Mathematical Methods in Engineering and Applied Sciences

Hemen Dutta

• Publisher: CRC Press
• Year: 2020
• eBook ISBN: 9781000764970
• Edition: 1
• Topic: Mathematics
• Subtopic: Operations
• Index: Mathematics

Recognized as a "Recommended" title by Choice for their October 2020 issue.

Choice is a publishing unit at the Association of College & Research Libraries (ACR&L), a division of the American Library Association. Choice has been the acknowledged leader in the provision of objective, high-quality evaluations of nonfiction academic writing.

This book covers tools and techniques used for developing mathematical methods and modelling related to real-life situations. It brings forward significant aspects of mathematical research by using different mathematical methods such as analytical, computational, and numerical with relevance or applications in engineering and applied sciences.

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• Presents theory, methods, and applications in a balanced manner

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• Includes the basic developments with full details

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• Contains the most recent advances and offers enough references for further study

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• Written in a self-contained style and provides proof of necessary results

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• Offers research problems to help early career researchers prepare research proposals

Mathematical Methods in Engineering and Applied Sciences makes available for the audience, several relevant topics in one place necessary for crucial understanding of research problems of an applied nature. This should attract the attention of general readers, mathematicians, and engineers interested in new tools and techniques required for developing more accurate mathematical methods and modelling corresponding to real-life situations.

1 Semi-Analytical Source (SAS) Method for Heat Conduction Problems with Moving Heat Source

Barbaros Çetin

I.D. Bilkent University

Barɩş Çetin

FNSS Defense Systems Co. Inc. Atilim University

Kevin D. Cole

University of Nebraska-Lincoln

CONTENTS

1.1 Introduction

1.2 Problem Statement

1.2.1 Dimensionless Problem Statement

1.2.2 Heating Regime of Interest

1.3 SAS Method

1.3.1 Discretization into Sub-intervals

1.3.2 Green’s Function

1.3.3 Construction of Source Terms

1.3.4 Time-Stepping Solution

1.4 Results and Discussions

1.5 Concluding Remarks

Acknowledgment

References

1.1 Introduction

Many scientific problems and industrial applications, such as welding, ablation, and specific surface treatments like laser hardening operations of materials, involve a moving heat source. Modeling of these processes for precise prediction of thermal effects is essential to understand the physics of the processes and to optimize process parameters [1, 2 and 3]. From a thermal engineering point of view, such a process is a heat conduction problem containing a moving-heat-source term and can be expressed as analytical equations. The heat source can be applied internally (volumetric heating) or at the surface (boundary heating) in many manufacturing processes. In the case of constant thermophysical material properties, the problem is governed by a linear differential equation, and it is possible to use analytical methods such as separation of variables, integral transformations, or Green’s function method (GFM) [4,5]. Although analytical methods may be limited and may include some mathematical challenges (determining the eigenvalues of complex matrices, difficult-to-calculate integral expressions, etc.), modern symbolic solution tools such as Mathematica, Maple, MatLab may extend existing limits of analytical solution strategies.

Among different techniques, GFM is a powerful tool to obtain solutions of problems which are governed by linear partial differential equations [6, 7 and 8]. A GF is an analytical expression for the response to an impulsive point source of heat with homogenous boundary conditions, and it may be considered as a building block from which many useful solutions may be constructed for problems with more complex boundary conditions. Once the GF is obtained, solutions can be written directly in terms of integrals. However, the key challenge to be overcome for practical application of this method is that of determining the GF which is specific to each geometry. From this perspective, the open-source libraries where GFs are available for a variety of geometries are very important [9]. Although in its classical form the GFM applies to linear problems on regular geometries (i.e. orthogonal bodies), the method can be extended to overcome these constraints to some extent. For example, non-orthogonal bodies may be treated using Green’s functions built from polynomial basis functions whose coefficients are chosen by Galerkin’s method [5, Ch. 10]. Such an approach was also implemented for moving-boundary problems to obtain the closed form for temperature distribution in the liquid and solid phases including the contribution of the internal heat capac...

Table of contents

• Cover
• Half Title
• Series Page
• Title Page
• Copyright Page
• Table of Contents
• Preface
• Editor
• Contributors
• Chapter 1 Semi-Analytical Source (SAS) Method for Heat Conduction Problems with Moving Heat Source
• Chapter 2 Complete Synchronization of a Time-Fractional Reaction–Diffusion System with Lorenz Nonlinearities
• Chapter 3 Oblique Scattering by Thin Vertical Barriers in Water of Finite Depth
• Chapter 4 Existence of Periodic Solutions for First-Order Difference Equations Subjected to Allee Effects
• Chapter 5 Numerical Investigation of Heat Flow and Fluid Flow in a Solar Water Heater with an Evacuated-Tube Collector
• Chapter 6 Point Potential in Wave Scattering
• Chapter 7 Complete Synchronization of Hybrid Spatio-temporal Chaotic Systems
• Chapter 8 Statistical and Exact Analysis of MHD Flow Due to Hybrid Nanoparticles Suspended in C2H6O2-H2O Hybrid Base Fluid
• Chapter 9 Lyapunov Functionals and Stochastic Stability Analyses for Highly Random Nonlinear Functional Epidemic Dynamical Systems with Multiple Distributed Delays
• Chapter 10 Linear Multistep Method with Application to Chaotic Processes
• Index