This work contributes mainly an analysis of the impact of a generated magnetic dipole on the magneto heat transport inside a deformable cylinder. Magnetic dipole signifies, magnotherapy and spectroscopy which are medical applications, generate static magnetic fields. The investigation considers the influence of non-linear heat sources and sinks, which result in a noteworthy phenomenon. The flow field is governed by accurate and nondimensional factors, which are used to convert the initial set of highly nonlinear and coupled partial differential equations into a set of nonlinear ordinary differential equations. These nonlinear ordinary differential equations are then solved mathematically using the bvp4c function in MATLAB, taking into account the boundary conditions. Ultimately, this section provides an overview of the ramifications stemming from various physical constraints on the movement of fluids, including nonlinear source/sink effects and other more factors. Ultimately, the discovered results that impose limitations are juxtaposed with those documented in the scientific literature, revealing a significant connection.