Here　in,　heat　transfer　characteristics　of　a　magnetized　Casson　sodium　alginate-alumina/copper　hybrid　nanofluid　flowing　through　the　permeable　moving　plane　are　investigated　considering　the　effects　of　thermal　radiation　and　Joule　heating　with　Tiwari　and　Das　model.　The　primary　objective　of　the　present　study　is　to　investigate　the　influence　of　the　velocity　ratio　parameter　on　the　solid　volume　fraction　and　the　Casson　parameter.　In　addition,　the　velocity　and　temperature　profiles　used　in　the　current　study　illustrate　the　effects　of　the　velocity　ratio　parameter　R,　solid　volume　fraction,　suction　effect,　magnetic　field,　Joule　heating,　and　thermal　radiation.　To　apply　the　three-stage　Lobatto　IIIa　with　boundary　value　problems　(bvp4c)　approach　to　implement　the　appropriate　similarity　variables　to　transform　the　partial　differential　equations　(PDEs)　into　a　system　of　nonlinear　ordinary　differential　equations　(ODEs).　It　has　been　determined　that　there　are　two　branch　solutions　for　the　velocity　ratio　parameter　against　using　the　Casson　parameter　and　copper　volume　fraction　values.　Non-unique　branch　at　R　＜　Rci　however,　no　branch　happens　at　R　＞　Rci.　As　the　Eckert　number　and　radiation　grew,　the　rate　of　heat　transmission　surged.　The　increase　of　Casson　hybrid　nanofluid　parameter　values　caused　to　drop　the　skin　friction　in　both　upper　and　lower　branch.　©　2023　The　Authors