Heat and mass transfer in gold nanoparticle-enhanced synovial fluid for biomedical applications: a Carreau-Yasuda study

Bader Saad Alshammari; Shahid Hasnain; Muhammad Saqib; Bader Saad Alshammari; Shahid Hasnain; Muhammad Saqib

doi:10.3934/math.2026911

AIMS Mathematics

2026, Volume 11, Issue 7: 22543-22575. doi: 10.3934/math.2026911

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Heat and mass transfer in gold nanoparticle-enhanced synovial fluid for biomedical applications: a Carreau-Yasuda study

1.
Department of Mathematics, Northern Border University, Arar 73222, Saudi Arabia
2.
Department of Mathematics, University of Chakwal, 48800, Pakistan
3.
Department of Mathematics, Khwaja Fareed University of Engineering and Information Technology (KFUEIT), Rahim Yaar Khan, 64200, Pakistan

Received: 08 June 2026 Revised: 13 July 2026 Accepted: 16 July 2026 Published: 27 July 2026
MSC : 76A05, 92C35

Osteoarthritis affects more than 500 million people worldwide, yet existing viscosupplements suffer from rapid clearance and poor cartilage penetration. This study investigates how the coupled effects of viscous dissipation, thermophoretic migration, magnetic induction, and porous absorption govern the spatial distribution of gold nanoparticles injected into the osteoarthritic knee joint. A finite volume solver is developed for flow through a wavy, porous channel with a second-order velocity slip condition at the cartilage surface, incorporating a temperature and concentration-dependent Carreau-Yasuda viscosity, an absorption term in the concentration equation, and the full magnetic induction equation. The results reveal that each transport process is governed by a distinct mechanism: thermal buoyancy and surface slip shape the velocity field, viscous dissipation controls the temperature distribution, and thermophoresis provides a means of actively guiding nanoparticles. Most significantly, cartilage absorption emerges as the dominant barrier to effective drug delivery, while the axial pressure gradient is governed by cartilage permeability and fluid rheology, with second-order slip exerting a strong, previously neglected influence on the pressure distribution. These findings establish that nanoparticle absorption and second-order surface slip cannot be neglected in predictive models of synovial joint biomechanics and intra-articular drug delivery.
- non-Newtonian biofluid,
- nanofluid transport,
- finite volume method
Citation: Bader Saad Alshammari, Shahid Hasnain, Muhammad Saqib. Heat and mass transfer in gold nanoparticle-enhanced synovial fluid for biomedical applications: a Carreau-Yasuda study[J]. AIMS Mathematics, 2026, 11(7): 22543-22575. doi: 10.3934/math.2026911

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Abstract

Osteoarthritis affects more than 500 million people worldwide, yet existing viscosupplements suffer from rapid clearance and poor cartilage penetration. This study investigates how the coupled effects of viscous dissipation, thermophoretic migration, magnetic induction, and porous absorption govern the spatial distribution of gold nanoparticles injected into the osteoarthritic knee joint. A finite volume solver is developed for flow through a wavy, porous channel with a second-order velocity slip condition at the cartilage surface, incorporating a temperature and concentration-dependent Carreau-Yasuda viscosity, an absorption term in the concentration equation, and the full magnetic induction equation. The results reveal that each transport process is governed by a distinct mechanism: thermal buoyancy and surface slip shape the velocity field, viscous dissipation controls the temperature distribution, and thermophoresis provides a means of actively guiding nanoparticles. Most significantly, cartilage absorption emerges as the dominant barrier to effective drug delivery, while the axial pressure gradient is governed by cartilage permeability and fluid rheology, with second-order slip exerting a strong, previously neglected influence on the pressure distribution. These findings establish that nanoparticle absorption and second-order surface slip cannot be neglected in predictive models of synovial joint biomechanics and intra-articular drug delivery.

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