Application of the method of fundamental solutions to the analysis of fully developed laminar flow and heat transfer

Abstract

In this study, fully developed laminar flow and heat transfer in an internally longitudinally finned tube are investigated through application of the meshless method. The flow is assumed to be both hydrodynamically and thermally developed, with a uniform outside-the-wall temperature. The governing equations have been solved numerically by means of the method of fundamental solutions in combination with the method of particular solutions to obtain the velocity and temperature distributions. The advantage of the proposed approach is that it does not require mesh generation on the considered domain or its boundary, but uses only a cloud of arbitrarily located nodes. The results, comprising the friction factor as well as the Nusselt number, are presented for varied length values and fin numbers, as well as the thermal conductivity ratio between the tube and the flowing fluid. The results show that the heat transfer improves significantly if more fins are used.

A meshless procedure for analysis of fluid flow and heat transfer in an internally finned square duct

“…3) and r Sj denotes distance between the point (X, Y) and the j-th source point (X Sj , Y Sj ) defined in Eq. (27). The wall temperature is also approximated using the MMFS.…”

“…7) and r Sj denotes distance between the point (X, Y) and the j-th source point (X Sj , Y Sj ) defined in Eq. (27). The harmonic functions in the local polar coordinates (r G , θ G ) in this solution are given by…”

“…The MFS has been successfully applied for solving different boundary value problems, e.g., direct [24,25] or inverse problems [26]. To the best knowledge of the author, the MFS has been applied for solving fluid flow and heat transfer only in one paper [27].…”

“…The paper presents quite new application of a meshless procedure for solving fluid flow and heat transfer in a internally finned square duct. In comparison to the previous paper on application of the MFS and RBFs for solving fluid flow and heat transfer in internally corrugated or finned ducts [27,[41][42][43], in this paper, the MMFS is applied in order to obtain stable solution because of boundary singularities. Furthermore, instead of the commonly used DRM, the GRBFCM is employed in the paper for obtaining the particular solution in the Picard iteration process, what is also not so typical for application of the MFS for nonlinear and inhomogeneous problems.…”

Selective induction heating to eliminate the fundamental defects of thin‐walled moldings used in electrical industry

“…The wall of the form during the injection phase has to be as hot so the plastic could fill the cavity without any problem and largely mapped the shape of its forming surface . However, during the cooling phase the wall has to be cold so could rapidly channeled the additional heat provided in the former phase …”