An extended iterative direct-forcing immersed boundary method in thermo-fluid problems with Dirichlet or Neumann boundary conditions

Immersed boundary method for MHD unsteady natural convection around a hot elliptical cylinder in a cold rhombus enclosure filled with a nanofluid

“…In this study, the immersed boundary method (IBM) is used to solve the governing equations. In fact, the IBM method presented in references [42] and [40] is developed in such a way to solve the natural convection heat transfer problems in nanofluids and considering the presence of a magnetic field, as well. Hence, the developed method is applied to study the effect of magnetic field on the flow control and the heat transfer.…”

“…So far, there have been many revisions to this method. In addition, some other methods such as the direct forcing method, and cut cell method have also been developed in the area of IBM method [42]. According to Fig.…”

“…In the above equations, ⃗ f is the external momentum source used to impose the no-slip boundary condition in IBM, h is the external heat source, which is added to the energy equation in order to implement the specified thermal boundary condition in IBM (more details on implementing immersed boundary method would be found in [41,42] and [40]). The third and fourth term, respectively, on the right hand side of Eq.…”

“…In this study, an IBM method presented in literatures [40,42] and [46] is used to solve the problem of fluid flow and heat transfer in nanofluids in the presence of a magnetic field. As is described in [46], two distribution D(Φ) and integration I(∅) operators are used to calculate the force within the boundaries of the flow field.…”

“…These source terms, derived directly from the governing equation and boundary conditions, would be applied to the Cartesian grid nodes (Eulerian points) in order to apply the velocity and temperature boundary conditions. Other details of the current algorithm are the same as the described approaches in literatures [42] and [40].…”