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The article analyzes a shell and tube type condenser’s thermal performance using concepts of efficiency and effectiveness. Freon 134a is used as a coolant flowing through the shell. Water or water-based aluminum oxide nanoparticles are at relatively low saturation pressure in the tube. The condenser consists of 36 tubes divided into three central regions for analysis: superheated steam, saturated steam, and subcooled liquid. The three regions contain four tubes with three steps each, that is, 12 tubes. Region I, superheated steam, includes three horizontal baffles. Profiles of temperature, efficiency, and effectiveness are presented graphically for the three regions, with fixed refrigerant flow equal to 0.20 kg/s and fluid flow rate in the tube ranging from 0.05 kg/s to 0.40 kg/s. The experimental result for vapor pressure equal to 1.2 MPa and water flow equal to 0.41 kg/s was used as one of the references for the model’s physical compatibility.

Shell and tube heat exchangers are widely used in industrial processes. These heat exchangers are characterized by their versatility, applicability, and are still objects of study due to the countless possible physical arrangements that they allow. However, the deposition rate in media, shell, and tube can significantly affect the heat transfer rate, with a greater weight to the shell’s side.

The article’s objective is to analyze the thermal performance of a shell and tube type condenser using concepts of efficiency and effectiveness. Freon 134a is used as a coolant flowing through the shell. Water or water-based aluminum oxide nanoparticles are at relatively low saturation pressure in the tube. The condenser consists of 36 tubes divided into three central regions for analysis: superheated steam, saturated steam, and subcooled liquid. Region I, superheated steam, includes three horizontal baffles.

The length of the heat exchanger and the tube’s diameter are, respectively, 0.762 m and 0.0127 m. The steam flow rate is fixed and equal to 0.20 kg/s, and the fluid flow rate in the tube varies from 0.05 kg/s to 0.40 kg/s. The steam enters at a temperature equal to 70.5˚C, and the fluid flows into the tube at a temperature equal to 25˚C. The tubes’ configuration is of the square pitch type. Each Region consists of 12 tubes, with rows of 4 tubes and three passes in each Region. Region 1, superheated steam, uses three horizontal baffles for better heat exchange performance. The concepts of efficiency and effectiveness are used in each region for analysis of the thermal performance of the heat exchanger.

The article uses as a primary reference to the work carried out by Tzong-Shing and Jhen-Whei Mai [

Ammar Ali Abd et al. [

Mohammad Reza Saffarian et al. [

Naveed ul Hasan Syed et al. [

Rafał Laskowski et al. [

Élcio Nogueira [

Nogueira, E. [

Freon R134a has properties similar to CFC R-12 and has been used as the most appropriate alternative for the new environmental safety parameters. The work carried out by Ranendra Roy and Bijan Kumar Mandal [

The input data for each of the regions are:

TREntr = 70.5˚C

TWEntr = 25.0˚C

Tsat = 46.02˚C

Properties | Freon R134a | Water | Al_{2}O_{3} | |
---|---|---|---|---|

I | III | |||

k W/(m∙˚C) | 15.447 | 74.716 | 0.60 | 31.922 |

Cp J/(kg∙˚C) | 1144.5 | 1498.4 | 4180 | 837.336 |

µ kg/(m∙s) | 12.373 × 10^{−6} | 161.45 × 10^{−6 } | 0.758 × 10^{−3 } | 4.65 × 10^{−5 } |

Ρ kg/m^{3} | 50.085 | 1146.7 | 997 | 3950 |

ν Ν∙m^{2}/s | 2.47 × 10^{−7 } | 0.14 × 10^{−6 } | 0.8 × 10^{−7 } | 0.118 × 10^{−7} |

α m^{2}/s | 2.695 × 10^{−4 } | 4.35 × 10^{−5 } | 1.43 × 10^{−7 } | 9.65 × 10^{−6 } |

Pr | 1091.1 | 310.7 | 5.68 | 818 |

N T u b e = 4 (1)

N p a s s = 32 (2)

D W = 0.0127 m (3)

L = 0.762 m (4)

B = 0.0145 m (5)

C L = 1.0 (6)

C T P = 0.85 (7)

So, we have:

P t = 1.25 D W (8)

D e = ( 1.27 / D W ) ( P t 2 − 0.785 D W 2 ) (9)

D c = 3.0 D W (10)

P R = P t / D W (11)

A W = π D W L N t u b e N p a s s (12)

D s = 0.637 C L / C T P ( A T P R 2 D c ) / L (13)

A s = D s B ( 1.0 − D W / P t ) (14)

At where Pt is the tube pitch, De is the equivalent hydraulic diameter, D_{W} is the tube diameter, B is the baffles spacing, A_{W} is the heat exchange area on the side of the tubes, Ds is the shell diameter associated with each Region, As is the shell-side pass area.

