NTU heat transfer#

The block allows modeling heat exchange between two environments using the NTU method.

In combination with the Heat exchanger interface (TL) block, it allows modeling heat exchangers calculated using the NTU method.

Note

In the block settings, the user can select the required Heat exchanger type.

Heat flow by the method NTU (1) :

(1)#\[Q=\epsilon \cdot C_{мин} \cdot (T_{вх}^{ср1} - T_{вх}^{ср2})\]

where:

\(\epsilon\) – heat exchanger efficiency coefficient;

\(C_{min}\) – minimum value of \(\dot m_1 \cdot C_{p1}\) and \(\dot m_2 \cdot C_{p2}\), [W/℃];

\(\dot m_1, \dot m_2\) – mass flow rate of medium 1 and 2, [kg/s];

\(C_{p1},C_{p2}\) – specific heat capacity of environment 1 and 2 [\(\frac{J}{kg \cdot ℃}\)];

\(T_{вх}^{ср1},T_{вх}^{ср2}\) – температура среды 1 и 2 на входе в теплообменник, [℃].

Heat exchanger efficiency (2):

(2)#\[\epsilon = \frac{Q}{Q_{макс}}\]

where:

\(Q\) – actual heat flow, [W];

\(Q_{max}\) - maximum possible heat flow, [W].

Formula for calculating the efficiency of a heat exchanger for different mutual movement of the coolant [1]

Pipe-in-pipe heat exchanger (Fig. 1):

Heat exchanger pipe in pipe — Fig. 1 Pipe-in-pipe heat exchanger [1]#

Direct flow (3) : [1]

(3)#\[\epsilon = \frac{1 - e^{-NTU\cdot(1+C_{отн})}}{1 + C_{отн}}\]

where:

NTU - number of heat transfer units;

\(C_{отн} = \frac{C_{мин}}{C_{макс}}\).

Counterflow (4) : [1]

(4)#\[\epsilon = \frac{1 - e^{-NTU\cdot(1-C_{отн})}}{1 - C_{отн} \cdot e^{-NTU\cdot(1-C_{отн})}}\]

For the case \(C_{rel}\) = 1 (5) :

(5)#\[\epsilon = \frac{NTU}{1+NTU}\]

Shell-and-tube heat exchanger (Fig. 2):

For the case of one flow of the medium in the housing and 2, 4… flows of the medium in the pipes (6) : [1]

(6)#\[\epsilon_1 = 2 \cdot \{1+C_{отн} + (1+C_{отн}^2)^{1/2}\cdot \frac{1+exp \cdot (-(NTU)_1\cdot (1+C_{отн}^2)^{1/2})}{1-exp \cdot (-(NTU)_1\cdot (1+C_{отн}^2)^{1/2})} \}^{-1}\]

For the case of n passages in the housing and 2n, 4n… passages of the medium in the pipes (7) : [1]

(7)#\[\epsilon = ((\frac{1-\epsilon_1 \cdot C_{отн}}{1 - \epsilon_1})^n-1) \cdot ((\frac{1-\epsilon_1 \cdot C_{отн}}{1 - \epsilon_1})^n-C_{отн})^{-1}\]

Cross-flow heat exchanger (Fig. 3):

Cross flow heat exchangers — Fig. 3 Cross-flow heat exchangers [1]
a) Finned (both media do not mix)
b) Non-finned (one liquid mixes, the other does not)#

Both environments are miscible (8) : [1]

(8)#\[\epsilon = \frac{1}{\frac{1}{1-exp \cdot (-NTU)}+\frac{C_{отн}}{1-exp \cdot (-C_{отн} \cdot NTU)}-\frac{1}{NTU}}\]

The two environments are immiscible (9) : [1]

(9)#\[\epsilon = 1-exp((\frac{1}{C_{отн}})(NTU)^{0.22} \{exp \cdot (-C_{отн}(NTU)^{0.78})-1 \})\]

\(C_{max}\) is miscible - \(C_{min}\) is not miscible (10) : [1]

(10)#\[\epsilon =(\frac{1}{C_{отн}})\cdot (1 - exp \cdot \{ -C_{отн} \cdot(1 - exp \cdot (-NTU))\})\]

