Convective heat transport of high-pressure flows inside active, thick walled-tubes with isothermal outer surfaces: usage of Nusselt correlation equations for an inactive, thin walled-tube

Abstract

A semi-analytical analysis was conducted for the prediction of the mean bulk- and interface temperatures of gaseous and liquid fluids moving laminarly at high pressures inside thick-walled metallic tubes. The outer surfaces of the tubes are isothermal. The central goal of this article is to critically examine the thermal response of this kind of in-tube flows utilizing two versions of the 1-D lumped model: one is differential-numerical while the other is differential-algebraic. For the former, the local Nusselt number characterizing an inactive, isothermal tube was taken from correlation equations reported in the heat transfer literature. For the latter, an streamwise-mean Nusselt number associated with an inactive, isothermal tube was taken from standard correlation equations that appear in textbooks on basic heat transfer. In each approach, the combination of the pertinent Nusselt number with the radii ratio of the tube wall and the solid/fluid thermal conductivity ratio, leads to the calculation of either local or mean, equivalent Nusselt numbers, which serve to regulate the thermal interaction between the two dissimilar media. For the two different versions of the 1-D lumped model tested, the computed results consistently demonstrate that the differential-algebraic, provides accurate estimates of both the mean bulk- and the interface temperatures when compared with those temperature results computed with formal 2-D differential models.