An Improved Numerical Analysis of Couette-Poiseuille Flow Using Hybrid Shooting-Differential Transform Method
DOI:
https://doi.org/10.4314/njtd.v22i1.2938Keywords:
Couette-Poiseuille flow, Differential Transform Method, Modified Shooting Method, Fluid Mechanics, Nonlinear Differential EquationsAbstract
Couette-Poiseuille flow is a fundamental concept in fluid mechanics that involves the combined effects of shear and pressure-driven forces in a channel that has a wide range of engineering applications such as lubrication, microfluidics, and heat exchangers. Appropriate methodological mechanism is important in the analysis of the effects and behaviour of such systems. Conventional numerical methods frequently encounter stability and convergence issues, particularly when dealing with nonlinear or stiff-flow problems. This study presents the application of the Modified Shooting Method (MSM) to solve and analyse the differential equation resulting from the Couette-Poiseuille Flow. The DTM reduces differential equations to a set of algebraic equations, providing improved efficiency and accuracy. On the other hand, the MSM boosts stability and convergence compared to conventional shooting procedures. The hybrid shooting-differential transform method combines the two techniques and leverages the strengths of both, creating a strong solution framework for the nonlinear differential equations that drive Couette-Poiseuille flow. The equations were first transformed into algebraic equations using the appropriate transforms. Finally, the shooting numerical scheme was deployed to solve the transformed equations. The results of our study show that the hybrid method achieved a percentage error of < 10-8% and an improved computing efficiency of >70%.
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