Buoyancy driven flow and heat transfer of nanofluids past a square cylinder in vertically upward flow

The present work simulates the buoyancy driven mixed convective flow and heat transfer characteristics of water-based nanofluid past a square cylinder in vertically upward flow using a SUPG (Streamline Upwind Petrov–Galerkin) based finite element method. Nano sized copper (Cu) and alumina (Al2O3) particles suspended in water are used with Prandtl number (Pr) = 6.9. The range of nanoparticle volume fractions (ϕ) considered is 0 ⩽ ϕ ⩽ 20%. Computations are carried out at a representative Reynolds number (Re) of 100. Effect of aiding and opposing buoyancy is brought about by considering the Richardson number (Ri) range −0.5 ⩽ Ri ⩽ 0.5. Al2O3–water and Cu–water nanofluids show suppression of vortex shedding at Ri ⩾ 0.15. Vortex shedding process is initiated and a completely new phenomenon is discovered when the nanofluid solid volume fraction,ϕ, is increased. For Al2O3–water nanofluids, at Ri = 0.15, completely periodic vortex shedding is found for ϕ ⩾ 10%. For Cu–water nanofluid, shedding is observed for both Ri = 0.15 and Ri = 0.5. At Ri = 0.15 shedding is found at ϕ ⩾ 5%, whereas at Ri = 0.5 it is at ϕ ⩾ 15%. A new expression for convective instability of nanofluids is derived to calculate critical nanofluid solid volume fraction. The local Nusselt number increases with increasing ϕ. At a fixed ϕ, the time averaged local Nusselt number is higher for Cu–water nanofluids, as compared to Al2O3–water nanofluids. The average Nusselt number (Nuavg) increases with the concentration of ϕ. Cu–water based nanofluids show higher magnitudes of Nuavg compared to Al2O3–water nanofluids.