Effectiveness-NTU Relations for Heat Exchangers With Streams Having Significant Kinetic Energy Variation

2003 ◽  
Vol 125 (2) ◽  
pp. 377-387 ◽  
Author(s):  
Gregory F. Nellis
Keyword(s):  
Heat Exchanger ◽  
Kinetic Energy ◽  
Differential Equations ◽  
Heat Exchangers ◽  
Parallel Flow ◽  
Temperature Profiles ◽  
Cryogenic Temperatures ◽  
Cold Side ◽  
Counter Flow ◽  
Flow Heat

Effectiveness-NTU equations are derived for counter and parallel-flow heat exchangers with fluids having high velocities. In this case, the change in the kinetic energy occurring within the heat exchanger will significantly affect the temperature profiles. The effectiveness is found to depend on the usual non-dimensional variables that compare the heat exchanger conductance to the hot- and cold-side capacity rates and on four additional nondimensional quantities that reflect the magnitude and distribution of the kinetic energy on the hot and cold-sides of the heat exchanger. The governing differential equations are derived, nondimensionalized, and solved analytically for the case of an exponentially distributed kinetic energy. Graphical solutions are presented and interpreted for several cases. The solutions are applied to a particular case involving high velocities within a counter-flow heat exchanger used to produce cryogenic temperatures.

A Transient Model for Parallel Flow and Counter Flow Heat Exchangers

2013 ◽  
Author(s):  
K. Abbasi ◽  
M. Del Valle ◽  
A. P. Wemhoff ◽  
A. Ortega
Keyword(s):  
Heat Exchanger ◽  
Heat Exchangers ◽  
Transient Behavior ◽  
Parallel Flow ◽  
Thermal Mass ◽  
Dimensionless Time ◽  
Internal Wall ◽  
Counter Flow ◽  
Thermal Capacitance ◽  
Flow Heat

The transient and steady-state response of single pass constant-flow (concentric parallel flow, concentric counter flow) heat exchangers was investigated using a finite volume method. Heat exchanger transients initiated by both step-change and sinusoidally varying hot stream inlet temperatures were investigated. The wall separating the fluid streams was modeled by conduction with thermal mass; hence the heat exchanger transient behavior is dependent on the thermal mass of the fluid streams as well as the internal wall. The outer wall is approximated as fully insulating. The time dependent temperature profiles were investigated as a function of heat exchanger dimensionless length and dimensionless time for both fluids. It was found that the transient response of the heat exchanger is controlled by a combination of the residence time and thermal capacitance of the fluid streams, the overall heat transfer coefficient between the fluid streams, and the thermal capacitance of the internal wall.

scholarly journals An Approximate Transfer Function Model for a Double-Pipe Counter-Flow Heat Exchanger

Energies ◽  
2021 ◽  
Vol 14 (14) ◽  
pp. 4174
Author(s):  
Krzysztof Bartecki
Keyword(s):  
Heat Exchanger ◽  
Transfer Function ◽  
Differential Equations ◽  
Transfer Functions ◽  
Counter Flow ◽  
Transfer Function Matrix ◽  
Rational Transfer ◽  
Flow Heat ◽  
Double Pipe ◽  
Function Matrix

The transfer functions G(s) for different types of heat exchangers obtained from their partial differential equations usually contain some irrational components which reflect quite well their spatio-temporal dynamic properties. However, such a relatively complex mathematical representation is often not suitable for various practical applications, and some kind of approximation of the original model would be more preferable. In this paper we discuss approximate rational transfer functions G^(s) for a typical thick-walled double-pipe heat exchanger operating in the counter-flow mode. Using the semi-analytical method of lines, we transform the original partial differential equations into a set of ordinary differential equations representing N spatial sections of the exchanger, where each nth section can be described by a simple rational transfer function matrix Gn(s), n=1,2,…,N. Their proper interconnection results in the overall approximation model expressed by a rational transfer function matrix G^(s) of high order. As compared to the previously analyzed approximation model for the double-pipe parallel-flow heat exchanger which took the form of a simple, cascade interconnection of the sections, here we obtain a different connection structure which requires the use of the so-called linear fractional transformation with the Redheffer star product. Based on the resulting rational transfer function matrix G^(s), the frequency and the steady-state responses of the approximate model are compared here with those obtained from the original irrational transfer function model G(s). The presented results show: (a) the advantage of the counter-flow regime over the parallel-flow one; (b) better approximation quality for the transfer function channels with dominating heat conduction effects, as compared to the channels characterized by the transport delay associated with the heat convection.

A Mathematical Confirmation for Higher LMTD Value of Counter Flow Versus Parallel Flow Heat Exchangers

2003 ◽  
Vol 125 (1) ◽  
pp. 182-184 ◽  
Author(s):  
Farshad Kowsary ◽  
Mohammad Biglarbegian
Keyword(s):  
Heat Exchangers ◽  
Parallel Flow ◽  
Counter Flow ◽  
Flow Heat ◽  
Increasing Function

A rigorous argument based on the characteristic of a monotonously increasing function is presented to establish the well-known fact of higher LMTD value of counter flow heat exchangers as compared to parallel flow ones.

