The aim of present research is to endorse the interactions of magnetohydrodynamics and ferrohydrodynamics on biomagnetic fluid flow- namely the flow of blood with magnetic particles over a cylinder with prescribed heat flux. The transformation of group theoretic approach namely one parameter group method is applied in this paper. By applying this method, the number of independent variables are reduced into one and the set of partial differential equations reduces to a system of ordinary differential equations along with boundary conditions. The results are presented graphically for blood-Fe₃O₄ and blood-CoFe₂O₄. The numerical simulation for ordinary differential equations is presented by applying an efficient numerical technique which based on common finite difference method along with central differencing, a tridiagonal matrix manipulation and an iterative procedure. The graphical results disclose that the presence of ferromagnetic number enhanced the temperature and more effectively for CoFe₂O₄ magnetic particles than Fe₃O₄. A reduction in blood velocity has been observed for magnetic particles volume fraction. Moreover, the rate of heat transfer enhanced for larger values of magnetic particles volume fraction and attained highest for CoFe₂O₄. The results compared with the previous literature and shows an excellent agreement, which assures the validity of the analysis. The novelty of the present problem is to study the biomagnetic fluid by taking magnetic particles using group theoretical method.