<p>The current mathematical model investigates the unsteady flow of fluid–particle suspension and multiphase heat exchange in ferrofluid flow over a spinning and upward migrating disk under the constant Kelvin magnetisation force. The motion of the disk along the rotational axis slows its angular velocity, reducing the radial and circumferential motion of the fluid. Excluding the effect of suspended particles, vertical movement of the disk and the Kelvin magnetisation force, the current problem is reduced to the Von Karman rotating disk problem. Normalised nonlinear differential equations of the system are solved using the technique of finite elements. When a magnetic field is present, increasing the volume concentration of ferromagnetic nanoparticles in the flow increases velocity and temperature. The variation in both temperature and velocity of the suspended particles is greater than that of fluid. The magnetic fluid and magnetic particle radial velocities fall by approximately 7% and 6%, respectively, with an increase in the ferromagnetic interaction number (<i>β</i>₁). On the other hand, there was an approximate 4.5% increase in axial velocity. The radial and tangential components of particle velocities, and the particle temperature, are greatly decreased by increasing the vertical motion parameter. The particle's axial velocity does, however, increase.</p>