Numerical simulation of convective heat transfer of non-Newtonian carbon-based nanofluids in U-bend tubes using Buongior
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Numerical simulation of convective heat transfer of non‑Newtonian carbon‑based nanofluids in U‑bend tubes using Buongiorno’s model S. H. Mousavi1 · A. Ahmadpour1 · M. Saffar‑Avval1 Received: 12 June 2020 / Accepted: 14 October 2020 © Akadémiai Kiadó, Budapest, Hungary 2020
Abstract The laminar forced convective heat transfer of multi-walled carbon nanotubes (MWCNTs)/water nanofluids with shearthinning rheological behavior inside curved tubes is addressed in the present study. The four-equation model was selected to model the fluid flow and heat transfer of the nanofluid accounting for the Brownian diffusion and thermophoresis forces, and the viscosity variation of the carbon-based nanofluid was approximated by the well-known power-law viscosity function. The governing equations were discretized using the finite volume method and solved in the OpenFOAM CFD package. The developed CFD code was validated against proper experimental data. A comprehensive parametric study was carried out to investigate the effect of pertinent parameters on the problem, including Reynolds and Dean numbers, bend radius and the concentration of the carbon nanotubes. It is shown that even for low Reynolds numbers, thermal performance factors up to 1.27 can be obtained in curved pipes using carbon-based nanofluids. Moreover, MWCNT/water nanofluids demonstrate superior thermal performance in comparison with metal oxide nanofluids inside curved flow passages (e.g., 14% heat transfer enhancement at Re = 900). Finally, an accurate numerical correlation is presented for the non-Newtonian nanofluid forced convective heat transfer inside curved tubes. Keywords Carbon-based nanofluids · Laminar forced convection · U-bend tube · Four-equation model · Power-law viscosity model Abbreviations V Nanofluid velocity (m s−1) cp Specific heat capacity (J kg−1 K−1) DB Brownian diffusion coefficient (m2 s−1) DT Thermophoresis diffusion coefficient (m2 s−1) kB Boltzmann constant (J K−1) T Temperature (K) Q̇ Heat (W) λ Thermal conductivity (W m−1 K−1) K Power-law consistency index (Pa sn) n Power-law index (–) Nu Local Nusselt number (–) Nu Average Nusselt number (–) d Diameter (m) * A. Ahmadpour [email protected] M. Saffar‑Avval [email protected] 1
Mechanical Engineering Department, Amirkabir University of Technology, 424 Hafez Ave, P.O. Box 15875‑4413, Tehran, Iran
P Pressure (Pa) g Gravity (m s−2) R Radius (m) h Heat transfer coefficient (W m−2 K−1) TPF Thermal performance factor (–) Re Reynolds number (–) De Dean number (–) D Pipe diameter (m) Pr Prandtl number (–) Gr Grashof number (–) q′′ Energy flux at the pipe wall (W m−2) f̄ Average Darcy friction factor (–) sbend Bend length (m) Greek symbols 𝜑 Nanoparticle’s volume concentration (–) 𝜇 Constant dynamic viscosity (kg m−1 s−1) ρ Density (kg m−3) τ Stress tensor (Pa) 𝛾̇ Sher rate (s−1) 𝛼 Cross-sectional angle (radian) 𝜃 Bend angle (°) 𝜐 Kinematic viscosity (m2 s−1)
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Subscripts s Pipe wall m Mean value p Particle f Base fluid
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