Heat Transfer

1.5: Numerical Solutions to Steady-State 1-D Conduction Problems using MATLAB

1.5 Numerical Solutions to Steady-State 1-D Conduction Problems using MATLAB

1.5.1 Introduction

Numerical models of 1-D steady-state conduction problems are introduced and implemented using EES in Section 1.4. EES internally provides all of the numerical manipulations that are needed to solve the system of algebraic equations that constitutes a numerical model. This capability reduces the complexity of the problem. However, there are disadvantages to using EES. For example, EES will generally require significantly more time to solve the equations than is required by a compiled computer language. There is an upper limit to the number of variables that EES can handle, which places an upper bound on the number of nodes that can be used in the model. The structure of EES requires that every variable be retained in the final solution. Therefore, you cannot define and then erase intermediate variables in the course of obtaining a solution and, as a result, numerical solutions in EES often require a lot of memory. Finally, some models require logic statements (e.g., if-then-else statements) that are difficult to include in EES. For these reasons, it is useful to learn how to implement numerical models in a formal programming language, e.g., FORTRAN, C++, or MATLAB. The steps required to solve the algebraic equations associated with a numerical model are demonstrated in this section using the MATLAB software. It is suggested that the reader stop and go through the tutorial provided in Appendix A.3 in order to become familiar with MATLAB. Appendix A.3 can...

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