ABSTRACT
This chapter presents methods to solve problems with two independent variables involving first-order differential equation and second-kind boundary condition. Therefore, the problems fall within the category of partial differential equations. Mathematically, this class of cases can be summarized as second-kind boundary condition. The chapter considers the problem of heating of a flowing liquid for which the solution by Laplace transform is presented. It highlights some information on the application of the method of similarity. The chapter examines the condition of a plug-flow reactor where a component A is injected into the porous tubes and then into the main reactor stream. The method of Laplace transform can be used for this case as well. The chapter also illustrates the relationship of dimensionless concentration against time and length.
