Impact of solar radiation in the presence of temperature-dependent thermal conductivity of non-Newtonian Casson flow on natural convection heat transfer in plume generated due to the combined effects of heat source and aligned magnetic field

Abstract

Understanding the non-Newtonian Casson fluid is crucial for addressing various challenges in industrial, biological, and environmental applications. In this novel research, Casson fluid with temperature-dependent variable thermal conductivity is analyzed by a natural convective plume generated by horizontal line heat source. The plume system is under the influence of solar radiation and an aligned magnetic field. The momentum equation is transmuted for Casson fluid, while energy equation transmuted for solar radiation and variable thermal conductivity. The coupled partial differential equations changed into ordinary differential equation by employing stream function formulation. For computational evaluation, bvp4c built-in tool of MATLAB is employed in combination with Shooting technique in order to analyze both missing and specified boundary conditions. The upshots of Casson parameter β 1 , thermal conductivity variable γ 1 , radiation parameter Rd , magnetic force parameter S , Prandtl number Pr and magnetic Prandtl number γ on specified and missing conditions are highlighted in the graphical illustrations. The computed outcomes for missing conditions depicts that for Casson parameter β 1 velocity f ′ and temperature θ drops while current density increased with increment in β 1 . Whereas, for specified boundary conditions, the skin friction f ″ and magnetic flux ϕ ′ decreases while heat transfer rate θ ′ enhances for increasing β 1 . For missing conditions, the increasing thermal conductivity variable γ 1 causes velocity f ′ , current density ϕ ″ , and temperature θ to drop. While for specified conditions, the skin friction f ″ , magnetic flux ϕ ′ increases but heat transfer rate θ ′ exhibits reverse trend with enhancing γ 1 . Additionally, a validation analysis has been performed by comparing the values of f ′ ( 0 ) for various values of Pr with prior work, while excluding the other parameters to check its limitations at the boundary layer.