NTU method (original) (raw)
移動単位数（いどうたんいすう、英: number of transfer units、NTU）とは、熱交換器の熱伝達率の計算に用いられる無次元数である。熱交換器の効率の解析では、通常、対数平均温度差を用いる方法が用いられる。しかし、流体の入口と出口の温度が未知な場合に移動単位数を用いる方法で効率を予測する。 移動単位数NTUは以下で定義される： ここで * U ：熱交換器の全体的な熱伝達係数 * A ：熱交換器の伝熱面積 Cmin の意味は後述する。
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| dbo:abstract | Der englische Begriff Number of Transfer Units (NTU, dt. etwa „Anzahl der Übertragungseinheiten“) bezeichnet eine dimensionslose Kennzahl aus dem Bereich der Wärmeübertragung. Der Nutzen der NTU besteht darin, einen Wärmeüberträger auszulegen oder ein vorhandenes Gerät nachzurechnen. Das NTU-Verfahren vereinfacht den Auslegungs- bzw. Nachrechnungsprozess erheblich, da es bei komplizierteren Strömungsformen schwierige Berechnungen erspart. Herleiten lässt sich NTU, indem man zunächst für den ohne Verlust übertragenen Wärmestrom die Formel für das Fluid (mit dem Massenstrom , der spezifischen Wärmekapazität bei konstantem Druck, der Temperaturdifferenz ) sowie die Formel für die Übertragungsfläche (mit dem Wärmedurchgangskoeffizient , dem Flächeninhalt der Übertragungsfläche sowie der logarithmischen Temperaturdifferenz ) notiert, die wegen der Energieerhaltung beide gleich sein müssen: Nun formt man diese Gleichung in das Verhältnis von Temperaturdifferenz und logarithmischer Temperaturdifferenz um, da letztere bei Wärmeübertragern, die nicht dem Gleich- oder Gegenstromprinzip folgen, schwer zu bestimmen ist: In der Literatur wird der Ausdruck auch als Wärmekapazitätsstrom (oft auch ) bezeichnet.Dieser Ausdruck bezeichnet den NTU für den Wärmeübergang. Der NTU für den Stoffübergang berechnet sich wie folgt: ist hier der Stoffübergangskoeffizient mit als Einheit und der Volumenstrom. Um mit NTU zu arbeiten benötigt man sogenannte NTU-Diagramme, die es für gängige Strömungstypen in der Fachliteratur gibt. Anhand bekannter Massenströme sowie Fluidtemperaturen kann im Diagramm die NTU abgelesen werden. Unter Schätzung des Wärmedurchgangskoeffizienten kann die wärmeübertragende Fläche ermittelt werden. (de) The Number of Transfer Units (NTU) Method is used to calculate the rate of heat transfer in heat exchangers (especially counter current exchangers) when there is insufficient information to calculate the Log-Mean Temperature Difference (LMTD). In heat exchanger analysis, if the fluid inlet and outlet temperatures are specified or can be determined by simple energy balance, the LMTD method can be used; but when these temperatures are not available The NTU or The Effectiveness method is used. The effectiveness-NTU method is very useful for all the flow arrangements (besides parallel flow and counterflow ones) because the effectiveness of all other types must be obtained by a numerical solution of the partial differential equations and there is no analytical equation for LMTD or effectiveness, but as a function of two variables the effectiveness for each type can be presented in a single diagram. To define the effectiveness of a heat exchanger we need to find the maximum possible heat transfer that can be hypothetically achieved in a counter-flow heat exchanger of infinite length. Therefore one fluid will experience the maximum possible temperature difference, which is the difference of (The temperature difference between the inlet temperature of the hot stream and the inlet temperature of the cold stream). The method proceeds by calculating the heat capacity rates (i.e. mass flow rate multiplied by specific heat) and for the hot and cold fluids respectively, and denoting the smaller one as : Where is the mass flow rate and is the fluid's specific heat capacity at constant pressure. A quantity: is then found, where is the maximum heat that could be transferred between the fluids per unit time. must be used as it is the fluid with the lowest heat capacity rate that would, in this hypothetical infinite length exchanger, actually undergo the maximum possible temperature change. The other fluid would change temperature more slowly along the heat exchanger length. The method, at this point, is concerned only with the fluid undergoing the maximum temperature change. The effectiveness, is the ratio between the actual heat transfer rate and the maximum possible heat transfer rate: where: Effectiveness is a dimensionless quantity between 0 and 1. If we know for a particular heat exchanger, and we know the inlet conditions of the two flow streams we can calculate the amount of heat being transferred between the fluids by: For any heat exchanger it can be shown that: For a given geometry, can be calculated using correlations in terms of the "heat capacity ratio" and the number of transfer units, where is the overall heat transfer coefficient and is the heat transfer area. For example, the effectiveness of a parallel flow heat exchanger is calculated with: Or the effectiveness of a counter-current flow heat exchanger is calculated with: For a balanced counter-current flow heat exchanger (balanced meaning , which is a scenario desirable to reduce entropy): A single-stream heat exchanger is a special case in which . This occurs when or and may represent a situation in which a phase change (condensation or evaporation) is occurring in one of the heat exchanger fluids or when one of the heat exchanger fluids is being held at a fixed temperature. In this special