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　conductivity,　but　the　velocity　field　diminishes　as　a　result　of　magnification　in　the　Weissenberg　number　and　power　law　index.　Amplification　in　the　reaction　rate　constant　parameter　diminishes　the　concentration　field.　Activation　energy　is　the　key　factor　responsible　for　magnification　in　the　concentration　field.　Furthermore,　smooth　agreement　is　found　during　comparison　with　the　existing　literature.　Statistical　analysis　is　also　conducted　for　physical　quantities.