On the admissibility of replacing the heat conduction equation of a pipe wall by the heat balance equation in investigating transients in heat exchangers

Abstract

An expression is obtained to determine the fraction of the thermal resistance of a pipe wall which must be referred to the inner boundary when using the heat balance equation for the wall instead of the heat conduction equation (for a heat exchanger with independent heating). Limits of applicability of the model with temperature concentrated along the pipe radius are given.Widely used in the analysis of transients in heat exchangers is the simplification that the heat conduction equation of the pipe wall can be replaced by the heat balance equation. To take account of the heat conduction of the metal, a certain fraction of the wall thermal resistance is referred to the inner (or outer) boundary, i.e., heat-exchange coefficients with a correction for the resistance of the metal heat conduction are introduced [1]. Up to now, individual computations of particular cases by exact and approximate methods are known on whose basis it is impossible to make general deductions.The possibility of using a simplified model to determine the frequency characteristics of a tubular heat exchanger with independent heating (internal heat liberation in the wail or heating from outside by radiation, say) for a heat carrier with changing properties (near-critical state, boiling fluid) is analyzed herein by comparing models with the pipe wall temperature distributed and concentrated along the radius 9Let us first examine the model with wall temperature distributed along the radius. The processes occurring in a tubular heat exchanger under the standard assumptions can be described by a system of equations including the energy, stream continuity and motion equations (in a one-dimensional approximation), and the wall heat conduction equation: