说明：  This paperproposesanoptimumdesignmethodfortwo-dimensionalheatconductionproblemwith heat transferboundaryconditionbasedontheboundaryelementmethod(BEM)andthetopology optimization method.Thelevelsetmethodisusedtorepresentthestructuralboundariesandthe boundary meshisgeneratedbasedoniso-surfaceofthelevelsetfunction.Amajornovelaspectofthis paper isthatthegoverningequationissolvedwithoutersatzmaterialapproachandapproximatedheat convectionboundaryconditionbyusingthemeshgeneration.Additionally,theobjectivefunctionalis defined alsoonthedesignboundaries.First,thetopologyoptimizationmethodandthelevelsetmethod are briefly discussed.Usingthelevelsetbasedboundaryexpression,thetopologyoptimizationproblem for theheattransferproblemwithheattransferboundaryconditionisformulated.Next,thetopological derivativeoftheobjectivefunctionalisderived.Finally,severalnumericalexamplesareprovidedto confirm th idityofthederivedtopologicalderivativeandtheproposedoptimumdesignmethod