Control of transport of energy by means of external force efects is one of the most important problems in modern applied mathematics. Magnetic force has an inluence on heat transport phenomena and has various applications in industrial, engineering, and medical sciences. The root theme of this work is to study MHD low with stagnation point and low of Cross nanoluid in contracting/extracting cylinder. The impacts of variable thermal conductivity, Lorentz’s force on unsteady Cross nanoluid 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 nanoluid low 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 luid 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 diferential equations are converted into a irst-order system of ordinary diferential equations. Furthermore, bvp4c Matlab built-in command is used for comparison of the numerical solutions to solve these linear ordinary diferential equations. The numerical solutions are plotted in igures as well as tabulated in some tables.