Introduction on Methodology*

This chapter explores various apparently unrelated problems and formulating them in the simplest form such that in most cases an analytical solution to the governing equations can be obtained. Lessons of general applicability are extracted from the solutions of the problems considered. The concept that the subjects of transport phenomena and of thermodynamics are strongly intertwined is strictly emphasized. All problems in engineering science are formulated on the basis of two types of equations: balance and constitutive. A balance equation can be written either for a quantity for which a general principle of conservation exists, or for a quantity for which no such principle exists provided its rate of generation is included in the balance equation. A constitutive equation is one that assigns the value of F ( X , t )—the flux of the quantity considered—in terms of C ( X , t )—the amount of the quantity considered per unit volume—so that the problem becomes a mathematically well posed one. The two types of equations are discussed by illustrating several classic problems such as the plug flow reactor with diffusion, shock waves in gases, and stefan problem.