379209 Assessing the Range of Validity of Asymptotic Solution for Heat Transfer in Tubes
Capillary and packed-bed tubes are used in various industrial applications important to the practical aspects of engineering processes such as reactors, heaters, evaporators, thermal, and energy storage units In this research, an analysis of capillary tubes (under laminar regime) and packed-bed tubes (under a PFR) for Newtonian fluids under incompressible conditions will be presented with focus on assessing the range of validity of an asymptotic solution for the heat transfer problem. An asymptotic solution for systems with axial convective and radial diffusive transport and with a constant heat flux at the wall was studied and analyzed. The results of the analysis are reported and their region of validity, determined. A restriction on the asymptotic solutions is based on the fact that the convective-diffusive transfer within the domain is controlled by a constant rate at the capillary walls. The role of asymptotic solution in describing the system behavior and its ranges) both for the packed-bed and capillary tubes were assessed and the ranges of their validity, reported. The solutions are useful to gain an understanding of the system behavior and for potentially helping the solution of other more complicated cases. To our best knowledge, these results are not available in the literature.