A simple staggered approach for comprehensive analysis of forced convection heat transfer using the improved element-free Galerkin–reduced integration penalty method to solve the fluid dynamics problem

Abstract

Forced convection heat transfer problems are successfully solved in this work via a simple staggered approach based on the improved element-free Galerkin (IEFG) formulation, which involves a fluid-dynamic analysis conducted in the framework of Navier–Stokes equations written in terms of velocity via a reduced integration penalty method (RIPM). Subsequently, the velocity field achieved from the solution of the Navier–Stokes equations is used in the IEFG-based solution of the internal energy balance formulated in terms of temperature. The proposed approach is tested in the solution and analysis of forced convection heat transfer problems concerning (i) the simultaneously (thermally and fluid-dynamically) developing flow between parallel plates and, (ii) the confined recirculating flow in non-isothermal lid-driven square cavities (also including viscous dissipation effects). A comprehensive parametric analysis developed in terms of characteristic dimensionless numbers is conducted for both problems, providing reliable benchmark results that will be useful to assess the performance of numerical techniques to model forced convection heat transfer phenomena. The versatility and reliability of the proposed approach are also demonstrated in the solution of a more complex problem with curved geometry, such as the non-isothermal lid-driven semicircular cavity with a circular obstacle. The accuracy and feasibility of solving forced convection heat transfer problems via the mesh-less procedure proposed in this communication are proven by comparison with results achieved via mesh-based techniques, and also with analytical solutions available in the literature. The outcomes demonstrate that the appropriate implementation of such numerical technique allows the achievement of accurate and stable results in a straightforward and remarkably simple manner, even under markedly advection-dominated flow conditions in both thermal and fluid dynamics problems.