Countercurrent Double-Pipe Heat Exchanger Subjected to Flow-Rate Step Change, Part I: New Steady-State Formulation

Abstract

This article deals with a new steady-state formulation of temperatures along a double-pipe heat exchanger in counter ow con guration when the mass ow rate is submitted to step change. The steady-state method is based on estimation of the exponential factor of temperature pro le. This method, compared to results obtained from correlations, gives an alternative approach to the well-known procedures for sizing and rating heat exchangers in industrial applications, such as the "-NTU and LMTD methods. It is based on the average convective heat transfer coef cients of the hot and cold sides, while the other methods are based on the overall heat transfer coef cient.Generally, industrial thermal equipment design is based on the calculation of characteristics only in steady state. However, many applications require knowledge of transient behavior of thermal devices. In fact, it is necessary to explore the unsteady state of thermal processes when real-time control, state computation, optimization, and rational use of energy are investigated . In addition, this kind of study gives more details and information on characterization and validation of the steady state. The steady-state problem is well de ned in the literature, while a general solution for transient problems is not obtainable, due to the complex solutions of transcendenta l governing equations of transport and coupled phenomena. As described in [1], the transient response depends on the initial and nal steady states when the heat exchanger is subjected to the ow-rate step change. In the open literature, steady-state solutions are commonly based on the global heat transfer coef cient [2][3][4]. The LMTD method consists of calculating the logarithmic mean temperature difference. This method is a simple method to use when the inlet temperatures are known and the outlet temperatures are speci ed. If the outlet temperatures are unknown, the effectiveness-NTU (number of transfer units) method should be used. This method is based on calculation of the maximum possible heat transfer rate and the 4

Countercurrent Double-Pipe Heat Exchanger Subjected to Flow-Rate Step Change, Part II: Analytical and Experimental Transient Response

“…As presented in Part I [14], the convective heat transfer coef cients deduced from experimental steady state are in agreement with those obtained from correlations. It is important to point out that the couple (N h , N c ) that satis es both theoretical and experimental results is not unique.…”

“…The theoretical curves of the time constants are obtained from the analytical expressions (1) and (2). The theoretical solutions are computed with the convective heat transfer coef cients deduced from correlations presented in Part I [14]. Theoretical and experimental evolution of time constants of both uids are in good agreement.…”

“…The system of equations (1) of Part I [14] is solved numerically using the MacCormack [12] method. Approximating the temporal response of dimensionless temperature along the heat exchanger to ow rate step with an exponential response, dimensionles s time constants s ¤ h (x ¤ ) and s ¤ c (x ¤ ) of both uids are computed using a quadratic criterion minimization technique.…”

“…The convective heat transfer coef cients h h and h c deduced from the steady-state case are used in the temporal response. Note that the expression of the Nusselt number presented in Part I [14] is used to evaluate the variation of convective heat transfer coef cient when a ow-rate step change is applied.…”

Counter-current tubular heat exchanger: Modeling and adaptive predictive functional control

“…A model obtained by first order approximation describing the response of the temperature along the heat exchanger to a step change of flow rate is proposed in Refs. [3][4][5]. This model is derived from the system of PDE describing the transport and the transfer of heat by convection.…”