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4 Discuss the various aspects involved in physical modelling. 5 What are the various model formulation principles? 6 Give a detailed account of the fundamental laws used in modelling. 7 Define cybernetics and discuss the controlled system by means of a neat schematic diagram. 8 What are the various similarity criteria? 9 Discuss physical modelling versus mathematical modelling. CHAPTER 3 CLASSIFICATION OF MATHEMATICAL MODELLING The choice of a particular type of mathematical model is determined by the specific conditions under which a given process can proceed in the processing unit of interest.

Special conditions are placed on the dependent variable at the end points of the range of independent variables. These are naturally called boundary conditions and are used to evaluate the arbitrary constants in the solution of differential equations. When time is the independent variable, the boundary condition is frequently called the initial condition since it specifies the starting state of the apparatus. The three most frequently used boundary conditions in heat transfer are 1. Boundary at a fixed temperature T = To 2.

This kind of consistency check may seem trivial, but experience shows that it can save many hours of frustration, confusion, and wasted computer time. This is required for a simulation exercise. For an optimization exercise, there should be some degrees of freedom available for optimizing, that is, an optimization problem is an underspecified problem. Checking to see that the units of all terms in all equations are consistent is perhaps another trivial and obvious step, but one that is often forgotten.

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