In　this　paper,　an　attempt　has　been　made　to　extend　the　modified　Buongiorno　model　of　nanofluids　originally　proposed　by　Yang　et　al.　(2013a,　J.　Heat　Transf.,　135,　054504)　from　the　continuum　flow　regime　to　the　slip　flow　regime,　in　consideration　of　the　effects　of　both　velocity　slip　and　temperature　jump　near　the　wall.　Since　the　use　of　velocity　slip　boundary　condition　has　been　extensively　applied　and　well-understood　in　the　literature,　the　focus　of　the　present　study　is　on　the　temperature　jump　boundary　condition.　Based　on　the　theoretical　results　obtained　using　the　Runge-Kutta-Gill　method,　one　can　conclude　that　the　temperature　jump　near　the　wall　has　more　significant　influence　on　the　dimensionless　temperature　than　the　dimensionless　velocity　and　volume　fraction　of　nanoparticles　in　the　cross　section　of　a　channel.　Moreover,　the　neglect　of　temperature　jump　leads　to　the　overestimation　of　Nusselt　number　based　on　the　bulk　mean　nanofluid　thermal　conductivity　NuB,　especially　in　the　slip　flow　regime.　Subsequently,　two　key　parameters　of　nanofluids,　namely　Knudsen　number　Kn　and　the　ratio　of　Brownian　and　thermophoretic　diffusivities　NBT,　were　discussed　in　order　to　investigate　their　effects　on　the　fluid　flow　and　heat　transfer　characteristics　of　nanofluids.　The　results　indicated　that　the　increase　of　Kn　not　only　enhances　heat　transfer　performance,　but　also　reduces　pressure　drop,　demonstrating　the　promising　prospect　of　nanofluids　applications　in　micro　and　nano-scales　devices.　Furthermore,　it　is　found　that　the　maximum　NuB　can　be　achieved　when　Kn　is　around　0.07　or　when　NBT　is　around　0.5,　which　is　useful　for　optimizing　nanoparticles　for　practical　applications.　©　2015　Elsevier　Ltd.