Zero-order Axisymmetric Volume-average Model

4 Zero-order Axisymmetric Volume-average Model 

Assuming that all the variables in the physical problem are independent of the azimuthal coordinate (axisymmetry), the projections of Table 11.3 model equations along the three coordinate axes are given in Table 11.4 together with the boundary conditions chosen at the four peripheral boundaries of the porous medium z = 0, z = L, r=0,r= R. We will assume without proof, uniqueness of solution for the system of equations describing this ferrohydrodynamic model. 

The pressure field is assumed to depend only on the axial coordinate. The external magnetic field is purposely chosen to exhibit only radial and axial dependences while fulfilling the divergenceless condition, thus Ho = 0 (Eqs. (11.50) and (11.67.1)). This entrains that the azimuthal component of the equilibrium magnetization vector is zero. In addition, the boundary conditions (Eqs. (11.79)-(11.90), Eqs. (11.103)-(11.106)) as well as Eqs. (11.58)-(11.60) and (11.64)) are verified by the trivial set 0, = = 0, = 0 and Vg = 0. These are taken as solu- 

---

In what follows the magnetoviscosity phenomenon is analyzed by formulating the local ferrohydrodynamic model, the upscaled volume-average model in porous media with the closure problem, and solution and discussion of a simplified zero-order steady-state isothermal incompressible axisymmetric model for non-Darcy-Forchheimer flow of a Newtonian ferrofluid in a porous medium of the... 

---