Control of transport of energy by means of external force effects is one of the most important problems in modern applied mathematics. Magnetic force has an influence on heat transport phenomena and has various applications in industrial, engineering, and medical sciences. The root theme of this work is to study MHD flow with stagnation point and flow of Cross nanofluid in contracting/extracting cylinder. The impacts of variable thermal conductivity, Lorentz’s force on unsteady Cross nanofluid and the cylindrical coordinate are investigated using the behavior of expanding/contracting cylinder. Discovering the impacts of physical parameters on movement, energy exchange and mass transport visibility of Cross nanofluid flow with respect to region (shear thinning/thickening) and on the basis of geometry (contracting/extracting) is most interesting and beauty of this attempt. Smooth debate on fluid behavior in light of numerical outcome classifying shear thinning/thickening and contracting/extracting of geometry is disclosed comprehensively. By keeping the idea of shooting methodology, the nonlinear higher order differential equations are converted into a first-order system of ordinary differential equations. Furthermore, bvp4c Matlab built-in command is used for comparison of the numerical solutions to solve these linear ordinary differential equations. The numerical solutions are plotted in figures as well as tabulated in some tables.