Purpose　-　The　purpose　of　this　paper　is　to　investigate　the　combined　effects　of　slip　and　rheological　parameters　on　the　flow　and　heat　transfer　of　the　Herschel-Bulkley　fluid.　Design/methodology/approach　-　The　combinative　dimensionless　parameter　method　is　introduced　into　the　equations　of　the　slip　flow　and　heat　transfer　to　make　the　discussion　more　comprehensive.　More　specifically,　the　slip　and　rheological　parameters　are　transformed　into　the　dimensionless　slip　number　as　well　as　Herschel-Bulkley　number.　We　solve　the　dimensionless　equations　and　then　focus　on　the　effects　of　these　parameters　on　the　slip　flow　and　heat　transfer.　Findings　-　The　results　show　that,　for　a　given　value　of　Herschel-Bulkley　number,　there　is　a　finite　critical　value　of　slip　number　at　which　the　pressure　gradient　reaches　the　lowest　value　and　both　the　dimensionless　yield　radius　and　slip　velocity　become　1.　Meanwhile,　the　Nusselt　number　tends　to　be　infinite　at　this　critical　value　of　slip　number.　For　the　case　of　slip,　the　Nusselt　number　also　approaches　infinity　at　a　finite　critical　value　of　Herschel-Bulkley　number.　Furthermore,　the　dimensionless　velocity　as　well　as　temperature　of　the　yield　pseudoplastic　fluid　with　higher　slip　number　is　lower　within　a　small　radius　but　becomes　higher　near　the　wall.　Meanwhile,　from　the　velocity　and　temperature　profiles,　the　effect　of　Herschel-Bulkley　number　on　these　two　parameters　of　the　Bingham　fluid　at　the　smaller　radius　is　opposite.　Originality/value　-　These　associated　expressions　can　be　generalized　to　the　flow　and　heat　transfer　of　a　Herschel-Bulkley　fluid　under　slip　boundary　condition.　It　can　provide　a　reference　for　the　engineering　application　relating　to　the　heat　transfer　and　flow　of　a　Herschel-Bulkley　fluid.　Meanwhile,　it　also　suggests　some　revelations　for　dealing　with　this　similar　problem.