In this study, we analyzed the time-dependent, 2D, inclined magnetohydrodynamics mixed convection stagnating point flow of nanoparticle toward a permeable stretchable surface with radiative heat effect. Four different types of water-based nanomaterials, namely titanium dioxide T i O 2 , copper C u , aluminum oxide A l 2 O 3 , and copper oxide C u O are analyzed in this investigation. Numerous engineering disciplines, including energy systems, material processing, thermal management, and environmental engineering, can benefit greatly from research in mixed convection, MHD, and nanofluids. The boundary layer representations of the dominating partial differential equations PDEs are converted into strong nonlinear ordinary differential equations ODEs utilizing similarities approach. The ODEs are computed numerically employing 4th order Runge–Kutta methodology-based shooting scheme. Few special situations, a remarkable alignment is determined between the present study and the outcomes obtained in the existing research. The impact of numerous pertinent variables on the prominent quantities such as velocity, temperature and concentration distributions, drag friction coefficient and heat transport are demonstrated graphically. It is noticed that the velocity and thermal curve decrease as the nanoparticle volume friction factor increases. Moreover, it is analyzed that higher values of nanoparticle concentration diminishes the velocity and temperature distributions.

An enhancement in the thermal conductivity of conventional base fluids has been a topic of great concern in recent years. An effective way to improve the heat transfer rate of conventional base fluids is the suspension of solid nanoparticles. In this framework, a theoretical study is performed to analyse the heat and mass transfer performance in the time-dependent flow of non-Newtonian Williamson nanofluid towards a stretching surface. There exist several studies focusing on the flow of Williamson fluid by assuming zero infinite shear rate viscosity. Nonetheless, there is a lack of knowledge regarding mathematical formulation for two-dimensional flow of the Williamson fluid by taking into account the impacts of infinite shear rate viscosity. In the current review, the Buongiorno model for nanofluids associated with Brownian motion and thermophoretic diffusion is employed to describe the heat transfer performance of nanofluids. The thermal system is composed of flow velocity, temperature, and nanoparticles concentration fields, respectively. The governing dimensionless equations are solved numerically by Runge–Kutta Fehlberg integration method. The numerical results are compared with published results and are found to have an excellent agreement. Effects of numerous dimensionless parameters on velocity, temperature, and nanoparticle concentration field together with the skin friction coefficient and rates of heat and mass transfer are presented with the assistance of graphical and tabular illustrations. With this analysis, we reached that the thermal boundary layer thickness as well as the nanofluids temperature has higher values with increase in thermophoresis and Brownian motion. It is further observed that the rate of heat transfer is significantly raised with an increment in Prandtl number and unsteadiness parameter.