Nanofluid flow in micro-annular tubes at constant wall temperature considering the non-uniform distribution of nanoparticles

In this paper, the modified two-component non-homogeneous mixture model of Buongiorno is developed for the case of forced convection of alumina–water non-homogeneous nanofluid flow in concentric micro-annular tubes at constant wall temperature (CWT). Two different thermal boundary conditions have been considered such that for Case A the inner wall is adiabatic and the outer wall is kept at a constant temperature while for Case B the inner wall temperature remains constant and the outer wall is thermally isolated. Assuming a hydrodynamically and thermally fully developed flow, the governing equations of nanofluids in a concentric annulus are reduced to a nonlinear system of ordinary differential equations and solved using an appropriate reciprocal numerical algorithm via Runge–Kutta–Fehlberg method. The effects of N _BT (from 0.7 to 10), ϕ _B (from 0.01 to 0.03), λ (from 0.05 to 0.2) and ζ (0.4, 0.5 and 0.6) on the non-dimensional volume fraction of nanoparticles, velocity, and temperature profiles have been investigated for both cases. It is indicated that the anomalous heat transfer enhancement depends on the thermal boundary condition as well as the ratio of thermophoresis and Brownian motion. Furthermore, for Case B, there is an optimum nanoparticle diameter around 0.5<N _BT<1 that the thermal performance reaches its peak. However, for Case A, the thermal performance increases as the nanoparticle diameter increases. For both cases, the thermal performance decreases with an increase in the nanoparticle concentration.