Ferrofluid flow in inclined vessel with temperature-dependent properties for tumour therapy

Magnetic fluid hyperthermia and magnetic drug delivery depend on accurate prediction of ferrofluid transport and heat transfer within tumour-surrounded blood vessels. Motivated by the need for physiologically realistic modelling of such therapies, the current study develops a mathematical model of ferrofluid flow and heat transfer in an inclined cylindrical vessel immersed in tumour tissue, taking into account temperature-dependent thermal conductivity and viscosity, as well as magnetic-field-induced body forces. This novel study integrates inclined flow within tumour-surrounded vessels, non-constant thermophysical properties, and magneto-thermal coupling. With the one-dimensional axisymmetric form of coupled momentum and energy equations, in tumour tissue, we describe a nonlinear thermal and flow response to excitation by a magnetic field. This creates a resulting boundary value problem that is non-dimensionalised using a similarity transformation and solved numerically with MATLAB's bvp4c, allowing for a parametric study over the inclination angle, ferromagnetic interaction parameter, and nanoparticle concentration. The results show that temperature-dependent properties influence velocity gradients, skin friction, and heat transfer, particularly near the vessel tumour interface. Thermal transport is further intensified by radiative effects and internal heat generation, leading to a notable enhancement of the Nusselt number, while inclination and curvature introduce secondary but non-negligible modifications. Overall, the study provides quantitative insight into magneto-thermal interactions in ferrofluid-based therapies and offers a theoretical basis for improving magnetic hyperthermia and targeted drug delivery strategies.