A mathematical model is proposed to describe the flow, heat, and mass transfer behaviour of a non-Newtonian (Jeffrey and Oldroyd-B) fluid over a stretching sheet. Moreover, a similarity solution is given for steady two-dimensional flow subjected to Buongiorno’s theory to investigate the nature of magnetohydrodynamics (MHD) in a porous medium, utilizing the local thermal non-equilibrium conditions (LTNE). The LTNE model is based on the energy equations and defines distinctive temperature profiles for both solid and fluid phases. Hence, distinctive temperature profiles for both the fluid and solid phases are employed in this study. Numerical solution for the nonlinear ordinary differential equations is obtained by employing fourth fifth order Runge–Kutta–Fehlberg numerical methodology with shooting technique. Results reveal that, the velocity of the Oldroyd-B fluid declines faster and high heat transfer is seen for lower values of magnetic parameter when compared to Jeffry fluid. However, for higher values of magnetic parameter velocity of the Jeffery fluid declines faster and shows high heat transfer when compared to Oldroyd-B fluid. The Jeffery liquid shows a higher fluid phase heat transfer than Oldroyd-B liquid for increasing values of Brownian motion and thermophoresis parameters. The increasing values of thermophoresis parameter decline the liquid and solid phase heat transfer rate of both liquids.

In the current paper, we endeavour to execute a numerical analysis in connection with the boundary layer flow induced in a non-Newtonian liquid by a stretching sheet with heat and mass transfer. The effects of chemical reactions and local thermal non-equilibrium (LTNE) conditions are considered in the modelling. The LTNE model is based on energy equations, and provides unique heat transfer for both liquid phases. As a result, different temperature profiles for both the fluid and solid phases are used in this work. The model equation system is reduced by means of appropriate similarity transformations, which are then numerically solved by employing the classical Runge–Kutta (RK) scheme along with the shooting method. The resultant findings are graphed to show the effects of various physical factors on the involved distributions. Outcomes reveal that Jeffrey fluid shows improved velocity for lower values of porosity when compared to Oldroyd-B fluid. However, for higher values of porosity, the velocity of the Jeffery fluid declines faster than that of the Oldroyd-B fluid. Jeffery liquid shows improved fluid phase mass transfer, and decays more slowly than Oldroyd-B liquid for higher values of chemical reaction rate parameter.