Two Principles of Differential Second Law Heat Exchanger Design

1991 ◽  
Vol 113 (2) ◽  
pp. 329-336 ◽  
Author(s):  
R. B. Evans ◽  
M. R. von Spakovsky
Keyword(s):  
Heat Exchanger ◽  
Temperature Difference ◽  
Heat Exchangers ◽  
Second Law ◽  
First Principle ◽  
Heat Exchanger Design ◽  
Geometric Average ◽  
Mean Temperature ◽  
Second Law Analysis ◽  
Basic Treatment

In this paper, two fundamental principles of differential Second Law analysis are set forth for heat exchanger design. The first principle defines a Second Law temperature, while the second principle defines a Second Law temperature difference. The square of the ratio of the Second Law temperature difference to the Second Law temperature is shown always to be equal to the negative of the partial derivative of the rate of entropy generation (for heat transfer) with respect to the overall conductance of the heat exchanger. For the basic design of elementary heat exchangers, each of these two Second Law quantities is shown to take the form of a simple geometric average. Nonelementary considerations result in corrected geometric averages, which relate directly to the corrected log-mean temperature difference. Both the corrected log-mean temperature difference (nonelementary considerations) and the uncorrected or just log-mean temperature difference (elementary considerations) are widely used in heat exchanger analysis. The importance of these two principles in both exergy and essergy analysis is illustrated by a unified basic treatment of the optimum design of elementary heat exchangers. This results in a single optimization expression for all flow arrangements (i.e., counterflow, parallel flow, and certain crossflow cases).

Arithmetic Mean Temperature Difference and the Concept of Heat Exchanger Efficiency

2003 ◽  
Author(s):  
Ahmad Fakheri
Keyword(s):  
Heat Transfer ◽  
Heat Exchanger ◽  
Heat Transfer Rate ◽  
Temperature Difference ◽  
Heat Exchangers ◽  
Transfer Rate ◽  
Arithmetic Mean ◽  
Counter Flow ◽  
Mean Temperature ◽  
Optimum Heat

In this paper, it is shown that the Arithmetic Mean Temperature Difference, which is the difference between the average temperatures of hot and cold fluids, can be used instead of the Log Mean Temperature Difference (LMTD) in heat exchanger analysis. For a given value of AMTD, there exists an optimum heat transfer rate, Qopt, given by the product of UA and AMTD such that the rate of heat transfer in the heat exchanger is always less than this optimum value. The optimum heat transfer rate takes place in a balanced counter flow heat exchanger and by using this optimum rate of heat transfer, the concept of heat exchanger efficiency is introduced as the ratio of the actual to optimum heat transfer rate. A general algebraic expression as well as a chart is presented for the determination of the efficiency and therefore the rate of heat transfer for parallel flow, counter flow, single stream, as well as shell and tube heat exchangers with any number of shells and even number of tube passes per shell. In addition to being more intuitive, the use of AMTD and the heat exchanger efficiency allow the direct comparison of the different types of heat exchangers.

The Influence of Availability Costs on Optimal Heat Exchanger Design

1988 ◽  
Vol 110 (4a) ◽  
pp. 830-835 ◽  
Author(s):  
L. C. Witte
Keyword(s):  
Heat Exchanger ◽  
Heat Exchangers ◽  
Operating Costs ◽  
Second Law ◽  
Optimal Point ◽  
Optimal Heat ◽  
Available Energy ◽  
Heat Exchanger Design ◽  
A New Technique ◽  
Made In

Optimizing heat exchangers based on second-law rather than first-law considerations ensures that the most efficient use of available energy is being made. In this paper, second-law efficiency is used to develop a new technique for optimizing the design of heat exchangers. The method relates the operating costs of the exchanger to the destruction of availability caused by the exchanger operation. The destruction of availability is directly related to the second-law efficiency of the exchanger. This allows one to find the NTU at which the benefits of reduced availability losses are offset by the costs of added area; this is the optimal point. It can be difficult to determine the proper cost of irreversibility to be used in the optimization process. This issue can be handled by including the irreversibility cost in a dimensionless parameter that represents the ratio of annual ownership costs to annual operating costs that include irreversibility costs. In this way, each heat exchanger designer can estimate the costs of irreversibilities for his particular system, and then use the generalized method that is developed herein for determining the optimal heat exchanger size. The method is applicable to any heat exchanger for which the ε-NTU-R relationships are known.

scholarly journals The Recuperative Heat Exchangers – The Mean Temperature Difference in the Special Cases of Heat Transfer

2020 ◽  
Vol 70 (1) ◽  
pp. 47-56
Author(s):  
Gužela Štefan ◽  
Dzianik František
Keyword(s):  
Heat Transfer ◽  
Heat Exchanger ◽  
Temperature Difference ◽  
Heat Exchangers ◽  
Operating Characteristic ◽  
Mean Temperature ◽  
Special Cases ◽  
Key Variables ◽  
The Mean

AbstractThe heat exchangers are used to heat or cool the material streams. To calculate the heat exchanger, it is important to know the type of heat exchanger and its operating characteristic. This characteristic determines one of the key variables (e.g., F, NTUmin, or θ). In some special cases, it is not necessary to know its operating characteristic to calculate the heat exchanger. This article deals with these special cases. The article also contains a general dependency that allows checking the key variables related to a given heat exchanger.

