Modified Buongiorno’s model for fully developed mixed convection flow of nanofluids in a vertical annular pipe

Abstract This paper deals with the mixed convective heat transfer of nanofluids through a concentric vertical annulus. Because of the non-adherence of the fluid–solid interface in the presence of nanoparticle migrations, known as slip condition, the Navier’s slip boundary condition was considered at the pipe walls. The employed model for nanofluid includes the modified two-component four-equation non-homogeneous equilibrium model that fully accounts for the effects of nanoparticles volume fraction distribution. Assuming the fully developed flow and heat transfer, the basic partial differential equations including continuity, momentum, and energy equations have been reduced to two-point ordinary boundary value differential equations and solved numerically. Two cases including constant heat flux at the outer wall and insulated inner wall (Case A) and constant heat flux at the inner wall with insulated outer wall (Case B) have been considered. Results indicate that the buoyancy has negative effects on the efficiency of the system; however, slip velocity at the surface enhances both the heat transfer rate and the efficiency.