Integral transforms solution for flow development in wavy wall ducts

Abstract

Purpose – The purpose of this paper is to provide an analysis of two‐dimensional laminar flow in the entrance region of wavy wall ducts as obtained from the solution of the steady Navier‐Stokes equations for incompressible flow. Design/methodology/approach – The study is undertaken by application of the generalized integral transform technique in the solution of the steady Navier‐Stokes equations for incompressible flow. The streamfunction‐only formulation is adopted, and a general filtering solution that adapts to the irregular contour is proposed to enhance the convergence behavior of the eigenfunction expansion. Findings – A few representative cases are considered more closely in order to report some numerical results illustrating the eigenfunction expansions convergence behavior. The product friction factor‐Reynolds number is also computed and compared against results from discrete methods available in the literature for different Reynolds numbers and amplitudes of the wavy channel. Research limitations/implications – The proposed methodology is fairly general in the analysis of different channel profiles, though the reported results are limited to the wavy channel configuration. Future work should also extend the analysis to geometries represented in the cylindrical coordinates with longitudinally variable radius. Practical implications – The error‐controlled converged results provide reliable benchmark results for the validation of numerical results from computational codes that address the solution of the Navier‐Stokes equations in irregular geometries. Originality/value – Although the hybrid methodology is already known in the literature, the results here presented are original and further challenges application of the integral transform method in the solution of the Navier‐Stokes equations.