Heat Exchanger Efficiency

2006 ◽  
Vol 129 (9) ◽  
pp. 1268-1276 ◽  
Author(s):  
Ahmad Fakheri
Keyword(s):  
Heat Capacity ◽  
Heat Exchanger ◽  
Temperature Difference ◽  
Heat Exchangers ◽  
Second Law Of Thermodynamics ◽  
Arithmetic Mean ◽  
Inlet Temperature ◽  
Mean Temperature ◽  
Flow Heat ◽  
The Ideal

This paper provides the solution to the problem of defining thermal efficiency for heat exchangers based on the second law of thermodynamics. It is shown that corresponding to each actual heat exchanger, there is an ideal heat exchanger that is a balanced counter-flow heat exchanger. The ideal heat exchanger has the same UA, the same arithmetic mean temperature difference, and the same cold to hot fluid inlet temperature ratio. The ideal heat exchanger’s heat capacity rates are equal to the minimum heat capacity rate of the actual heat exchanger. The ideal heat exchanger transfers the maximum amount of heat, equal to the product of UA and arithmetic mean temperature difference, and generates the minimum amount of entropy, making it the most efficient and least irreversible heat exchanger. The heat exchanger efficiency is defined as the ratio of the heat transferred in the actual heat exchanger to the heat that would be transferred in the ideal heat exchanger. The concept of heat exchanger efficiency provides a new way for the design and analysis of heat exchangers and heat exchanger networks.

Second Law Analysis of Heat Exchangers

2010 ◽  
Vol 132 (11) ◽  
Author(s):  
Ahmad Fakheri
Keyword(s):  
Heat Exchanger ◽  
Heat Exchangers ◽  
Performance Measure ◽  
Absolute Maximum ◽  
Heat Exchanger Design ◽  
Second Law Analysis ◽  
Entropy Flux ◽  
Shell And Tube ◽  
Open Question ◽  
Measure Entropy

This paper further explores the topic of an ideal heat exchanger, which is still an open question. It is shown that the minimization of entropy production or exergy destruction should not be an objective in heat exchanger design. It is further proven that heat exchanger effectiveness does not correlate with irreversibility. A new performance measure, entropy flux, is introduced and a general expression for its evaluation is presented. It is shown that entropy flux captures many desirable attributes of heat exchangers. For a given effectiveness, a single stream heat exchanger has the absolute maximum entropy flux, and for capacity ratios greater than zero, counterflow has the highest entropy flux, parallel flow the lowest, and the shell and tube heat exchangers are somewhere in between.

On Application of the Second Law to Heat Exchangers

2008 ◽  
Author(s):  
Ahmad Fakheri
Keyword(s):  
Heat Exchanger ◽  
Heat Exchangers ◽  
Performance Measure ◽  
Second Law ◽  
Design Information ◽  
Entropy Minimization ◽  
Heat Exchanger Design ◽  
Entropy Flux ◽  
Measure Entropy

The application of entropy minimization to heat exchangers leads to inconsistent results and does not yield much useful design information. In this paper it is shown that in applying the second law to heat exchangers, three assumptions are typically made that are incorrect and that once they are removed, useful and consistent results are obtained from the second law. In addition, a new performance measure, entropy flux is introduced and it is shown that the objective in heat exchanger design should be the maximization of the entropy flux.

Analysis of the Thermal Stress at the Tubesheet in Floating-Head or U-Tube Heat Exchangers

2017 ◽  
Vol 139 (2) ◽  
Author(s):  
Jiuyi Liu ◽  
Caifu Qian ◽  
Huifang Li
Keyword(s):  
Thermal Stress ◽  
Heat Exchanger ◽  
Temperature Difference ◽  
Heat Exchangers ◽  
Influence Factors ◽  
Area Ratio ◽  
Shell Side ◽  
Tube Heat Exchanger ◽  
Numerical Tests ◽  
Hole Area

Thermal stress is an important factor influencing the strength of a heat exchanger tubesheet. Some studies have indicated that, even in floating-head or U-tube heat exchangers, the thermal stress at the tubesheet is significant in magnitude. For exploring the value, distribution, and the influence factors of the thermal stress at the tubesheet of these kind heat exchangers, a tubesheet and triangle arranged tubes with the tube diameter of 25 mm were numerically analyzed. Specifically, the thermal stress at the tubesheet center is concentrated and analyzed with changing different parameters of the tubesheet, such as the temperature difference between tube-side and shell-side fluids, tubesheet diameter, thickness, and the tube-hole area ratio. It is found that the thermal stress of the tubesheet of floating-head or U-tube heat exchanger was comparable in magnitude with that produced by pressures, and the distribution of the thermal stress depends on the tube-hole area and the temperature inside the tubes. The thermal stress at the center of the tubesheet surface is high when tube-hole area ratio is very low. And with increasing the tube-hole area ratio, the stress first decreases rapidly and then increases linearly. A formula was numerically fitted for calculating the thermal stress at the tubesheet surface center which may be useful for the strength design of the tubesheet of floating-head or U-tube heat exchangers when considering the thermal stress. Numerical tests show that the fitted formula can meet the accuracy requirements for engineering applications.

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