A computer-aided parametric analysis of mixed convection in ducts (Q5936142)

This paper presents a novel technique of computer-aided parametric analysis (CAPA) to formulate simple correlation equations for thermal flow characteristics in a complex convective flow system. In this respect, steady laminar fully developed mixed convection flows are considered in uniformly heated horizontal ducts of square and circular cross-sections. The CAPA technique employs characteristic quantities, constant factors and multi-term relationships to reduce the governing equations to a set of algebraic equations. The authors show that only two point data obtained by numerical computations are needed to determine the constant factors in these correlation equations. The correlation equations are established for Prandtl numbers, Pr, in the range from 0 to 500 and ReRa \(= 0-1 \times 10^5\), where Ra and Re are the Rayleigh and Reynolds numbers, respectively. The range of Prandtl numbers includes the liquid metal at small Pr, and gases, water, and engine oils at large Pr. The correlation equations are obtained for the ratio of cross-sectional (peripheral) averages of friction factor, \(\frac{f\cdot \text{Re}}{(f\cdot\text{Re})_0}=1+A_4,\) and the ratio of Nusselt number, \(\frac {\text{Nu}}{(\text{Nu})_0}= 1+A_6 \text{Pr}\) , where \(A_4\) and \(A_6\) are constants and \(f\) is the non-dimensional stream function. These correlations equations are shown on graphs, and the results predicted by CAPA are compared with those obtained by solving numerically the governing equations for mixed convection in a square duct. It is shown that the results are quite satisfactory.