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<p>To maintain the reliability, safety, and stability of various machine components, particularly those involved in rotational motion, scientists are increasingly realizing the need of ongoing lubricant research. Due to improvements in mechanical processes and a rise in the need for durable technology, mechanical engineers use high molecular polymers as lubricants to enhance the performance of bearings under heavy loads and high speeds. These specialized lubricants display non-Newtonian behavior and adhere to various constitutive relationships. One such lubricant is the power-law lubricant, which abides by the Ostwald connection and is widely used in industrial lubrication. In this study, couple stress fluid is used as the bulk medium for theoretical examinations of a power-law lubricant on a spiral disk. The system of equations is converted into a standard system of ordinary equations, and the no-slip condition is replaced with a highly nonlinear interfacial condition. By incorporating the slip boundary condition, numerical results are generated to understand the effect of lubrication on the flow field. To compute the numerical results, a highly accurate numerical scheme named as Legendre wavelet spectral collocation methods is utilized . The error analysis is also carried out to validate the accuracy of the applied numerical scheme.</p>

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Mathematical modeling for interfacial lubrication conditions of couple stress fluid flow by a spiraling disk: a spectral collocation simulation

  • 期刊论文

  • 发表日期：

    2026年1月7日

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  • M. N. Sadiq,
  • S. Bashir,
  • M. Sajid,
  • M. Fahim,
  • W. Mahmood,
  • Ahmad,
  • R. A. Memon

摘要

To maintain the reliability, safety, and stability of various machine components, particularly those involved in rotational motion, scientists are increasingly realizing the need of ongoing lubricant research. Due to improvements in mechanical processes and a rise in the need for durable technology, mechanical engineers use high molecular polymers as lubricants to enhance the performance of bearings under heavy loads and high speeds. These specialized lubricants display non-Newtonian behavior and adhere to various constitutive relationships. One such lubricant is the power-law lubricant, which abides by the Ostwald connection and is widely used in industrial lubrication. In this study, couple stress fluid is used as the bulk medium for theoretical examinations of a power-law lubricant on a spiral disk. The system of equations is converted into a standard system of ordinary equations, and the no-slip condition is replaced with a highly nonlinear interfacial condition. By incorporating the slip boundary condition, numerical results are generated to understand the effect of lubrication on the flow field. To compute the numerical results, a highly accurate numerical scheme named as Legendre wavelet spectral collocation methods is utilized . The error analysis is also carried out to validate the accuracy of the applied numerical scheme.