简介：Neglectingtheconsumptionofthematerial,asteadyincompressibleflowofanexothermicreactingthird-gradefluidwithviscousheatinginacircularcylindricalpipeisnumericallystudiedforbothcasesofconstantviscosityandReynolds’viscositymodel.Thecoupledordinarydifferentialequationsgoverningtheflowincylindricalcoordinates,aretransformedintodimensionlessformsusingappropriatetransformations,andthensolvednumerically.SolutionsusingMaplearepresentedintabularformandgivenintermsofdimensionlesscentralfluidvelocityandtemperature,skinfrictionandheattransferrateforthreeparametricvaluesintheReynolds’case.Thenumericalresultsforthevelocityandtemperaturefieldsarealsopresentedthroughgraphs.Bifurcationsarediscussedusingshootingmethod.Comparisonsarealsomadebetweenthepresentresultsandthoseofpreviouswork,andthusverifythevalidityoftheprovidednumericalsolutions.Importantpropertiesofthermalcriticalityareprovidedforvariableviscosityparameterandreactionorder.Furthernumericalresultsarepresentedintheformoftablesandgraphsfortransitionofphysicalparameters,whilevaryingcertainflowandfluidmaterialparameters.Also,theflowbehaviourofthereactivefluidofthird-gradeiscomparedwiththoseoftheNewtonianreactivefluid.