A computer-aided parametric analysis of mixed convection in ducts

This study develops a novel technique of computer-aided parametric analysis (CAPA) to formulate simple correlations for thermal flow characteristics in a complex convective flow system. To demonstrate the validity of the technique, fully developed mixed convection in uniformly heated horizontal ducts of square and circular cross-sections are employed as illustrative examples. The effects of secondary flow generated by the thermal buoyancy force are included. The CAPA technique employs characteristic quantities, constant factors and multi-term relationships to convert the governing equations into a set of algebraic equations. Relatively, this technique generates more extensive results than the conventional order-of-magnitude and scaling analyses. With the aid of limited data from numerical results (or measurements), formulas for evaluating the cross-sectional averages of axial velocity and temperature, the strength of secondary vortices, friction factors and the heat transfer rates at various Pr and ReRa can be derived. Comparisons of the present results and the direct numerical solutions manifest quite satisfactory performance of the CAPA technique. Merits of the CAPA technique are: (1) less effort required in the developing procedure, (2) clear parameter-dependence of the thermal flow characteristics, and (3) convenience in using the resultant correlations of algebraic form.