Combined forced and free flow of a power-law fluid in a vertical annular duct

Abstract An investigation of mixed convection and flow reversal in a vertical annular duct is presented with reference to laminar and fully-developed flow of a power-law fluid. The boundary surfaces are supposed to be isothermal, with unequal temperatures. The momentum balance and the energy balance equations as well as the viscous stress constitutive equation are solved analytically in order to obtain the velocity field, the viscous stress field and the temperature field. First, two special cases are analyzed: mixed convection of a Newtonian fluid; forced convection of a power-law fluid. Then, in the general case, the evaluation of the friction factors is employed to determine the conditions for the occurrence of flow reversal, for fixed values of the power-law index and of the ratio between the duct inner and outer radii.

[1]  R. Byron Bird,et al.  Non-Newtonian Flow in Annuli , 1958 .

[2]  S. Olek.  Heat transfer in duct flow of non-Newtonian fluids with axial conduction , 1998 .

[3]  T. Irvine,et al.  Predictions of pressure drop and heat transfer in concentric annular ducts with modified power law fluids , 1992 .

[4]  Antonio Barletta,et al.  On the choice of the reference temperature for fully-developed mixed convection in a vertical channel , 1999 .

[5]  K. Raju,et al.  Combined Free and Forced Convection Laminar Heat Transfer in a Vertical Annulus , 1975 .

[6]  A. B. Metzner.  Heat Transfer in Non-Newtonian Fluids , 1965 .

[7]  D. Kalyon,et al.  Nonisothermal extrusion flow of viscoplastic fluids with wall slip , 1997 .

[8]  G. Lauriat,et al.  A new analytical solution for heat transfer in the entrance region of ducts: hydrodynamically developed flows of power-law fluids with constant wall temperature , 1997 .

[9]  Young I Cho,et al.  Non-Newtonian Fluids in Circular Pipe Flow , 1982 .

[10]  D. Ingham,et al.  Combined convection flow of a power-law fluid in a vertical duct with linearly varying wall temperatures , 1995 .

[11]  Jung Yul Yoo,et al.  Laminar convective heat transfer of a Bingham plastic in a circular pipe—I. Analytical approach—thermally fully developed flow and thermally developing flow (the Graetz problem extended) , 1997 .

[12]  D. Ingham,et al.  COMBINED CONVECTION FLOW AND HEAT TRANSFER TO A POWER LAW FLUID IN A VERTICAL DUCT. INCLUDING REVERSE FLOW SITUATIONS , 1994 .

[13]  R. Shah,et al.  Handbook of single-phase convective heat transfer , 1987 .

[14]  A. Shenoy,et al.  Thermal Convection in Non-Newtonian Fluids* , 1982 .

[15]  A. Barletta.  Fully developed laminar forced convection in circular ducts for power-law fluids with viscous dissipation , 1996 .

[16]  Effects of viscous dissipation on combined free and forced convection through vertical concentric annuli , 1971 .

[17]  J. Hartnett,et al.  Non-Newtonian fluid laminar flow and forced convection heat transfer in rectangular ducts , 1992 .

[18]  J. Hartnett,et al.  Heat transfer to newtonian and non-newtonian fluids in rectangular ducts , 1989 .

[19]  J. Prusa,et al.  ASYMPTOTIC AND NUMERICAL SOLUTIONS FOR THERMALLY DEVELOPING FLOWS OF NEWTONIAN AND NON-NEWTONIAN FLUIDS IN CIRCULAR TUBES WITH UNIFORM WALL TEMPERATURE , 1994 .

[20]  Hyoung G. Choi,et al.  Laminar convective heat transfer of a Bingham plastic in a circular pipe—II. Numerical approach hydrodynamically developing flow and simultaneously developing flow , 1997 .

[21]  A. Mujumdar,et al.  Effects of variable viscosity and viscous dissipation on laminar convection heat transfer of a power law fluid in the entrance region of a semi-circular duct , 1995 .