Effects of temperature-dependent properties on natural convection of power-law nanofluids in rectangular cavities with sinusoidal temperature distribution

In this paper, the effects of temperature-dependent properties on natural convection of nanofluids in rectangular cavities with sinusoidal temperature distribution are investigated in detail with lattice Boltzmann method. To improve the computational efficiency, all simulations are performed on the Graphics Processing Unit (GPU) using NVIDIA's CUDA. The fluid in the enclosure is a water-based nanofluid containing Al2O3 nanoparticles. The effects of power-law index (0.5⩽n⩽1.5), thermal Rayleigh number (104⩽Raf⩽106), diameter of nanoparticle (25nm⩽ds⩽100nm), nanoparticle volume fraction (0.0⩽ϕ⩽0.04), temperature of the cooled sidewall (315K⩽Tc⩽335K), temperature difference between the sidewalls (10K⩽ΔT⩽50K), amplitude ratio (0.0⩽A⩽1.0), wave number (0.0⩽ω⩽6.0), phase deviation (0.0⩽θ⩽π) and aspect ratio (0.250⩽AR⩽4.00) on heat and fluid flows are investigated. The results reveal that there is an optimal volume fraction ϕopt at which the maximum heat transfer enhancement is obtained, and the value of ϕopt is found to increase slightly with decreasing the nanoparticle diameter, and to increase remarkably with increasing the temperature of Tc or ΔT. In addition, the average Nusselt number is generally decreased with increasing power-law index, while increased with increasing A and ω. Further, we found that the average Nusselt number behaves nonlinearly with the phase deviation parameter. Moreover, the present results also indicate that there is an optimal value of aspect ratio at which the impact of AR on heat transfer is the most pronounced.