Magnetic fluids with magnetic field effect mediated by magnetic particles such as NiZnFe3O4 into base fluid like blood ignite new medical applications interests. Magnetic particles are investigated due to their remarkable properties like as exceptional thermal conductivity, which is considered one of the vital in modern nanotechnology to improve the thermal properties as coolants in heat transfer equipment such as drug administration, cancer treatment, and electronic cooling system. Therefore, the research on novel heat transfer of biomagnetic fluids is extremely potent and inspiring. Hence, the present computational study investigates a NiZnFe3O4-blood magnetic fluids steady heat and flow transmission mechanisms performance past a swirling stretchable cylinder. In addition, due to the difference in rotation between NiZnFe3O4 and blood for the purposes of the effects of rotational viscosity in flow, a magnetic field is applied in both radial and tangential directions. The governing equations describing the physical problem accompanied by boundary conditions have been transformed into a dimensionless form using a suitable similarity transformation. With the aid of the MATLAB computer program, the modified system of nonlinear ordinary differential equations has been computationally resolved using a precise numerical technique known as the parametric continuation method to explore the significance of pertinent physical parameters. With the use of graphs and tabular representations, the role of emerging physical factors in this model, including the Reynolds number, effective magnetization number, ferromagnetic interaction parameter, and particle volume fraction, is described in opposition to the flow and heat fields. The numerical results ultimately demonstrate that, when adding magnetic particles to base fluid (blood), which is superior to conventional fluids, Reynolds number and magnetization force play a key influence in the flow distributions and improvement of heat transfer. It is seen that fluid velocity reduced with enhancement values of ferromagnetic interaction parameter, and particles' volume fraction. Additionally, it is discovered that for Reynolds number, particles' volume fraction, and effective magnetization number, the rate of heat transfer is increased. With authors' best information, till to date, the study of heat and flow transmission of blood with NiZnFe3O4 particles under magnetic field effect over swirling extended cylinder has not been attempted by anyone. Sooth to say, the findings of this paper are entirely original and such numerical outcomes were never published by any scholar researchers. The present model can be applicable in medical sectors especially in drug delivery, cancer treatment, separation, and magnetic resonance imaging.