Liquid solidification in low peclet number pipe flows

Abstract

The combined effects of axial conduction and solidification on heat transfer and pressure drop in pipe flows are investigated by the use of a modified Galerkin finite element method. To allow for the upstream heat conduction, the domain of study is extended from X = ‐∞ to X = ‐∞ as has been done in previous analyses. As a preliminary study on the effect of axial conduction, the present investigation assumes a superheat ratio that is sufficiently large (To > Tf or Tw ≈ Tf) such that solidification begins at a location near X = 0. For numerical convenience, the infinite domain ‐∞ ≤ X ≤ ∞ is transformed onto a finite domain ‐1 ≤ z ≤ 1. The energy equation for the liquid‐phase is then solved by a modified Galerkin finite element method. For better numerical stability, a procedure is proposed for controlling the numerical error that might propagate from the singular point (X, R) = (O, Ro). The profile of the solid‐liquid interface, the heat transfer rate and the pressure drop are presented for various values of Peclet number, Pe = 1, 3, 5, 10 and 30, and for the modified superheat ratio, c = 0.1, 0.5, 5.0, and ∞.

Three-dimensional freezing of flowing water in a tube cooled by air flow

“…Since the tube wall temperature in the present study changes axially and circumferentially during the freezing process, a fixed tube wall temperature T w is not so advantageous to estimate the ice layer thickness in case of air flow cooling because T w is unknown [7][8][9]. It is noteworthy that for a critical value of T i't = 0°C, h w takes on infinity which is unreasonable.…”

Numerical and Experimental Investigations of Solidification in an Initially Emptied Horizontal Turbulent Pipe Flow

“…Lee and Hwang used a numerical approach for solidification problems to examine the combined effects of the following: axial conduction and solidification on the profile of the solid-to-liquid interface, the heat transfer rate, and the pressure drop in pipe flows at low Peclet number [14]. The numerical approach used a Galerkin finite element approach to solve for the energy equations, which was determined to be non-linear with the assumption of axial conduction.…”

“…The numerical model matched well with the experimental data, however, there was a difference in the rate of heat transfer for when the Peclet number was infinite. The authors noted that further investigation into the difference in heat transfer for an infinite Peclet number was required [14].…”