Investigation of Cattaneo–Christov Double Diffusions Theory in Bioconvective Slip Flow of Radiated Magneto-Cross-Nanomaterial Over Stretching Cylinder/Plate with Activation Energy

The present exploration examines the Cattaneo–Christov double diffusions theory in magneto-Cross nanomaterial flow conveying gyrotactic microorganisms over an extending horizontal cylinder/plate under the aspects of velocity slippage, and activation energy with chemically reacting features. The phenomena of thermophoresis, Brownian movement, and thermal radiation are also incorporated. Utilization of the adopted similarity transformations makes it convenient to transform our governing nonlinear higher-order coupled PDEs into ODEs which are further solved numerically by adopting well-known MATLAB function bvp4c. The quantitative outcomes of emerging thermo-physical and geometrical parameters on the associated non-dimensional profiles of interest are anatomized via requisite graphs and numerically erected tabular forms. It is detected that fluid velocity components decline due to upgraded magnetic field and velocity slippage parameter. When thermal time relaxation parameter varies from 0.0 to 0.9, Nusselt number augments about $$22.02\%$$ for cylindrical surface and about $$23.61\%$$ for plate surface. Likewise, with the same variations in thermal time relaxation parameter Sherwood number increases about $$17.32\%$$ for cylindrical surface and about $$18.24\%$$ for plate surface. Moreover, comparative exploration of the emerging flow features over a flat plate, and cylindrical surface is reported. It is visualized that flat plate offers less temperature than cylindrical surface when flow occurs. The results would offer primary guidance for many industrial, biological, medical and ecological challenges, for instance, bio-fuel, bio-diesel, ethanol, biological tissues, bio-fertilizers, bio-micro-systems, reproduction, infection, and marine life ecosystems, etc.