Laminar forced convection in power-law and Bingham plastic fluids in ducts of semi-circular and other cross-sections

In this work, the effects of the power-law and Bingham plastic viscosity on the flow and heat transfer characteristics of laminar forced convection through non-circular ducts of a range of cross-sections have been investigated numerically over the wide ranges of Peclet number, 10⩽(Pe=Re·Pr)⩽104, power-law index, 0.2⩽n⩽2 and Bingham number, 0⩽Bn⩽15. Two different thermal boundary conditions (constant wall temperature and constant wall heat flux) on the duct wall have been implemented. Extensive results for the flow and temperature fields in terms of the dimensionless velocity and temperature profiles, pressure drop and local and average Nusselt number are presented and discussed both in the developing and fully developed regions. For the sake of conciseness, the results for three duct shapes, namely, semi-circular, four cusped and rectangular, are presented and discussed in detail whereas that for the other shapes are summarised in a tabular form. The dependence of the Poiseuille number (f·Re) and asymptotic Nusselt number (Nu) on the power-law index (n) and Bingham number (Bn) is studied under fully developed (hydrodynamically and thermally) conditions. It is shown that the fanning friction factor has a positive dependence on the increasing values of power-law index while an opposite dependence is observed for the Nusselt number. Finally, simple predictive correlations for hydrodynamic entrance length and Nusselt number are developed as functions of the generalised Reynolds number (Reg), Graetz number (Gz), power-law index or the Bingham number. The paper is concluded by comparing the predictions of the power-law model with that of the extended modified power-law (EMPL) model for a semi-circular duct in order to ascertain the influence of the deficiencies of the power-law equation in capturing the zero- and infinite-shear viscosities on the present results.