In the current study, Kelvin force as an external source has been used to affect the ferrofluid flow style. The presence of wire below the pipe creates a variable magnetic force that generates rotating eddies near the wire inside the pipe. To augment the cooling rate, the type of operating fluid changes from pure water to Fe3O4-water ferrofluid. Laminar flow was studied with involving homogeneous model for the ferrofluid. A new term was added to momentum equations as Kelvin force due to the gradient of the magnetic field. Impacts of magnetic number (Mn), the fraction of ferrofluid (φ), and Reynolds number (Re) on the configuration of hydrothermal behavior as well as Nusselt number (Nu) and Darcy factor (f) have been investigated. Utilizing ferrofluid can enhance Nu, while the pressure drop augmentation is negligible. So, selecting such kind of ferrofluid is a promising way to gain better performance. Given Re = 50, Nu enhances by about 1.3% with an increase of the concentration of ferrofluid from 0.01 to 0.04. The rise of Re needs greater pumping power as a higher pressure drop will appear in this case. Besides, a thinner boundary layer has been formed with the growth of Re, which offers a higher Nu. When Mn* = 1.57, the growth of Re provides an augmentation of Nu by 39%. With augmenting Kelvin force, the velocity of ferrofluid enhances, which results in a higher pressure drop.