Scale-adaptive simulation of turbulent mixed convection of nanofluids in a vertical duct Farzad Bazdidi-Tehrani 1 • Seyed Iman Vasefi 1 • Arash Khabazipur 1 Received: 22 May 2017 / Accepted: 24 September 2017 Ó Akade ´miai Kiado ´, Budapest, Hungary 2017 Abstract The present paper focuses on the turbulent mixed convection of nanofluids through a vertical square duct. The prediction accuracy of scale-adaptive simulation (SAS) approach is investigated versus RANS-based models (k - e and k - x), in terms of Nusselt number and friction factor. A thermal-dependent model is considered to deter- mine the effective thermal conductivity and effective dynamic viscosity of nanofluids. The present numerical simulations are performed for CuO–water and SiO 2 –water nanofluids and compared with various experimental data. Results indicate that the SAS approach can predict the unsteady flow and heat transfer of nanofluids more accu- rately than the k - e and k - x models. Moreover, it is found that the turbulent velocity fluctuations enhance in streamwise, spanwise and wall-normal directions with an increasing nanoparticle volume fraction, whilst this incre- ment is higher in streamwise direction. Also, in the near- wall region the effect of the presence of nanoparticles on the turbulent velocity fluctuations is more considerable, which increases the turbulence content of the flow field. Keywords Nanofluid  Turbulent  Mixed convection  SAS approach  Vertical duct List of symbols a Duct width (m) c P Specific heat (J kg -1 K -1 ) d p Particle diameter (nm) D h Hydraulic diameter (m) f Peripherally averaged friction factor ð¼ 2DPD h =ðLu 2 ÞÞ g Gravitational acceleration (= 9.80665 m s -2 ) Gr Grashof number ð¼ gbq 00 D 4 h =ðkm 2 ÞÞ h Convective heat transfer coefficient (W m -2 K -1 ) ð¼ q 00 =ðT wall  T bulk ÞÞ i, j, k Coordinate index k Turbulence kinetic energy (m 2 s -2 ) L Duct length (m) MCP Mixed convection parameter ð¼ Ra 1=4 =ðRe 1=2 pr 1=3 ÞÞ Nu Nusselt number ð¼ hD h =kÞ P Pressure (Pa) Pr Prandtl number ð¼ m=aÞ Q Second invariant of the velocity gradient tensor (s -2 ) q 00 Uniform heat flux (W m -2 ) Ra Rayleigh number (= Gr Pr) RANS Reynolds-averaged Navier–Stokes Re Reynolds number (¼ðuD h =mÞ) S Strain rate tensor (s -1 ) SAS Scale-adaptive simulation t Time (s) T Temperature (K) URANS Unsteady Reynolds-averaged Navier–Stokes u i Velocity vector (m s -1 )  u Mean velocity component (m s -1 ) u 0 Fluctuating velocity component (m s -1 ) u, v, w Velocity along x, y, z (m s -1 ) u * Friction velocity (m s -1 ) x, y, z Coordinate system x ? Dimensionless wall distance in x direction z ? Dimensionless wall distance in z direction & Farzad Bazdidi-Tehrani bazdid@iust.ac.ir 1 School of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran 123 J Therm Anal Calorim DOI 10.1007/s10973-017-6747-9