An efficient immersed boundary method for thermal flow problems with heat flux boundary conditions

A boundary condition implemented-immersed boundary method (IBM) involving velocity correction and heat flux correction is presented in this paper. In the framework of IBM, the velocity correction is made with Dirichlet condition (non-slip), and the temperature correction is made with Neumann (heat flux) condition. The main feature of present approach is to accurately satisfy the governing equations and boundary conditions through velocity and heat flux correction, which is performed by introducing a forcing term in the momentum equation and a heat source/sink term in the energy equation to consider the effect of the immersed boundary. The forcing term and heat source/sink are determined in such a way that the physical boundary conditions for velocity and temperature can be accurately satisfied. Numerical experiments for both forced convection and natural convection problems are conducted to validate the capability and efficiency of present method. Good agreements with available data in the literature have been achieved.