MHD Micro Polar Fluid Flow on Porous Triangular Plates

Abstract

This study examines the combined effects of deformable surface roughness (DSR) and magneto hydrodynamics (MHD) on the squeeze film behavior between triangular plates (TP). Utilizing Christensen’s stochastic theory, a modified Reynolds equation is developed for a one-dimensional structure featuring both azimuthal and radial roughness patterns. A micro polar fluid is used as the lubricant. Analytical solutions are obtained for the mean squeeze film pressure and workload. Comparisons between MHD and non-MHD scenarios reveal that the inclusion of MHD significantly enhances both pressure and workload. Moreover, as the roughness parameter increases, the pressure and workload also increase with radial distance and film thickness, respectively. Additionally, higher values of the coupling number, Hartmann number, and roughness parameter are found to extend the squeeze time of the lubricant. Keywords: Reynolds’ type equation (RE), Micro polar fluid flow (MPFF), MHD, Porous surface (PS), Deformable surface roughness (DSR), Triangular plates (TP).

Introduction

Squeeze film lubrication is widely used in machines ranging from small clutches to large turbines. The use of non-Newtonian fluids, particularly micro polar fluids (MPFs), has grown due to their enhanced lubrication properties like micro-rotation and particle inertia handling. Blending base oils with long-chain additives improves performance by reducing friction and wear.

2. Literature Review

• Micro Polar Fluids (MPFs): Based on Eringen’s micro-continuum theory, MPFs have been studied in various geometries, consistently showing improved load-carrying capacity.

• Magneto-Hydrodynamics (MHD): Initiated by Hartmann’s study on magnetic fields in fluid flow, MHD applications enhance performance due to electromagnetic forces.

• Surface Roughness: Lubricants alter surface conditions over time, introducing randomness. Christensen and Tonder’s stochastic model is widely used to quantify roughness effects.

• Combined Effects: Prior work shows that MHD and surface roughness both enhance performance. This study explores their combined impact, especially in triangular geometries inspired by wet clutches.

3. Geometrical and Mathematical Model

• The model involves two triangular plates, one fixed and porous, the other moving, separated by an MPF.

• The film thickness is modeled as a combination of deterministic and stochastic (roughness) components.

• Key parameters used include mean (α), standard deviation (σ), and skewness (ε) of roughness, all governed by a probability density function.

• The model incorporates:

  • Conservation equations (momentum, angular momentum, mass)

  • Magnetic field (B?) effects

  • Porosity (Darcy's law)

  • Modified Reynolds equation, capturing the effects of roughness, porosity, and MHD

  • Dimensionless analysis for pressure, load, and time-height relation

4. Solution Approach

• Boundary conditions are applied to solve the system.

• Roughness is treated using stochastic averaging for radial and azimuthal patterns.

• Dimensionless Reynolds equations are derived and solved to obtain:

  • Pressure distribution

  • Load capacity

  • Time-height relationship

5. Results and Discussion

• The study evaluates how MHD and surface roughness, both independently and combined, affect performance parameters.

• Key findings:

  • MHD increases film pressure and load capacity

  • Rough surfaces, especially with appropriate stochastic characteristics, further boost performance

  • Porosity influences fluid flow and pressure

• The research demonstrates the interdependence of MHD and roughness, which is more realistic than treating them separately.

• Graphs and tables in the study highlight this synergy and its implications for real-world bearing systems, particularly wet clutch designs.

References

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Copyright

Copyright © 2025 Prin. Dr. Ms. Pragna A. Vadher, Dr. Ajmeera Chandulal, Dr. Dhinesha Ruwanthi Perera, Dr. Gunamani B. Deheri, Dr. Priti Vasantbhai Tandel, Rakesh Manilal Patel. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.