In　this　paper,　the　material　forming　process　(such　as　that　of　the　functionally　graded　materials)　of　adding　nanoparticles　into　non-Newtonian　fluids　is　considered.　By　adding　nanoparticles　to　a　non-Newtonian　fluid,　a　new　non-Newtonian　fluid　is　created.　Thus,　the　rheological　characteristics　of　the　original　fluid　matrix　have　been　changed.　This　research　attempts　to　consider　the　influence　of　the　rheological　characteristics　combined　with　the　Brownian　diffusion,　and　the　thermophoresis　diffusion,　the　distribution　of　nano-sized　particles,　the　heat　transfer,　and　the　pressure　drop　on　the　process　of　material　formation.　The　configuration　of　material　treatment　process　is　an　H-height　horizontal　parallel　plate　channel　with　laminar　forced　convection　nanofluids-based　non-Newtonian　fluids　flowing　through.　The　channel　is　separated　by　three　different　boundary　conditions:　heating,　cooling,　and　isolated,　to　simulate　the　melting,　the　freezing,　and　the　flowing　processes　of　materials　in　liquid　form.　The　non-Newtonian　behaviour　of　nanofluids　is　described　by　the　power-law　model.　To　highlight　the　rheological　factors　of　power-law　nanofluids　which　are　not　the　same　as　those　of　the　base　non-Newtonian　fluids,　they　are　assumed　to　vary　with　the　quantity　of　the　added　nanoparticles　in　the　fluid　matrix,　that　is　to　say,　both　the　consistency　coefficient　m　and　the　power-law　index　n　are　considered　as　functions　of　particle　loading　parameter　phi.　Two　sets　of　different　functions　of　consistency　coefficient　m　and　power-law　index　n　are　used　and　compared　in　the　later　calculation.　Method　of　finite　element　is　adopted　to　solve　the　coupled　momentum,　energy　and　concentration　equations,　and　conquer　the　difficulties　arsing　in　the　iteration　of　calculation.　It　is　found　that　whether　the　rheological　factors　of　non-Newtonian　nanofluids　are　considered　changeable　or　not　would　lead　to　very　different　results　of　the　mass　transfer.　Also,　as　the　parameter　N-T　(depicting　the　thermophoresis　diffusion)　increases,　both　temperature　and　concentration　profiles　rise,　while　volume　fraction　of　particles　and　temperature　both　fall　as　N-B　number　(presenting　the　Brownian　diffusion)　increases.　Furthermore,　when　two　models　are　compared,　different　rheological　models　may　possess　different　change　rule　of　power-law　index,　but　in　both　rheological　models,　the　diversification　of　power-law　index　is　so　large　that　it　cannot　be　ignored　in　calculation.　Above　all,　the　detailed　information　of　velocity,　temperature,　and　pressure　drop　obtained　by　rheological　models　highlights　the　necessity　of　studying　the　impact　of　rheological　characteristics　of　non-Newtonian　fluids　in　elaborate　industrial　requirements.