case the heat exchanger behavior is independent of the flow arrangement and the effectiveness is given by: The effectiveness-NTU relationships for crossflow heat exchangers and various types of shell and tube heat exchangers can be derived only numerically by solving a set of partial differential equations. So, there is no analytical formula for their effectiveness, but just a table of numbers or a diagram. These relationships are differentiated from one another depending (in shell and tube exchangers) on the type of the overall flow scheme (counter-current, concurrent, or cross flow, and the number of passes) and (for the crossflow type) whether any or both flow streams are mixed or unmixed perpendicular to their flow directions. (en) 移動単位数（いどうたんいすう、英: number of transfer units、NTU）とは、熱交換器の熱伝達率の計算に用いられる無次元数である。熱交換器の効率の解析では、通常、対数平均温度差を用いる方法が用いられる。しかし、流体の入口と出口の温度が未知な場合に移動単位数を用いる方法で効率を予測する。 移動単位数NTUは以下で定義される： ここで * U ：熱交換器の全体的な熱伝達係数 * A ：熱交換器の伝熱面積 Cmin の意味は後述する。 (ja) Il numero di unità di trasporto (abbreviato NTU) è un numero criptico di cui si fa uso in termodinamica nell'analisi e nella progettazione di scambiatori termici a fluido col metodo ε-NTU. (it) Metoda NTU (z ang. number of transfer units; metoda wyznaczania liczby jednostek przenikania ciepła) – metoda analizy wymienników ciepła wykorzystującą równania cieplne przekształcone do postaci bezwymiarowej. (pl) O método das NTU (número de unidades de transferência, em inglês Number of Transfer Units), também conhecido por método ε-NTU (eficiência térmica-número de unidades de transferência) é usado para calcular a taxa de transferência térmica em trocadores de calor (especialmente trocadores em contracorrente) quando não existe informação suficiente para calcular a Diferença de temperatura média logarítmica (DTML). Na análise de trocadores de calor, se as temperaturas de entrada e de saída de fluido são especificados ou podem ser determinadas pelo balanço de massa simples, o método LMTD pode ser usado, mas quando essas informações não estão disponíveis o método NTU ou da eficiência" é usado. (pt) NTU法是熱傳單元數法的簡稱，也稱為熱交換有效性法，是在一熱交換器（特別是逆流交换的熱交換器）沒有對數平均溫差（LMTD）的條件下，計算其熱交換速率的方式。 在熱交換器分析中，若流體的入口溫度和出口溫度已知，或是可以用能量平衡的方式計算，可以用對數平均溫差來進行分析，但若沒有這些資訊，可以用NTU法來分析。 (zh) |
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| rdfs:comment | 移動単位数（いどうたんいすう、英: number of transfer units、NTU）とは、熱交換器の熱伝達率の計算に用いられる無次元数である。熱交換器の効率の解析では、通常、対数平均温度差を用いる方法が用いられる。しかし、流体の入口と出口の温度が未知な場合に移動単位数を用いる方法で効率を予測する。 移動単位数NTUは以下で定義される： ここで * U ：熱交換器の全体的な熱伝達係数 * A ：熱交換器の伝熱面積 Cmin の意味は後述する。 (ja) Il numero di unità di trasporto (abbreviato NTU) è un numero criptico di cui si fa uso in termodinamica nell'analisi e nella progettazione di scambiatori termici a fluido col metodo ε-NTU. (it) Metoda NTU (z ang. number of transfer units; metoda wyznaczania liczby jednostek przenikania ciepła) – metoda analizy wymienników ciepła wykorzystującą równania cieplne przekształcone do postaci bezwymiarowej. (pl) O método das NTU (número de unidades de transferência, em inglês Number of Transfer Units), também conhecido por método ε-NTU (eficiência térmica-número de unidades de transferência) é usado para calcular a taxa de transferência térmica em trocadores de calor (especialmente trocadores em contracorrente) quando não existe informação suficiente para calcular a Diferença de temperatura média logarítmica (DTML). Na análise de trocadores de calor, se as temperaturas de entrada e de saída de fluido são especificados ou podem ser determinadas pelo balanço de massa simples, o método LMTD pode ser usado, mas quando essas informações não estão disponíveis o método NTU ou da eficiência" é usado. (pt) NTU法是熱傳單元數法的簡稱，也稱為熱交換有效性法，是在一熱交換器（特別是逆流交换的熱交換器）沒有對數平均溫差（LMTD）的條件下，計算其熱交換速率的方式。 在熱交換器分析中，若流體的入口溫度和出口溫度已知，或是可以用能量平衡的方式計算，可以用對數平均溫差來進行分析，但若沒有這些資訊，可以用NTU法來分析。 (zh) Der englische Begriff Number of Transfer Units (NTU, dt. etwa „Anzahl der Übertragungseinheiten“) bezeichnet eine dimensionslose Kennzahl aus dem Bereich der Wärmeübertragung. Der Nutzen der NTU besteht darin, einen Wärmeüberträger auszulegen oder ein vorhandenes Gerät nachzurechnen. Das NTU-Verfahren vereinfacht den Auslegungs- bzw. Nachrechnungsprozess erheblich, da es bei komplizierteren Strömungsformen schwierige Berechnungen erspart. ist hier der Stoffübergangskoeffizient mit als Einheit und der Volumenstrom. (de) The Number of Transfer Units (NTU) Method is used to calculate the rate of heat transfer in heat exchangers (especially counter current exchangers) when there is insufficient information to calculate the Log-Mean Temperature Difference (LMTD). In heat exchanger analysis, if the fluid inlet and outlet temperatures are specified or can be determined by simple energy balance, the LMTD method can be used; but when these temperatures are not available The NTU or The Effectiveness method is used. The effectiveness-NTU method is very useful for all the flow arrangements (besides parallel flow and counterflow ones) because the effectiveness of all other types must be obtained by a numerical solution of the partial differential equations and there is no analytical equation for LMTD or effectiveness (en) |
| rdfs:label | Number of Transfer Units (de) Numero di unità di trasporto (it) 移動単位数 (ja) NTU method (en) Metoda NTU (pl) Método das NTU (pt) NTU法 (zh) |
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