The current investigation explains the chemical reaction and bioconvection process for an inclined magnetized Cross nanofluid over an inclined cylinder using a spectral relaxation approach. Additionally, the facts concerning swimming gyrotactic microorganisms, non-uniform thermal conductivity, and variable decrease or increase in heat sources are taken together. Each profile is checked for inclined and orthogonal magnetic impact. Appropriate transformations made for conversion of nonlinear PDEs into systems of ODEs. For obtaining numerical results, a spectral relaxation approach is utilized, and graphs are plotted with each physical parameter attached. It is well established that the temperature field intensifies owing to an amplification of thermal conduction and Brownian diffusivity phenomena. The heat transfer rate amplifies owing to a magnification in magnetic parameter and thermal c...