Application of the method of fundamental solutions and the radial basis functions for laminar flow and heat transfer in internally corrugated tubes

Abstract

Paper presented to the 10th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, Florida, 14-16 July 2014.

Heat transfer characteristics for a laminar fully developed flow in an internally corrugated circular tube with axially uniform heat flux with peripherally uniform temperature are obtained using the method of fundamental solution and the radial basis functions. The internal shape of the tube is modelled by cosine function. The nonlinear governing equation of temperature field problem was converted into the hierarchy of non-homogenous problems using the Picard iteration method. The non-homogenous part of the equation was interpolated using the radial basis functions. On each iteration step the solution of the governing equation consists of general solution as linear combination of fundamental solutions and particular solution. Boundary conditions were satisfied using the boundary collocation method. The results of the numerical experiments, that are velocity profiles, temperature field, friction factor, Nusselt number, errors of method were presented.