The improvement of heat transport is a very important phenomenon in nuclear reactors, solar collectors, heat exchangers, and coolers, which can be achieved by choosing the nanofluid as the functional fluid. Nanofluids improve thermophysical properties; as a result, they have made great progress in engineering, biomedical, and industrial applications. Therefore, a numerical study has been proposed to analyze the flow and heat transport of nanoliquids over an extendable surface near a stagnation point with variable thermal conductivity under the influence of the magnetic field, due to their importance in the engineering field. Nanoliquid attributes explain the Brownian motion and the diffusion of thermophoresis. The effects of the chemical reaction and the uniform internal heat source/heat sink are also considered. The Nachtsheim‐Swigert shooting procedure based on the Runge‐Kutta scheme is used for numerical calculation. The impact of effective parameters on velocity, temperature, and volume fraction of the nanoparticles is shown in the graphs and reported in detail. The surface criteria are also estimated with respect to the shear stress and the rate of heat and mass transfer. The aspects of the Brownian moment and Lorentz force are positively correlated to the thermal field of the nanoliquid. Also, the variable thermal conductivity aspect favors the growth of the thermal boundary layer.