where V is the fluid velocity vector, H is the induced magnetic field vector, P = ( p + μ | H | 2 / 8 π ) is the magneto-hydrodynamic pressure, p is the fluid pressure, μ, ν, σ, ρ and ς = ( 4 π μ σ ) − 1 denote the magnetic permeability, kinematic viscosity, electric conductivity, fluid density and magnetic diffusivity, respectively.
Since the fluid streamline vector acting on the particle extremity farther from the wall is greater, the rotational vector might aid in the impact of the particle against the wall, similarly to a flying javelin falling on the ground.
The Navier-Stokes equation, in modern notation, is, where u is the fluid velocity vector, P is the fluid pressure, ρ is the fluid density, υ is the kinematic viscosity, and ∇2 is the Laplacian operator (see Laplace's equation).
Euler's original equation, in modern notation, is, where u is the fluid velocity vector, P is the fluid pressure, ρ is the fluid density, and ∇ indicates the gradient differential operator.
Three orthogonal components of the velocity (Vx, Vy and Vz) are acquired such that the fluid velocity vector is determined at a pore-scale resolution of 156 μm.
is the applied fluid pressure vector at the interface obtained by integrating the pressure over the area of the surface.
where u ( x, t ) denotes the fluid velocity vector field, b is the magnetic field, P = P ( x, t ) is the scalar pressure; while u 0 ( x ) and b 0 ( x ) are the given initial velocity and initial magnetic fields, respectively, in the sense of distributions, with ∇ ⋅ u 0 = ∇ b 0 = 0 ; α, β > 0 are the parameters.
where u = ( u 1 ( x, t ), u 2 ( x, t ), u 3 ( x, t ) ) denotes the fluid velocity vector field, p = p ( x, t ) is the scalar pressure, e 3 = ( 0, 0, 1 ) T, while u 0 and θ 0 are given initial velocity and initial temperature, respectively, with ∇ ⋅ u 0 = 0.
Substituting the known value of fluid velocity vector v n into (14), pOC n +1 can be obtained and then v n +1 is obtainable from (12).
