Analysis of finite volumes and integral transform solutions for thermally developing non-Newtonian fluid flow

Abstract

The current work provides a comparison between two different methodologies for solving convection-diffusion problems: the Generalized Integral Transform Technique (GITT) and the Finite Volumes Method (FVM). The problem of thermally developing laminar flow of non-Newtonian fluids between parallel plates is selected for illustrating purposes. Both solutions focus on the transformation of a partial-differential formulation into an ordinary-differential form, either through integral transformation or discretization of the directional variable transversal to the flow. The resulting ODE systems are solved analytically and comparison results are presented, indicating advantages and disadvantages of each methodology. Once comparisons are performed advantages and disadvantages of each methodology are discussed. The results indicate that, in general, the integral transform technique presents a better convergence rate.