Mathematical Determination of Transient Temperatures in Solids

Eugene Isaacson, J. Orten Gadd

ISBN 10: 1333481144 / ISBN 13: 9781333481148

Published by Forgotten Books, 2018

About this Item

Print on Demand. This book examines the intricacies of partial differential equations using finite difference methods, a key technique in scientific computing. By exploring a particular problem in heat conduction, the author demonstrates the power and accuracy of this approach. The work provides a detailed account of the underlying mathematical concepts, numerical methods, and computational strategies involved. The author meticulously analyzes the problem, considering its physical and mathematical implications. They introduce readers to the process of discretizing the problem and transforming it into a system of recurrence relations. The book highlights the computational challenges faced and offers practical solutions, such as using parallel storage and exploiting special properties of the solution function. The insights gained from this in-depth analysis shed light on the broader significance of finite difference methods in solving complex scientific problems. The book contributes to the understanding of numerical methods and their applications, making it a valuable resource for researchers and practitioners in computational science and engineering. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book.

Seller Inventory # 9781333481148_0

Bibliographic Details

• Title: Mathematical Determination of Transient Temperatures in Solids
• Publisher: Forgotten Books
• Publication Date: 2018
• Language: English
• ISBN 10: 1333481144
• ISBN 13: 9781333481148
• Binding: Paperback
• Condition: New
• Book Type: print-on-demand item
• Seller catalogs:
  • Calculus

About this title

Synopsis

Excerpt from Mathematical Determination of Transient Temperatures in Solids

In Sections 1-7 we formulate the mathematical prob lems and the numerical procedures which can be used to evaluate the solutions of these problems.

In Section 10 we present a description of the tech niques that were employed to make the large-scale auto matic machine computation feasible on the Mark I. In ad dition an analysis of the pertinent operational and nu merical procedures is given which would be of use in the future should other problems of this type be tackled.

In order to measure the temperature in the steel wall of a rocket, a thin cylindrical thermocouple is inserted into a hole that was drilled through the outer surface of the wall. The conductivity and the heat capacitance of the various parts of the thermocouple are different from those of steel and consequently the temperatures which are measured are not those which would obtain in the wall when the thermocouple is absent. The purpose of this report is to mathematically determine the difference between the measured temperature and the actual temperature.

We consider a simplified physical model. A steel cylinder of radius 5l and height 5l has a concentric hole of radius L and depth 4l. Into this hole a thermocouple of radius L and height 4l is inserted. The thermocouple is composed of a nonconducting cylindrical outer shell of thickness and a conducting cylindrical core of radius (figure We assume that, except for the hot wall of the rocket, all of the outer surface is nonconducting.

About the Publisher

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This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.