Non-Newtonian fluid flow around a Y-shaped fin embedded in a square cavity

This study investigates the free convection of Casson fluid inside a square cavity with intruded Y-shaped fin at the bottom surface. The Casson fluid is a non-Newtonian fluid and has an infinite viscosity at zero rates of shear. This is the first time that this fluid is used in the square cavity containing Y-shaped fin at the bottom surface. The Y-shaped fin helps in understanding the constructal theory and enhancing the heat transfer rate from the fin. The main objective of using this fin is to increase the convective heat transfer surface area. The sidewalls of the cavity are kept at cold temperature, the bottom surface at a hot temperature, and the top surface as adiabatic. The tips of the Y-shaped fin are considered as hot, cold, and adiabatic. The effects of the magnetic field and radiation are included in the momentum and energy equations. The influence of viscous heating is neglected. The buoyancy term is included in the momentum equation using Boussinesq approximation. The dimensionless governing equations are solved numerically using a Galerkin weighted residual technique of the finite element method. The effects of Rayleigh number (Ra = 10 4 –10 6 ), radiation parameter ( R d = 0–10 3 ), Hartmann number (Ha = 0–10 3 ), and Casson parameter ( γ = 0.1–1) on streamlines, isotherms, dimensionless velocity components, temperature, and local Nusselt numbers along the fin and the bottom heated wall are investigated and presented graphically. It is demonstrated that, in the presence of Y-shaped fin, all the pertinent parameters and dimensionless numbers help in enhancing the heat transfer rate along the bottom surface.