Prediction of friction factors and axial descent of convective coefficients in laminar flows through internally finned tubes by way of solving two-dimensional heat conduction equations

This paper reports a simple numerical procedure for the prediction of the friction factors and the axial descent of the convection coefficients in the upstream region of internally finned tubes for prevalent laminar regimes. When single-phase viscous fluids are fully developed, the velocity profiles are invariant with the axial coordinate, while the temperature distributions do vary with it. Since the 2-D momentum equation corresponds to a 2-D heat conduction equation, the 2-D velocity profiles supply the product of the friction factor and the Reynolds number, f Re. By implementing the transversal method of lines (TMOL) in the sub-domain z → 0, the 3-D energy equation is transformed into an equivalent quasi 2-D heat conduction equation. The local convective coefficient asymptotes h_{c, z→0} changing with the axial coordinate z → 0 come from the quasi 2-D temperature distributions. The fRe and h_{c, z→0} results have been synthesized for commensureate fin configurations in the sub-domain z → 0 of the heat exchange region where the largest heat transfer activity occurs. The modeling and numerical simulation of the present heat/fluid flow problem articulates concepts learned by students in courses on fluid mechanics, heat transfer and numerical methods.