Ternary　nanofluid　is　a　novel　class　of　working　fluids　with　excellent　heat　transfer　properties.　A　combination　of　three　solid　nanoparticles　consisting　of　SWCNTs,　TiO2,　and　MoS2　is　investigated　for　Darcy-Forchheimer　water-based　ternary　nanofluids.　The　related　mathematical　models　are　established　by　considering　linear,　quadratic　and　nonlinear　thermal　radiations.　Numerical　results　and　entropy　generation　analysis　reveal　the　considerable　influence　of　nonlinear　thermal　radiation　on　temperature　and　the　reduced　Nusselt　number　of　ternary　nanofluids.　With　the　help　of　multiple　quadratic　regression,　the　impact　of　relevant　parameters　on　the　reduced　Nusselt　number　is　studied　in　depth.　The　results　show　that　the　temperature　and　Nusselt　number　are　always　the　highest　in　the　nonlinear　thermal　radiation　model　compared　with　the　linear　and　quadratic　ones,　and　they　are　most　sensitive　to　the　changes　of　Rd　and　δ.　The　thermal　radiation　properties　of　ternary　nanofluids　may　potentially　lead　to　more　efficient　solar　energy　conversion.　This　comparative　study　illustrates　the　advantages　of　ternary　nanofluids　in　improving　solar　radiation　utilization　efficiency　with　nonlinear　thermal　radiation.　©　2023　The　Authors