Laminar mixed convection of a nanofluid consisting of Al 2 O 3 and water through an inclined tube has been investigated numerically. As mathematical model two-phase mixture model has been adopted, thus three dimensional elliptical governing equations have been solved to understand the flow behavior at different Re-Gr combinations. Control volume technique is used for discretization of the governing equations. For the convective and diffusive terms the second order upwind method was used while the SIMPLEC procedure was adopted for the velocity-pressure coupling. For different nanoparticle mean diameters and tube inclinations thermo-fluid parameters such as secondary flow, axial velocity profiles, nanoparticles distribution at the tube cross section, axial evolution of peripheral average convective heat transfer coefficient and pressure drop along the tube, have been presented and discussed. Maximum enhancement on the heat transfer coefficient is seen at tube inclination of 45°.
List of symbolsC p Specific heat (J/kg K) D Tube diameter (m) DPD Dimensionless pressure drop along the tube [DP/(q nf V in 2 )] d p Nanoparticle diameter (nm) d f Molecular diameter of base fluid g Gravitational acceleration (m s -2 ) Gr Grashof number ¼ gb eff q 00 D 4 K eff t 2 eff h Convection heat transfer coefficient ¼ W m 2 K K Thermal conductivity (W/m K) Nu Peripheral average Nusselt number ¼ q w D k eff ðT w ÀT b Þ P Pressure (pa) Pr Prandtl number ¼ t eff a eff q w Uniform heat flux (W m -2 ) r Radial direction Re Reynolds number ¼ V m D m eff Ri Richardson number (= GrRe -2 ) T Temperature (K) V Velocity (m s -1 ) Z Axial directionGreek letters a Thermal diffusivity (m 2 /s) and tube inclination with respect to horizon (degree) b Volumetric expansion coefficient (K -1 ) h Angular coordinate / Volume fraction l Dynamic viscosity (N s m -2 ) m Kinematic viscosity (m 2 s -1 ) q Density (Kg m -3 )