R e R = ( m ˙ R D e ) / ( A s μ R ) (15)

N u R = 0.36 R e R 0.55 P r R 1 / 3 (16)

At where, m ˙ R is the mass flow rate of the refrigerant, μ R is the dynamic viscosity of the refrigerant, R e R is the Reynolds number associate of the refrigerant, P r R is the Prandtl number of the refrigerant and N u R is the Nusselt number associate with the refrigerant.

h R = ( N u R k R ) / D e (17)

k R is the thermal conductivity of the refrigerant and h R is the convection heat transfer coefficient associated with refrigerant.

ρ W = ϕ ρ A l + ( 1.0 − ϕ ) ρ W (18)

μ W = μ W ∗ ( 1.0 + 2.5 ϕ ) (19)

ν W = μ W / ρ W (20)

C p W = ( ϕ ρ A l C p A l + ( 1.0 − ϕ ) ρ W C p W ) / ρ W (21)

k W = ( K A l + 2 k W + 2 ( k A l − k W ) ( 1 + 0.1 ) 3 ϕ ) / ( K A l + 2 k W − ( k A l − k W ) ( 1 + 0.1 ) 2 ϕ ) k W (22)

α W = k W / ( ρ W C p W ) (23)

P r W = α W / ν W (24)

At where ρ W is the density of the fluid in the tube, μ W is the dynamic viscosity of the fluid in the tube, ν W is the kinematic viscosity of the fluid in the tube, C p W is the specific heat of the fluid in the tube, k W is the thermal conductivity of the fluid in the tube and P r W is the number of Prandtl associated with the fluid in the tube.

m ˙ W T = m ˙ W / N T u b e (25)

R e W = ( 4 m ˙ W T ) / ( π D W μ W ) (26)

At where m ˙ W is the flow inlet of the fluid in the tubes, m ˙ W T is the flow in each tube and R e W is the Reynolds number associated with the flow in the tube.

N u W = 4.364 + ( 0.0722 R e W P r W D W ) / L for R e W ≤ 2100 (27)

N u W = ( ( f t / 8 ) ( R e W − 10 3 ) P r W ) ( 1 + ( D W / L ) ) 0.67 / ( 1 + 1.27 ( f t / 8 ) ( P r W 0.67 − 1 ) ) for 2100 < R e W ≤ 10 4 (28)

f t = ( 1.82 log ( R e W ) − 1.64 ) − 2 (29)

N u w = 0.027 R e w 0.8 P r w 1 / 3 for R e W > 10 4 (30)

At where ft is the friction factor and N u W is the Nusselt number associate with the flow in the tube.

h W = ( N u W K W ) / D W (31)

U o = 1 / ( 1 / h R + 1 / h W ) (32)

At where U O is the global heat transfer coefficient.

C R = m ˙ R C p R (33)

C W = m ˙ W C p W (34)

N T U = ( A W U O ) / C m i n (35)

F a = ( N T U / 2 ) ( 1 − C * ) (36)

C * = C m i n / C m a x (37)

C R is the thermal capacity of the refrigerant, C W is the thermal capacity of the fluid in the tubes, NTU is called the Number of Thermal Units, Cmin is the smallest of the specific heats.

σ T = T a n h ( F a ) / F a (38)

η T = 1 / ( 1 / ( σ T N T U ) + ( 1 + C * ) / 2 ) (39)

σ T is thermal efficiency and η T is the thermal effectiveness.

T W i = T s a t − Δ T 1 (40)

Δ T 1 it is a value that makes it possible to determine the fluid inlet’s actual temperature in Region I, for a given flow in the tube. It was determined by the difference between theoretical and experimental values. We used as reference the experimental data from the second line of

Δ T 1 = 0.0 for theoretical results (41)

Δ T 1 = 2.0 for the model with experimental results (42)

T R i = T R E n t r (43)

Q A c t u a l = ( T R i − T W i ) C m i n / ( 1 / ( σ T N T U ) + ( 1 + C * ) / 2 ) (44)

T W = ( Q a c t u a l / C W ) + T W i (45)

T R = T R i − ( Q A c t u a l / C R ) (46)

At where, Q A c t u a l is the exchange of local heat between fluids, T W i is the inlet temperature of the fluid flowing into the tube, T R i is the fluid inlet temperature in the shell.

Do it:

T R i = T R i − ∈ 1 (47)

Return to Equation (44) and recalculate Q A c t u a l , TW, TR.

∈ 1 It is a value that allows greater precision in determining TR and TW.

