Purpose This is a 3D numerical study of convective heat transfer through a micro concentric annulus governing non-uniform heat flux boundary conditions employing water-Al2O3 nanofluid. The nanofluid is modeled using two-phase mixture model, as it has a good agreement to experimental results. Design/methodology/approach Half of the inner pipe surface area of the annulus section of a double pipe heat exchanger is exposed to a constant heat flux which two models are considered to divide the exposing surface area to smaller ones considering the fact that in all cases half of the inner pipe surface area has to be exposed to the heat flux: in model (A), the exposing surface area is divided radially to two parts (A1), four parts (A2) and eight parts (A3) by covering the whole length of the annulus and in model (B) the exposing surface area is divided axially to two parts (B1), four parts (B2) and eight parts (B3) by covering half of the annulus radially. Findings The results reveal that model (B) leads to higher Nusselt numbers compared to model (A); however, at Reynolds number 10, model (A3) exceeds model (B3). The average Nusselt number is increased up to 142 and 83 per cent at models (A3) with Reynolds number 10 and model (B3) with Reynolds number 1000, respectively. Originality/value This paper is a two-phase investigation of water-Al2O3 nanofluid in a micro concentric annulus under non-uniform heat flux boundary conditions.