\(C_{max}\) is not miscible - \(C_{min}\) is miscible (11) : [1]

(11)#\[\epsilon = 1 - exp \cdot (-C_{отн}^{-1}\cdot \{1 - exp \cdot (-C_{отн} \cdot (NTU)) \} )\]

Number of heat transfer units (12) :

(12)#\[NTU = \frac{1}{C_{мин}\cdot R_{общ}}\]

where \(R_{total}\) is the total thermal resistance between two liquids without taking into account the thermal conductivity of the liquids, [℃/W], (13) :

(13)#\[R_{общ}=\frac{1}{\alpha_1 \cdot A_{ср1}}+\frac{R_{f1}}{A_{ср1}}+ R_{ст} + \frac{R_{f2}}{A_{ср2}} + \frac{1}{\alpha_2 \cdot A_{ср2}}\]

where:

\(\alpha_1, \alpha_2\) – heat transfer coefficients for environment 1 and 2, [\(\frac{W}{m^2 \cdot ℃}\)];

\(A_{ср1}, A_{ср2}\) – area of heat exchange surface for environment 1 and 2, [m\(^2\)];

\(R_{f1},R_{f2}\) – surface contamination coefficients for environments 1 and 2, [\(\frac{m^2 \cdot ℃}{W}\)];

\(R_{st}\) – thermal resistance of the wall, [\(\frac{℃}{W}\)].

1. Properties#

Property	Default Value	Description	Units of measurement
Heat exchanger type: Parallel or counter flow; Shell and tube; Cross flow; Generic - effectiveness table	Parallel or counter flow	-	-
Number of shell passes, available when selecting `Heat exchanger type` - `Shell and tube`	1	-	pieces
Cross flow type: Both fluids mixed; Both fluids unmixed; Fluid 1 mixed fluid 2 unmixed; Fluid 1 unmixed fluid 2 mixed	Both fluids mixed	-	-
Number of heat transfer unit vector, available when selecting `Heat exchanger type` - `Generic - effectiveness table`	0.5;1.0;2.0;3.0;4.0;5.0;	-	-
Thermal capacity ratio vector, available when selecting `Heat exchanger type` - `Generic - effectiveness table`	0.0;0.25;0.5;0.75;1.0;	-	-
Effectiveness table, available when selecting `Heat exchanger type` - `Generic - effectiveness table`	\u003C0.3;0.3;0.3;0.3;0.3\u003E_ \u003C0.6;0.55;0.5;0.47;0.43\u003E_ \u003C0.85;0.76;0.68;0.61;0.55\u003E_ \u003C0.94;0.83;0.72;0.65;0.58\u003E_ \u003C0.98;0.86;0.75;0.66;0.58\u003E_ \u003C0.99;0.86;0.75;0.66;0.58\u003E	-	-
Wall thermal resistance	1.5E-4	-	°C/W
Heat transfer surface area (medium 1)	0.01	-	m\(^2\)
Fouling factor (medium 1)	1.0E-4	-	°С·m²/W
Minimum fluid wall heat transfer coefficient (medium 1)	5.0	-	W/(m² ·°С)
Heat transfer surface area (medium 2)	0.01	-	m\(^2\)
Fouling factor (medium 2)	1.0E-4	-	°С·m²/W
Minimum fluid wall heat transfer coefficient (medium 2)	5.0	-	W/(m² ·°С)

2. Inputs and outputs#

Parameters	Input/Output	Description	Units of measurement	Port type
Heat port (medium 1)	Input	-	-	Heat exchange
Heat port (medium 2)	Input	-	-	Heat exchange
Thermal capacity rate (medium 1)	Input	-	W/°C	Automation
Heat transfer coefficient (medium 1)	Input	-	W/(m² ·°С)	Automation
Thermal capacity rate (medium 2)	Input	-	W/°C	Automation
Heat transfer coefficient (medium 2)	Input	-	W/(m² ·°С)	Automation

In order to see the connection capabilities of the block, you need to go to page Description of block ports

NTU heat transfer#

1. Properties#

2. Inputs and outputs#

3. Sources#