Numerical analysis of the Graetz problem with natural convection in a uniformly heated horizontal tube (Q1117109)

Without the aid of the large Prandtl number assumption, the Graetz problem with the effect of natural convection in a uniformly heated horizontal tube is studied numerically by a relatively novel vorticity- velocity method. Variations in local friction factor and Nusselt number with Rayleigh number are shown for Prandtl numbers, \(\Pr =5,2\) and 0.7. Comparing with the available experimental data for water, the present results for \(\Pr =5\) show a better agreement than those with Pr\(\to \infty\). The asymptotic solutions for \(z\to \infty\) are further compared against the existing analytical and experimental data. A reasonably good agreement is observed.