ABSTRACT
This chapter provides an introduction to the combined use of finite differences and integral transforms in the hybrid numerical–analytical solution of convection–diffusion problems by considering an example taken from transient forced convection in channels. It briefly considers an alternative integral transform solution for the same class of transient convection–diffusion problems, through which the convective effects can be fully or partially incorporated into the eigenfunction expansion basis, by obtaining a generalized diffusive formulation via an algebraic transformation in the original problem formulation coefficients. The chapter presents a more advanced and unified view of the modern hybrid approach, generalized integral transform technique (GITT) and also describes the formal solution through both the total and partial transformation schemes. It also provides an overview of the computational algorithm based on the UNified Integral Transform (UNIT) algorithm. The chapter then introduces the hybrid approach combining the GITT and finite differences.
