Nanoscale energy exchange and movement of fluid by Lorentz force is the most recent problem that has a strong connection with applied mathematics due to the consumption of energy. Imposing the inclination of Magnetic dipole in the fluid has abundant applications in magnetic drug engineering, astrophysics, sensors, geophysics, cosmology, and targeting. This study is associated with the exchange of energy under the influence of the inclination of Magnetic dipole with cylinder geometry. The Cross nanofluid mathematical model is launched to carry the nanoscale energy exchange with temperature-dependent thermal conductivity. The permeable cylinder geometry along with the different effects is provided during the expanding/contracting cylinder. Whereas Cross fluid helps to investigate the problem in shear thinning/thickening regions. The numerical representations of the problem are provided via the BVP4C scheme.