The procedure at Region I ends when:

T R i ≤ T s a t (48)

when the exit condition of Region I is satisfied, we have the fluid’s outlet temperature in the tube and inlet temperature for refrigerant, in Region II.

X = 1.0 (49)

h l v = h v − h l (50)

μ R = μ R l X + μ R V ( 1. d 0 − X ) (51)

ρ R = ρ R l X + ρ R V ( 1. d 0 − X ) (52)

k R = k R l X + k R V ( 1. d 0 − X ) (53)

C p R = C p R L X + C p R V ( 1. d 0 − X ) (54)

P r R = P r R l X + P r R V ( 1. d 0 − X ) (55)

At where X is the steam fraction, the other terms are physical and thermodynamic properties in Region II.

R e R = ( m ˙ R D e ) / ( A s μ R ) (56)

Δ f = T s a t − T R E f (57)

h R = 0.943 ( ( k R ρ R g h l v ) / ( μ R D s Δ f ) ) 0 , 25 (58)

At where, R e R is the number of Reynolds associated with the refrigerant in Region II, ∆f is a reference temperature difference, h R is the convection heat transfer coefficient, and T R E f = 0 .

X varies from 1.0 to 0.0 in Region 2 and h R varies with properties, which leads to different values for Uo, the global heat transfer coefficient. Thus, we have new calculations for efficiency and effectiveness. Heat exchange between fluids in Region II is achieved by:

σ T = T a n h ( F a ) / F a (59)

η T = 1 / ( 1 / ( σ T N T U ) + ( 1 + C * ) / 2 ) (60)

Q A c t u a l = ( T s a t − T W i ) C m i n / ( 1 / ( σ T N T U ) + ( 1 + C * ) / 2 ) (61)

T W = T W i − ( Q R / C * ) (62)

Do it:

T W i = T W i − ∈ 2 (63)

Return to Equation (60) and recalculate Q A c t u a l , TW.

∈ 2 It is a value that allows greater precision in determining TW.

The procedure at Region II ends when:

X < 0.0 (64)

when the exit condition of Region II is satisfied, we have the outlet and the inlet temperatures of the fluid in the tube, and inlet temperature for refrigerant, in Region III.

T W i = 25 ˚ C (65)

T R i = T s a t (66)

The initial calculations are identical to those of Region I, with a change in the refrigerant properties to Region III, as shown in

Q A c t u a l = ( T R i − T W i ) C m i n / ( 1 / ( σ T N T U ) + ( 1 + C * ) / 2 ) (67)

T W o = T W − ( Q A c t u a l / C W ) (68)

T R o = T R − ( Q A c t u a l / C R ) (69)

T W = T W o (70)

T R = T R − Δ T 2 (71)

Do it:

T W i = T W i − ∈ 2 (72)

Return to Equation (67) and recalculate Q A c t u a l , TWo, TRo.

∈ 2 It is a value that allows greater precision in determining TRo and TWo.

The procedure at Region III ends when:

T W i ≤ T W E n t r (73)

when the exit condition of Region III is satisfied, we have the outlet temperature of the refrigerant.

Δ T 2 it is a value that makes it possible to determine the fluid inlet’s actual temperature in Region I, for a given flow in the tube. It was determined by the difference between theoretical and experimental values. We used as reference the experimental data from the second line of

Δ T 2 = 0.0 for theoretical results (75)

Δ T 2 = 0.085 for the model with experimental results (76)

Note: In Region I, the temperature varies with the refrigerant, since it knows its inlet and outlet temperatures. In Region III, the temperature in the tube varies with the temperature since the inlet and outlet temperatures are known.

MPa. The heat exchange with the water in the tubes depends on the steam’s enthalpy and the mass flow rate of the steam, equal to 0.20 kg/s, in almost all situations analyzed in this work. The steam inlet temperature is 70.5˚C. The enthalpy saturation corresponds to 273.9 kJ/kg. The data used for interpolation for saturation temperature and enthalpy, highlighted in

relatively lower flow rate in the tube. Higher outlet temperatures for water and nanofluid are associated with lower mass flow rates in the tubes. Nanofuido has a higher outlet temperature compared to water. Also, the nanofluid temperature is slightly higher at the entrance to the Region I, for lower flow rates of the fluid in the tube.

Note that we have a fixed amount of energy to be donated by the steam in Region I since we have an inlet temperature of 70.5˚C and an outlet temperature of 46.02˚C. Another known quantity and defined a priori, imposed through experimental data, is the fluid inlet temperature in the tube in Region I. Thus, a more significant temperature difference between the outlet and the inlet for lower flow rates justifies the greater value of output for flow in the tube equal to 0.05 Kg/s. As nanofluid has thermal properties superior to water, like specific heat, the outlet temperature is higher for all flow rates analyzed.

