A handy approximate solution for a squeezing flow between two infinite plates by using of Laplace transform-homotopy...

Area of Science:

• Fluid Dynamics
• Applied Mathematics
• Numerical Analysis

Background:

• Investigating fluid behavior under confinement is crucial for various engineering applications.
• Newtonian fluid dynamics between parallel plates presents a classic problem with practical relevance.
• Approximate analytical methods are sought for efficient problem-solving.

Purpose of the Study:

• To propose and evaluate the Laplace Transform Homotopy Perturbation Method (LT-HPM) for solving the axisymmetric Newtonian fluid squeezing problem.
• To assess the accuracy and efficiency of the LT-HPM by comparing its results with exact solutions.
• To demonstrate the applicability of LT-HPM for complex fluid flow scenarios.

Main Methods:

• The study employs the Laplace Transform Homotopy Perturbation Method (LT-HPM).
• The method is applied to model an axisymmetric Newtonian fluid squeezed between two large parallel plates.
• Numerical comparisons are made between the approximate solutions generated by LT-HPM and existing exact solutions.

Main Results:

• The LT-HPM provides approximate solutions that are found to be highly accurate when compared to exact solutions.
• The proposed method is demonstrated to be computationally efficient and easy to implement.
• Figures comparing approximate and exact solutions validate the effectiveness of LT-HPM.

Conclusions:

• The Laplace Transform Homotopy Perturbation Method (LT-HPM) is a powerful and efficient technique for solving fluid dynamics problems.
• LT-HPM offers a reliable approach for obtaining accurate approximate solutions for Newtonian fluid flow.
• The method's handiness and high accuracy make it a valuable tool for researchers and engineers in fluid mechanics.