Heat and mass transfer analysis of tangent hyperbolic nanofluid flow over a paraboloidal surface with quadratic mixed convection in porous medium
Tadesse Lamesse, Wubshet Ibrahim
Abstract
This paper investigate the effects of nonlinear mixed convection and magneto hydrodynamic (MHD) flow, incorporating heat generation and a second-order chemical reaction, on the unsteady boundary layer flow of a three-dimensional tangent hyperbolic nanofluid over a paraboloid surface. The governing coupled nonlinear partial differential equations for flow, heat, and mass transfer are transformed into a system of nonlinear ordinary differential equations using similarity transformations. These dimensionless equations are then solved numerically via the Galerkin finite element method, with a grid independence test conducted to verify accuracy across varying mesh densities. The study analyzes the influence of key parameters, including the Weissenberg number, Forchheimer number, unsteady parameter, magnetic parameter, and Eckert number, on velocity, temperature, and concentration profiles. Results indicate that the unsteady parameter significantly impacts system behavior, as increases in this parameter reduce the velocity profile while affecting temperature and concentration profiles oppositely. Variable thickness and nonlinear mixed convection enhance the velocity, whereas a higher magnetic parameter induces magnetic drag, slowing the flow. The range of parameter ranges reflect typical values our findings. It is given by 0.1 ≤ M ≤ 7 , 0.72 ≤ Pr ≤ 6.2 , 0.01 ≤ N b ≤ 7 , 0.1 ≤ N t ≤ 5 , 0.01 ≤ L e ≤ 0.5 , 0.01 ≤ k ≤ 0.9 , 0.1 ≤ A 1 ≤ 4 , 0.1 ≤ H 0 ≤ 0.4 , 0.1 ≤ ℵ ≤ 4 , 1 ≤ α r ≤ 1.7 , 0.1 ≤ m ≤ 0.99 , 0.1 ≤ R a ≤ 4 , 0.1 ≤ B 1 ≤ 0.4 , 0.1 ≤ B 2 ≤ 0.7 , 0.01 ≤ E c ≤ 4 , 0.1 ≤ F r ≤ 2.5 , 0.03 ≤ M * ≤ 1.5 , 0.1 ≤ W e ≤ 7 , 0.1 ≤ λ 1 = λ 2 ≤ 7 , 0.1 ≤ λ 3 ≤ 0.9 . The present solutions are compared with published results from the literature, demonstrating excellent agreement. This underscores the effects of non-Newtonian fluid behavior, nanoparticle presence, porous medium permeability, and mixed convection on heat and mass transfer rates. These insights are valuable for applications in aerodynamics, space sciences, thermal management systems, oil recovery, geothermal energy , and industrial heat exchangers .