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Get Full Access to Linear Algebra And Its Applications - 5 Edition - Chapter 1.1 - Problem 34e
Get Full Access to Linear Algebra And Its Applications - 5 Edition - Chapter 1.1 - Problem 34e

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# Answer: An important concern in the study of heat transfer ISBN: 9780321982384 49

## Solution for problem 34E Chapter 1.1

Linear Algebra and Its Applications | 5th Edition

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Problem 34E

PROBLEM 34E

An important concern in the study of heat transfer is to determine the steady-state temperature distribution of a thin plate when the temperature around the boundary is known. Assume the plate shown in the figure represents a cross section of a metal beam, with negligible heat flow in the direction perpendicular to the plate. Let T1,…,T4 denote the temperatures at the four interior nodes of the mesh in the figure. The temperature at a node is approximately equal to the average of the four nearest nodes—to the left, above, to the right, and below.3 For instance,

T 1 = (10 + 20 T2 + T4)/4, or 4T1 – T2 – T4 = 30 Solve the system of equations from Exercise 33. [Hint: To speed up the calculations, interchange rows 1 and 4 before starting “replace” operations.]

Exercise 33:

Write a system of four equations whose solution gives estimates for the temperatures T1,…,T4.

Step-by-Step Solution:

Solution:
Step 1

In this problem we need to find the temperature at the nodes 1, 2, 3 and 4 given in the figure.

Step 2 of 4

Step 3 of 4

##### ISBN: 9780321982384

Since the solution to 34E from 1.1 chapter was answered, more than 4895 students have viewed the full step-by-step answer. Linear Algebra and Its Applications was written by and is associated to the ISBN: 9780321982384. This full solution covers the following key subjects: plate, temperature, equations, system, temperatures. This expansive textbook survival guide covers 65 chapters, and 1898 solutions. The answer to “An important concern in the study of heat transfer is to determine the steady-state temperature distribution of a thin plate when the temperature around the boundary is known. Assume the plate shown in the figure represents a cross section of a metal beam, with negligible heat flow in the direction perpendicular to the plate. Let T1,…,T4 denote the temperatures at the four interior nodes of the mesh in the figure. The temperature at a node is approximately equal to the average of the four nearest nodes—to the left, above, to the right, and below.3 For instance,T 1 = (10 + 20 T2 + T4)/4, or 4T1 – T2 – T4 = 30 Solve the system of equations from Exercise 33. [Hint: To speed up the calculations, interchange rows 1 and 4 before starting “replace” operations.]Exercise 33:Write a system of four equations whose solution gives estimates for the temperatures T1,…,T4.” is broken down into a number of easy to follow steps, and 149 words. The full step-by-step solution to problem: 34E from chapter: 1.1 was answered by , our top Math solution expert on 07/20/17, 03:54AM. This textbook survival guide was created for the textbook: Linear Algebra and Its Applications , edition: 5.

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Answer: An important concern in the study of heat transfer