Mathematical modeling of a cancer treatment and drug delivery at the macroscale requires evaluating the leakage of solute flux into the targeted tumor or healthy tissue. This study provides a 2D model for the blood and nanoparticle transport in a single vessel surrounded by a tumor. In the vessel, the blood flow is described by Navier-Stokes equations which are coupled to advection–diffusion equation and energy equation for the fluid and nanoparticle transport. Impacts of the Brownian motion and thermophores parameters together with a thermal radiation are examined. Constant vascular fluid velocity across the vessel walls are assumed, and two phase nanofluid model is considered to represent the nanoparticle concentration. The solution methodology is depending on the finite volume method and features of the blood velocity, temperature and nanoparticle concentration are presented graphically. The major outcomes reveal that the blood temperature within the vessel is enhanced as the nanoparticle extravasation coefficient is increasing, while the concentration of the nanoparticles around the tumor is reduced.