Numerical model development analysis for the efficiency of convectively heated radiative ferromagnetic nanoparticles configured by oxytactic moment of microorganisms

• Magnetic dipole analysis for magnetized convectively heated Cross fluid is studied here. • Important characteristics of Ferromagnetic nanoparticles are investigated. • Numerical Technique is employed here. • Oxytactic moment of microorganisms is accounted for modeling nanofluid. This study present investigation is exploration of 2-D fluid flow of Cross model under magnetic effects. The important features of thermophoresis diffusion and radiation parameter for Cross ferrofluid model with effects of convectively heated surface and microorganisms’ features. Under consideration the set of PDEs are then changed in resultant ODEs by use of appropriate similarity variables, after that we tackled these resultant ODEs by use of famous arithmetical scheme called bvp4c. These relationships are expressed pictorially. The graphs reveal that temperature gradient of ferrofluid rises with Brownian motion parameter along with radiation parameter, while reduction is observed for Weissenberg number. Moreover, it is perceived through graphical data that Biot number significantly affect the motile microorganism. Notably, we demonstrate for the first time that the motile microorganism density significantly increases with the Biot number in the context of Cross ferrofluids. This study enhances our understanding of the complex interactions within ferrofluids and their applications in biomedical and engineering fields.