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Modeling in Materials Processing by Jonathan A. Dantzig, Charles L. Tucker

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CHAPTER THREEScaling and Model Simplification

3.1 INTRODUCTION

The balance equations derived in the preceding chapter are the basis for all of the modeling work to come. When combined with constitutive equations and initial or boundary conditions, they provide the governing equations for most models. However, these governing equations are often difficult to solve in their general form, because they are multidimensional and nonlinear.

In this chapter we discuss a method for systematically simplifying the governing equations by determining which terms can be safely neglected in a given problem. We use the values of the physical parameters in the problem to estimate the relative importance of each term in the governing equations, using a particular ...

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