A numerical analysis of the magnetohydrodynamic mixed convection hybrid nanofluid flow over a Bi-directional extending sheet subject to slip conditions

• The main focus of this study is to investigate the significance of steady, laminar, and incompressible flow of hybrid nanofluid through the stretching vertical plate. • The hybrid nanofluid flow considers alumina ( A l 2 O 3 ) and silver ( A g ) nanoparticles while water is utilized as base fluid. • The influences of hall current, thermal radiation, magnetic field, and exponential heat source on the hybrid nanofluid flow are examined. • The computation of the transformed system of equations has been achieved by employing a semi-analytical approach called the homotopy analysis method (HAM). • The graphical representations has been considered to show the convergence of HAM. This work investigates a novel analysis of a hybrid nanofluid flow over a vertical extending surface subject to the magnetic field, mixed convection, Joule heating and thermal radiation effects. The research addresses a vertical gap in the literature by incorporating the CattaneoChristov heat flux model to capture thermal relaxation time effect, a feature often neglected in the previous analyses of MHD flows with buoyancy. The resulting system in dimensionless form is handled numerically using the bvp4c technique, allowing detailed evaluation of temperature patterns, flow characteristics, and heat transfer performance under varying physical conditions. This analysis reveals that, both the velocities augment for progression in mixed convection factor while decline with surge in magnetic factor. Primary velocity declines while secondary velocity augments for higher stretching factor. Thermal profiles augment with growth in magnetic factor, radiation factor and Eckert numbers along x- and y-axes while decline with surge in thermal slip factor, thermal relaxation time factor and mixed convection parameter. Comparison of current results with established dataset has conducted, with a strong consistency across all findings that confirms the reliability and validity of the present results. This study offers novel insights into the intricate interactions between many forces and useful recommendations for the design of modern energy systems' thermal management.