Tangent hyperbolic MHD nanoliquids on non-isothermal stretched sheets: Analyzing the impact of transport parameters, variable fluid properties and convective boundary conditions

• The primary focus of this research is to examine the behavior of tangent hyperbolic magnetohydrodynamic (MHD) nano-liquids on a non-isothermal coagulated stretched sheet. • This study clarifies the complex interactions among various physical parameters affecting nano-liquids’ dynamics, which is crucial for numerous industrial applications. • The findings reveal that an increase in variable thermal conductivity and variable viscosity parameters leads to a higher temperature profile in all scenarios while simultaneously decreasing the velocity profile. • An improved Biot number enhances the rate of temperature transfer, highlighting the significant impact of these parameters on predicting the behavior of MHD tangent hyperbolic nanofluids. • Both magnetic effects and varying thermal conductivity can increase heat transfer rates and reduce skin friction coefficients. The key focus of this research is to look at how tangent hyperbolic magnetohydrodynamic (MHD) nano-liquids move in a non-isothermal coagulated stretched sheet. In this study, we intend to explore how fluid behavior responds to alternations in transport physical parameters. The coagulated sheet is subjected to two distinct boundary conditions to inspect the heat and mass transport rate of the nano liquid. The convective heat boundary condition (CBC) and mass-convective boundary condition (MCBC) are employed to specify the physical conditions at the boundaries of the problem domain. The boundary conditions, responsible for regulating heat flow and mass transfer rates, play a crucial role in shaping the liquid’s behavior. Using a similarity solution, the partial differential equation describing the flow of mass and heat within the system transforms into an interconnected network of non-linear ordinary differential equations. These mathematical equations are subsequently figured out using a numerical finite difference method. This study additionally examines the correlation between thermophoresis and Brownian motion, two fundamental concepts in the dynamics of colloidal suspensions. The study’s findings indicate that the temperature profile increases in all scenarios when the variable thermal conductivity and variable viscosity parameters are increased. In contrast, for the same parameters, the velocity profile is decreased. Further, increasing wall thickness reduces heat dissipation; consequently, the temperature profile similarly affects the velocity power index. The Biot number improves the rates of temperature transfer. These results underscore the significant influence of these parameters in predicting the behavior of MHD tangent hyperbolic nanofluids. This study elucidates the intricate interaction among different physical parameters in the dynamics of nano liquids, which holds significant implications for various industrial applications.