Modeling of Recuperative Heat Exchanger in a Joule-Thomson Cooler

2001 ◽  
Author(s):  
Kim Choon Ng ◽  
Jinbao Wang ◽  
Hong Xue
Keyword(s):  
Heat Conduction ◽  
Heat Exchanger ◽  
Heat Exchangers ◽  
Cooling System ◽  
Experimental Measurements ◽  
Temperature Dependent ◽  
Counter Flow ◽  
Flow Heat ◽  
Temperature Dependent Properties ◽  
Recuperative Heat Exchanger

Abstract To develop effective heat exchangers for miniature and micro Joule-Thomson (J-T) cooling system, the performance of a recuperative heat exchanger is analyzed and evaluated. The evaluation is based on a theoretical model of the Hampson-type counter-flow heat exchanger. The effect of the pressure and temperature-dependent properties and longitudinal heat conduction are considered. The results of the numerical simulation are validated with the corresponding experimental measurements. The performance of the heat exchanger on effectiveness, flow and various heat conduction losses as well as liquefied yield fraction are analyzed and discussed. The simulation model provides a useful tool for miniature J-T cooler design.

A Constant-Wall-Temperature Model for Prediction of Thermal Performance of Gas-to-Gas Counter-Flow and Parallel-Flow Microchannel Heat Exchangers

2011 ◽  
Author(s):  
Kohei Koyama
Keyword(s):  
Heat Transfer ◽  
Heat Exchanger ◽  
Difference Method ◽  
Heat Exchangers ◽  
Parallel Flow ◽  
Counter Flow ◽  
Partition Wall ◽  
Transfer Rates ◽  
Flow Configuration ◽  
Microchannel Heat Exchanger

Thermal performances of gas-to-gas counter-flow and parallel-flow microchannel heat exchanger have been investigated. Working fluid used is air. Heat transfer rates of both heat exchangers are compared with those calculated by a conventional log-mean temperature difference method. The results show that the log-mean temperature difference method can be employed to a parallel-flow configuration whereas that cannot be employed to a counter-flow configuration. This study focuses on the partition wall which separates hot and cold passages of the microchannel heat exchanger. The partition wall is negligibly thin for a conventional-sized heat exchanger. In contrast, the partition wall is thick compared with channel dimensions for a microchannel heat exchanger. A model which includes the effect of the thick partition wall is proposed to predict thermal performances of the microchannel heat exchangers. The heat transfer rates obtained by the model agree well with those obtained by the experiments. Thermal performances of the counter-flow and parallel-flow microchannel heat exchangers are compared with respect to one another based on temperature of the partition wall. The comparison results show that thermal performances of the counter-flow and parallel-flow microchannel heat exchangers are identical. This is due to performance degradation induced by the thick partition wall of the counter-flow microchannel heat exchanger. This study reveals that the thick partition wall dominates thermal performance of a gas-to-gas microchannel heat exchanger.

Differential-Discrete Mathematical Model of the Recuperative Counter-Flow Heat Exchanger

2008 ◽  
Author(s):  
G. Simeunovic´ ◽  
P. Zi´tek ◽  
D. Lj. Debeljkovic´
Keyword(s):  
Mathematical Model ◽  
Heat Exchanger ◽  
Differential Equations ◽  
Power Plants ◽  
Initial Conditions ◽  
Time Lag ◽  
Experimental Investigations ◽  
Counter Flow ◽  
Real Process ◽  
Flow Heat

The heat exchangers are always constructive elements of nuclear power plants and their dynamics is very important since they introduce a significant time lag in control actions. That’s why their dynamics cannot be ignored. On the basis of the accepted and critically clarified assumptions, a linearized mathematical model of the recuperative counter flow heat exchanger has been derived, taking into account the wall dynamics. The model is based on the fundamental law of energy conservation, covers all heat accumulation storages in the process, and leads to the set of partial differential equations, which solution is not possible in closed form. In order to overcome the solution difficulties, the procedure of differential discrete modelling is applied, leading to the set of ordinary differential equations of a rather high order. These equations are transformed into the state space form suitable for the Matlab environment. The experimental investigations were made, putting some different typical input variables. Specifying the input temperatures and output variables, under the constant initial conditions, the step transient responses have been simulated and presented in graphic form for the particular positions in the heat exchanger in order to compare these results with the experimental data collected from the real process.

Differential Methods for the Performance Prediction of Multistream Plate-Fin Heat Exchangers

1992 ◽  
Vol 114 (1) ◽  
pp. 41-49 ◽  
Author(s):  
B. S. V. Prasad ◽  
S. M. K. A. Gurukul
Keyword(s):  
Heat Transfer ◽  
Heat Exchanger ◽  
Performance Prediction ◽  
Heat Exchangers ◽  
Loss Functions ◽  
Computer Algorithms ◽  
Counter Flow ◽  
Flow Heat ◽  
Differential Methods ◽  
Section Level

Use of traditional methods of rating can prove inaccurate or inadequate for many plate-fin heat exchanger applications. The superiority in practical situations of differential methods, based on dividing the heat exchanger into several sections and a step-wise integration of the heat transfer and pressure loss functions, is discussed. Differential methods are developed for counterflow, crossflow, and cross-counter-flow heat exchangers. The methods developed also avoid iterations at the section level calculations. Design of computer algorithms based on these methods is outlined. Two computer programs developed using the methods are presented and the results for a few typical cases are discussed.

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