Numerical Analysis of the Magnetic Dipole Effect on a Radiative Ferromagnetic Liquid Flowing over a Porous Stretched Sheet

The effects of a magnetic dipole on a nonlinear thermally radiative ferromagnetic liquidflowing over a stretched surface in the presence of Brownian motion and thermophoresis are investigated.By means of a similarity transformation,ordinary differential equations are derived and solved afterwards using a numerical(the BVP4C)method.The impact of various parameters,namely the velocity,temperature,concentration,is presented graphically.It is shown that the nanoparticles properties,in conjunction with the magnetic dipole effect,can increase the thermal conductivity of the engineered nanofluid and,consequently,the heat transfer.Comparison with earlier studies indicates high accuracy and effectiveness of the numerical approach.An increase in the Brow-nian motion parameter and thermophoresis parameter enhances the concentration and the related boundary layer.The skin-friction rises when the viscosity parameter is increased.A larger value of the ferromagnetic para-meter results in a higher skin-friction and,vice versa,in a smaller Nusselt number.

Melting Flow Analyzation of Radiative Riga Plate Two-Phase Nano-Fluid Across Non-Flatness Plane with Chemical Reaction

There is a strong relationship between analytical and numerical heat transfers due to thermodynamically anticipated findings,making thermo-dynamical modeling an effective tool for estimating the ideal melting point of heat transfer.Under certain assumptions,the present study builds a mathematical model of melting heat transport nanofluid flow of chemical reactions and joule heating.Nanofluid flow is described by higher-order partial non-linear differential equations.Incorporating suitable similarity transformations and dimensionless parameters converts these controlling partial differential equations into the non-linear ordinary differential equations and resulting system of nonlinear equations is established.Plotted graphic visualizations in MATLAB allow for an indepth analysis of the effects of distinguishing factors on fluid flow.Innovative applications of the findings include electronic cooling,heat transfer,reaction processes,nuclear reactors,micro heat pipes,and other related fields.If the exponential index increases,however,the thermal profile becomes worse.By comparing the current findings to those already published in the literature for this particular example,we find that they are highly congruent,therefore validating the present work.Every one of the numerical findings exhibits asymptotic behavior by meeting the specified boundary conditions.