<p>The choice of coolants in automobiles, power plants, electrical appliances etc. is basically dependent on the fluid’s thermal characteristics. Thus, the better thermal characteristics of MWCNT (Multi–walled Carbon Nanotubes) helps in modeling an efficient coolant. Further, the flow of fluid is controlled with a magnetic dipole that creates a magnetic field around it. Since ferrite particles respond better to magnetic field, the base fluid for this study is considered to be ferrofluid formed by suspending Fe₃O₄ in H₂O. In order to ensure stability of this combination, CuO nanoparticles are suspended into the ferrofluid along with the MWCNT that possess higher thermal conductivity. Thus, the ternary nanofluid formed with the composition MWCNT−CuO−Fe₃O₄−H₂O is assumed to flow in the presence of exponential heat source/sink. The theoretical model describing such a particular flow is designed by partial differential equation and these equations are further transferred to ordinary differential equation with the help of apt transformation. The numerical solution obtained for this system and the outcomes are analyzed graphically which indicates that the upsurge in the velocity power index enhances the velocity and the temperature profiles of the ternary nanofluid. Furthermore, as the space between the magnetic dipole and the origin expands, the nanofluid flows faster whereas the temperature of the nanofluid diminishes. Also, An Artificial Neural Network model is applied to check the correlation between the parameter and observed that output data and targeted data are strongly co-related with each other.</p>