ABSTRACT
This chapter presents methods to solve problems with two independent variables involving first-order differential equations and third-kind boundary conditions. Therefore, the problems fall in the category of partial differential equations. Mathematically, this class of problems can be summarized as third-kind boundary condition. The chapter examines the condition of heating a flowing liquid involving a combination heat transfer by conduction and convection at the grid for which the solution is presented by using Laplace transform. It also examines the condition of a plug-flow reactor where the rate of component injection is dictated by its diffusion-convective combination mass transfer. The solution is provided by Laplace transform. The chapter illustrates the relationships of dimensionless concentration against dimensionless time and space in a plug-flow reactor for two values of reaction rate and diffusivity.
