Fully developed flow and heat transfer of nanofluids inside a vertical annulus

Thermally fully developed mixed convection flow of nanofluids in a vertical annular pipe was investigated. Because of the non-adherence of the fluid–solid interface in the presence of nanoparticles, known as slip condition, the Navier’s slip condition was considered at the pipe walls. The Buongiorno’s model was employed for nanofluids that incorporate the effects of Brownian motion Nb and thermophoresis Nt numbers. Using the similarity variables, the governing partial differential equations were transformed into a system of ordinary ones with a constraint parameter and a solution was prepared via a reciprocal numerical algorithm. The effects of Grashof number Gr and slip parameter λ on nanoparticle volume fraction, velocity, temperature, average Nusselt number Nuavg, and pressure coefficient σ have been investigated in details. Results indicate that an increase in Gr and λ reduces the peak value of the dimensionless velocity profile in the core region of the annulus, away from the pipe walls, however, the velocity closer to the pipe walls increases. Furthermore, it was shown that nanofluids can transfer heat more efficiently in a slip condition than in a no-slip condition.