Sharif University of Technology Scientia Iranica 1026-3098 32 13 2025 08 01 Diffusions of nanoparticles and existence of multiple solutions for Magnetohydrodynamics Williamson nanofluid with slip mechanism 24195 10.24200/sci.2024.63355.8353 EN Aamir Hamid Department of Mathematics, Women University of Azad Jammu and Kashmir, Bagh, Azad Kashmir, Pakistan. Taseer Muhammad Department of Mathematics, College of Science, King Khalid University, Abha, Saudi Arabia. Muhammad Irfan Department of Computer Science, Bahria University, Islamabad Pakistan. Journal Article 2023 10 18 Here the concept of heat transport mechanisms and stagnation point of the MHD Williamson nanofluid have been elaborated with Brownian motion and thermophoresis diffusion past a permeable stretching/shrinking cylinder. Both the conditions of velocity slip and heat source/sink effects are considered. The shooting algorithm with Runge-Kutta-Fehlberg method has been exploited for solutions of ODEs. The effect on drag coefficient, heat and mass transport rates as well as the dimensionless velocity, temperature and concentration fields of the physical boundaries objectives of the study are graphically delineated and thoroughly discussed. As nanoparticle concentration increases at the outer surface of the boundary layer, the rising patterns of Nusselt number as well as skin friction are observed. Dual solutions with the critical value of the mass transfer parameter (0<s_c<s)and the shrinking parameter (χ_c<χ) are obtained for different related parameters in some domains and shrinking parameter. It's worth mentioning that just for the contracting scenario; there are a range of solutions. The slip factor increases the thermal transport amount at the surface of the shrinking cylinder. Here the outcomes noted the average increase of skin friction with respect to γ (curvature) factor to 24.8% with brilliant results compared with former prose.... https://scientiairanica.sharif.edu/article_24195_c1ef3ad7be128ad4969110639a741f23.pdf