18, 08:28PM. This textbook survival guide was created for the textbook: Numerical Analysis (Available Titles CengageNOW) , edition: 8.

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