Models Based on Simple Laws
A large number of models for transfer processes that contain equations are based on laws of conservation of momentum, mass and energy. Some of the models that were developed initially are based on simple laws and were inspired by experimental observations. The laws, though limited in scope, are still used not only as sub-models of various rigorous models but also in various engineering calculations. However, it is essential to understand the simplicity as well as limitations of these models. The simple laws provide us with initial guess values required while using rigorous models. These laws can be used as sub-models or as assumptions if a given process is not very sensitive to a particular parameter. The use of numerical methods is helpful in easily solving some of the problems based on these simple laws. A few commonly used simple laws will be presented in this chapter. They include the ideal gas law, which is used for estimation of thermodynamic properties; the cubic equation of state (EOS), particularly the Peng-Robinson EOS; Newton’s law of viscosity and its application in flow problems; Fourier’s law for conduction; Fick’s first and second laws for diffusion; kinetic rate expressions; the Arrhenius equation and isotherms for adsorption. Definitions of the heat and mass transfer coefficients and resistances to heat and mass transfer are presented. A few applications of the simple laws are presented to demonstrate the importance of these problems.