Assessment of Smoothed Particle Hydrodynamics (SPH) models for predicting wall heat transfer rate at complex boundary

Nowadays, the use of Smoothed Particle Hydrodynamics (SPH) approach in thermo-fluid application has been starting to gain popularity. Depending on the SPH boundary condition treatment, different methods can be devised to compute the total wall heat transfer rate. In this paper, for the first time, the accuracies of using the popular dummy particle methods, i.e. (a) the Adami Approach (AA) and (b) the higher-order mirror + Moving Least Square (MMLS) method in predicting the total wall heat transfer rate are comprehensively assessed. The modified equation of the 1D wall heat transfer rate is formulated using Taylor's series. For uniform particle layout, MMLS is first-order accurate. Nevertheless, for an irregular particle layout, its order of accuracy drops to ~O(1), the order similar to that of the computationally simpler AA. The AA method is then used to simulate several steady and unsteady natural convection problems involving convex and concave wall geometries. The estimated wall heat transfer rate and the flow results agree considerably well with the available experimental data and benchmark numerical solutions. In general, the current work shows that AA can offer a practical means of estimating wall heat transfer rate at reasonable accuracy for problems involving complex geometry.