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