The　Cattaneo–Christov　heat　flux　is　first　utilized　to　explore　the　heat　transfer　characteristics　of　Marangoni　boundary　layer　flow　in　a　copper–water　nanofluid.　The　Marangoni　boundary　layer　flow　is　driven　by　exponential　temperature.　Five　different　types　of　nanoparticle　shapes　including　sphere,　hexahedron,　tetrahedron,　column　and　lamina　are　considered　for　the　copper–water　nanofluid.　The　nonlinear　system　of　partial　differential　equations　is　reduced　by　similarity　transformations　and　then　solved　numerically　by　the　shooting　method.　It　is　found　that　sphere　nanoparticle　has　better　heat　transfer　enhancement　than　other　nanoparticle　shapes　and　both　the　temperature　and　the　thickness　of　the　thermal　boundary　layer　are　lower　for　the　Cattaneo–Christov　heat　flux　model　than　the　classical　Fourier＇s　law　of　heat　conduction.　©　2017　Wiley　Periodicals,　Inc.