An analysis has been performed to study magneto-hydrodynamic (MHD) squeeze flow between two parallel infinite disks where one disk is impermeable and the other is porous with either suction or injection of the fluid. We investigate the combined effect of inertia, electromagnetic forces, and suction or injection. With the introduction of a similarity transformation, the continuity and momentum equations governing the squeeze flow are reduced to a single, nonlinear, ordinary differential equation. An approximate solution of the equation subject to the appropriate boundary conditions is derived using the homotopy perturbation method (HPM) and compared with the direct numerical solution (NS). Results showing the effect of squeeze Reynolds number, Hartmann number and the suction/injection parameter on the axial and radial velocity distributions are presented and discussed. The approximate solution is found to be highly accurate for the ranges of parameters investigated. Because of its simplicity, versatility and high accuracy, the method can be applied to study linear and nonlinear boundary value problems arising in other engineering applications.

https://downloads.hindawi.com/journals/mpe/2009/603916.pdf

Approximate Analysis of MHD Squeeze Flow between Two Parallel Disks with Suction or Injection by Homotopy Perturbation Method

Fluid inertia effects in squeeze films are analyzed. Experimental results are also presented. The agreement between theory and experiment is very good.

Fluid inertia effects in squeeze films

The flow of a viscous incompressible fluid between two parallel plates due to the normal motion of the plates is investigated. The unsteady Navier-Stokes equations are reduced to a nonlinear fourth-order differential equation by using similarity solutions. Homotopy analysis method (HAM) is used to solve this nonlinear equation analytically. The convergence of the obtained series solution is carefully analyzed. The validity of our solutions is verified by the numerical results obtained by fourth-order Runge-Kutta.

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Analytic approximate solutions for unsteady two-dimensional and axisymmetric squeezing flows between parallel plates.

The present paper analyses the unsteady 2‐dimensional flow of a viscous MHD fluid between two parallel infinite plates. The two infinite plates are considered to be approaching each other symmetrically, causing the squeezing flow. A similarity transformation is used to reduce the partial differential equations modeling the flow, to a single fourth‐order non‐linear differential equation containing the Reynolds number and the magnetic field strength as parameters. The velocity functions are obtained for a range of values of both parameters by using the homotopy perturbation method. The total resistance to the upper plate is presented.

Unsteady squeezing flow of a viscous MHD fluid between parallel plates, a solution using the homotopy perturbation method

Numerical investigation for three dimensional squeezing flow of nanofluid in a rotating channel with lower stretching wall suspended by carbon nanotubes

: Magnetohydrodynamic squeeze films are investigated theoretically and experimentally. The theory of magnetohydrodynamic lubrication as applied to squeeze films is extended to include fluid-inertia effects and buoyant forces. Excellent agreement is obtained between theory and experiment. (Author)

The magnetohydrodynamic squeeze film

The magnetohydrodynamic lubrication flow in an externally pressurized thrust bearing is investigated both theoretically and experimentally. The ordinary magnetohydrodynamic lubrication theory for this bearing is extended to include fluid inertia effects. Very good agreement is obtained between theory and experiment.

Dennis C. Kuzma

Papers

Fluid inertia effects in squeeze films

The magnetohydrodynamic squeeze film

Magnetohydrodynamic lubrication flow between parallel plates

Magnetohydrodynamic Squeeze Films

The Magnetohydrodynamic Journal Bearing