A cell-based smoothed finite element method for three-dimensional laminar flow and convective heat transfer on mixed meshes

The smoothed finite element method has demonstrated substantial potential in computational fluid dynamics, but its application to three-dimensional (3D) convective heat transfer remains limited, particularly for coupled flow and thermal transport on mixed meshes. In this work, the cell-based smoothed finite element method (CS-FEM) is extended to 3D incompressible laminar flow with convective heat transfer. A characteristic-based split scheme is incorporated into a fractional-step framework to improve numerical stability and suppress pressure oscillations. The proposed method is first assessed using a manufactured solution on tetrahedral, wedge, and hexahedral meshes, demonstrating accuracy and convergence across different element topologies. It is then validated using 3D natural convection in a side-heated cubic cavity, where comparisons with benchmark data and a strongly distorted mesh test confirm its accuracy and robustness. Transient forced convection past a sphere is further considered to evaluate the method under unsteady thermo-fluid conditions. Finally, CS-FEM on a mixed mesh is applied to laminar flow and heat transfer in a Gyroid-type triply periodic minimal surface (TPMS) structure. The predicted flow and thermal fields agree closely with those obtained using a commercial finite volume solver, with smooth velocity and temperature profiles near highly curved walls in the unstructured mesh regions. The Gyroid TPMS application demonstrates the method's capability to resolve topology-induced secondary-flow features, steep near-wall thermal gradients, and pressure redistribution in tortuous passages, supporting its applicability to thermo-fluid simulations in engineering configurations with intricate 3D geometries. An assessment of five combinations of Reynolds number (Re) and wall temperature shows that increasing Re from 5 to 20 raises the pressure loss and average Nusselt number by factors of 6.47 and 2.26, respectively. At Re = 10, doubling the temperature difference between the heated wall and inlet doubles the heat transfer rate while leaving the average Nusselt number essentially unchanged under constant fluid properties.