The influence of temperature-dependent variable viscosity and suction on a natural convective heat transfer in magneto generated plume

The study provides novel and valuable insights into the behavior of fluid flow and heat transfer in a generated plume under the influence of an aligned magnetic field, which is a complex and less-explored area in fluid dynamics. Incorporating variable viscosity and suction effects adds to the realism and applicability of the model, as it accounts for more realistic conditions where fluid properties change with temperature and external forces influence the flow. A mathematical model is formulated as a system of coupled partial differential equations to analyze the flow dynamics. Subsequently, a numerical solution is derived with stream function formulation for the system of coupled partial differential equations, which transmuted it into ordinary differential equations. To achieve this, the numerical properties of the problem are established through the utilization of a Shooting method in tandem with the MATLAB tool bvp4c. The graphical representations of both missing and specified boundary conditions, analyzes the influences of the viscosity parameter ε , suction parameter ξ , magnetic force parameter S , Prandtl number Pr and magnetic Prandtl number γ . The impact of these parameters on the heat transfer and fluid flow is given in detail. Inclusion of suction velocity counteracted the effects of temperature-dependent viscosity. The velocity f ′ , current density ϕ ″ , temperature θ , skin friction f ″ and magnetic flux ϕ ′ depicted an enhanced behavior while heat transfer rate θ ′ dropped with an increment in viscosity parameter ε . However, for an increasing suction parameter ξ , the reverse trend of these properties is observed as compared to the viscosity parameter ε . The inclusion of suction counteracted to the effects of variable viscosity. Understanding how heat plumes behave under magnetic fields the study aims to provide insights that can be applied to real-world scenarios, such as improving cooling systems in industrial applications, enhancing environmental safety measures, and optimizing biomedical engineering processes.