Effects of temperature-dependent viscosity on fluid flow and heat transfer in a helical rectangular duct with a finite pitch

Abstract

An incompressible fully developed laminar flow in a helical rectangular duct having finite pitch and curvature with temperature-dependent viscosity under heating condition is studied in this work. Both the cases of one wall heated and four walls heated are studied. The cross-sectional dimensions of the rectangular duct are 2a and 2b. The aspect ratio n=2b/2a is 0.5. Water is used as the fluid and Reynolds number (Re) is varied in the range of 100 to 400. The secondary flow with temperature-dependent viscosity is enhanced markedly as compared to constant viscosity. An additional pair of vortices is obtained near the center of the outer wall at Re=400 for the model of four walls heated with temperature-dependent viscosity, y, while for constant viscosity, the appearance of two additional vortices near the outer wall cannot be found. Besides, the axial velocity decreases and the temperature increases at the central region of the rectangular duct when the temperature-dependent viscosity is considered. Due to the decrease of the viscosity near the walls, the friction factor obtained with temperature-dependent viscosity is lower than that of constant viscosity, while the convective heat transfer for temperature-dependent viscosity is significantly enhanced owing to the strengthened secondary flow. Especially for four heated walls, the effects of viscosity variation on the flow resistance and heat transfer are more significant.