An Updated Lagrangian particle hydrodynamics (ULPH) implementation of heat conduction model in weakly-compressive fluid

Heat conduction is quite common in natural, industrial, and military applications. In this work, the updated Lagrangian particle hydrodynamics (ULPH) theory, is utilized and applied to solve heat conduction problems. Since heat conduction is a second-order problem, the high-order ULPH theory is employed to establish the governing equations of heat conduction in ULPH, which is then validated using various numerical simulations. In this work, numerical simulations have been carried out to solve both static heat conduction problems and dynamic heat convection problems. The results show good accuracy and capability of the ULPH heat conduction model, suggesting promising prospects of the ULPH theory in multiphysics problems. The findings of this paper suggest that ULPH is effective in addressing convective heat transfer problems.