The objective of this study is to numerically analyse the natural convection of magnetohydrodynamic (MHD) ferrofluid along a vertical thin cylinder with temperature-dependent viscosity (ϵ\documentclass[12pt]{minimal}
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\begin{document}$$\epsilon$$\end{document}). The governing equations are transformed into a non-dimensional form by using suitable transformation and then solved by the implicit finite difference method through the Keller box scheme. The model validation was conducted with the literature, and excellent agreement was obtained by varying fluid characteristics with two different Prandtl numbers (Pr\documentclass[12pt]{minimal}
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\begin{document}$$\text{ Pr }$$\end{document}). The numerical results are discussed in terms of velocity (f′\documentclass[12pt]{minimal}
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\begin{document}$$f'$$\end{document}) and temperature (θ\documentclass[12pt]{minimal}
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\begin{document}$$\theta$$\end{document}) distribution, local skin friction coefficient (Cf\documentclass[12pt]{minimal}
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\begin{document}$$C_{\text{ f }}$$\end{document}), local Nusselt number (Nu\documentclass[12pt]{minimal}
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\begin{document}$$\text{ Nu }$$\end{document}), streamlines, and isotherms. The rheological influence of nanoparticles and magnetic field has been included in the sensitivity analyses through volume fraction parameter (ϕ\documentclass[12pt]{minimal}
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\begin{document}$$\phi$$\end{document}) and Hartmann number (Ha\documentclass[12pt]{minimal}
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\begin{document}$${\text{ Ha }}$$\end{document}), respectively. The presence of nanoparticles was defined by assigning a non-zero value of ϕ\documentclass[12pt]{minimal}
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\begin{document}$$\phi$$\end{document}; however, the comparison was also made in the absence of ϕ\documentclass[12pt]{minimal}
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\begin{document}$$\phi$$\end{document} under different circumstances. The findings from this study suggest that the inclusion of magnetic parameter weakens the convective flow due to the presence of both electric field and magnetic field, due to the existence of the Lorentz force. Furthermore, the mobility of the fluid was also restricted, leading to a reduction in the ferroparticle velocity. At a constant Ha\documentclass[12pt]{minimal}
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\begin{document}$${\text{ Ha }}$$\end{document}, the inclusion of ϕ\documentclass[12pt]{minimal}
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\begin{document}$$\phi$$\end{document} led to similar corresponding characteristic curves, yet not as pronounced as Ha\documentclass[12pt]{minimal}
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\begin{document}$${\text{ Ha }}$$\end{document}. However, under the same Ha\documentclass[12pt]{minimal}
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\begin{document}$${\text{ Ha }}$$\end{document}, as ϵ\documentclass[12pt]{minimal}
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\begin{document}$$\epsilon$$\end{document} increased, the impact on temperature was the opposite due to a reduction in the boundary layer of the thin cylinder. The findings of this study also suggest that in any thermal industrial application concerning flow matter, the natural convective flow under variable ϵ\documentclass[12pt]{minimal}
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\begin{document}$$\epsilon$$\end{document} could be controlled by applying a magnetic field at different strengths to maximise the output for the thin-walled cylindrical device, and yet the whole system can remain stable. The stability of the system is observed and explained through the simulated results on the fluid velocity and temperature profiles under different parametric conditions.
