magnetic field effects on convective heat transfer of ferrofluid from a heated sphere in porous media

The impact of a magnetic field on the convective heat transfer of ferrofluids from a heated sphere immersed in a porous medium is investigated. the dimensional governing boundary layer equations are initially transformed into a convenient non-dimensional form utilizing the non-dimensional variables. the resulting nonlinear systems of equations are then numerically solved inside the computing domain into a regular rectangle using the effective finite difference method (fdm).  numerical outcomes are then represented in terms of local nusselt number, velocity, temperature profile, and skin friction coefficient, respectively for a range of porosity parameters, ϵ = 0.4, 0.6, 0.8, magnetic effect parameter or hartmann number, ha = 0.0, 1.0, 3.0, 5.0 and the ferroparticle volume fraction coefficients, ϕ = 0%, 2%, 4%, 6%. it is thought that the base fluid’s prandtl number, pr=6.8733, is constant. in addition, the flow pattern inside the boundary layer region is shown using streamlines and isotherms, and the underlying physics of the flow behavior is then explored. there is a graphical presentation of the data. the findings show that velocity decreases with increasing value ha, ϕ and ϵ. an increase in the hartmann number ha causes the temperature to rise. the local n_u  and c_(f  )are decreasing as ha and ϕ values increase. with an increase in the porosity parameter ϵ and ϕ, the temperature profile rises and the c_f and local n_u decrease. for increasing ha, the figure of streamlines seems to depict functions with more gradual changes, and for isotherms, it represents functions with sharper, exponential-like increases. while many works focus on ferrofluids or porous media individually, combining the study of heat transfer in ferrofluids within porous structures can represent a distinct focus. the problem is crucial for developing advanced heat transfer technologies for more efficient energy management in various engineering applications.