The fluid inlet temperatures in the tube at Region I, for the entire mass flow range considered, are represented through

Below,

REGIÃO I ( m ˙ R = 0.20 kg/s) | ||||
---|---|---|---|---|

Freon 134a | Pure Water | Nanofluid | ||

Mass Flow rate 0.05 kg/s | Input pressure | 1.2 MPa | 1.2 MPa | 1.2 MPa |

Input temperature | 70.50˚C | 44.46˚C | 44.57˚C | |

Output temperature | 46.02˚C | 49.76˚C | 51.23˚C | |

Mass Flow rate 0.10 kg/s | Input pressure | 1.2 MPa | 1.2 MPa | 1.2 MPa |

Input temperature | 70.50˚C | 44.25˚C | 44.33˚C | |

Output temperature | 46.02˚C | 46.95˚C | 47.92˚C | |

Mass Flow rate 0.20 kg/s | Input pressure | 1.2 MPa | 1.2 MPa | 1.2 MPa |

Input temperature | 70.50˚C | 44.18˚C | 44.21˚C | |

Output temperature | 46.02˚C | 45.87˚C | 46.28˚C | |

Mass Flow rate 0.40 kg/s | Input pressure | 1.2 MPa | 1.2 MPa | 1.2 MPa |

Input temperature | 70.50˚C | 44.14˚C | 45.14˚C | |

Output temperature | 46.02˚C | 45.19˚C | 45.27˚C |

However, the effectiveness is very low for the mass flow rate of the refrigerant equal to 0.20 kg/s, demonstrating that there is a heat exchange much lower than the potential available; that is, the heat exchange is much lower than the maximum possible. For analysis, we vary the refrigerant flow rates in this single case, imposing slightly lower values. It can be seen that the effectiveness increases

with the decrease in the mass flow of the refrigerant, demonstrating that lower refrigerant flow rates allow greater heat exchange and that the heat transfer rate approaches the maximum possible.

All the previous results mentioned used Δ T 1 = 2.0 ˚ C which, in this case, is called a theoretical model with an experimental result taken from the reference [

It is observed that the outlet temperatures of the fluid in the tube, in Region II, are close for different values of the mass flow rate. The available energy comes from the steam and has the same value for each fraction of steam X. In this case, higher flows of liquid in the tube have smaller differences in temperature between

inlet and outlet. In contrast, lower flow rates, which absorb the same amount of energy, present a higher temperature difference between inlet and outlet. The nanofluid, which has more significant specific heat and thermal diffusivity, absorbs more energy. The temperature difference between the entry and exit of Region II is greater to water.

wide range of Reynolds number. The results cover a laminar, transition, and turbulent regime.

REGIÃO III ( m ˙ R = 0.20 kg/s) | ||||
---|---|---|---|---|

Freon 134a | Pure Water | Nanofluid | ||

Mass Flow rate 0.05 kg/s | Input pressure | 1.2 MPa | 1.2 MPa | 1.2 MPa |

Input temperature | 46.02˚C | 25.00˚C | 25.00˚C | |

Output temperature | 45.19˚C 45.28˚C | 42.46˚C | 42.11˚C | |

Mass Flow rate 0.10 kg/s | Input pressure | 1.2 MPa | 1.2 MPa | 1.2 MPa |

Input temperature | 46.02˚C | 25.00˚C | 25.00˚C | |

Output temperature | 43.91˚C 44.43˚C | 42.70˚C | 42.37˚C | |

Mass Flow rate 0.20 kg/s | Input pressure | 1.2 MPa | 1.2 MPa | 1.2 MPa |

Input temperature | 46.02˚C | 25.00˚C | 25.00˚C | |

Output temperature | 42.30˚C 42.90˚C | 42.71˚C | 42.48˚C | |

Mass Flow rate 0.40 kg/s | Input pressure | 1.2 MPa | 1.2 MPa | 1.2 MPa |

Input temperature | 46.02˚C | 25.00˚C | 25.00˚C | |

Output temperature | 39.07˚C 39.84˚C | 42.70˚C | 42.65˚C |

The energy absorbed by the fluid in the tube is a function of its thermal capacity, which means that, if the inlet and outlet temperatures are practically the same for all flows, the one with the highest flow absorbs more energy. Greater energy absorption for higher flow rates leads to a lower outlet temperature for the refrigerant, as shown in

General observation to be emphasized, before presenting the conclusion, is that the theoretical and altered models for the experimental value approach for lower flow rates of the fluid in the tube. Note that, in this case, the calculated effectiveness value is relatively the highest in all situations analyzed. It is believed that it is possible to use it as a criterion for sizing the ideal condenser, one with high efficiency and high effectiveness.

The results presented demonstrate that the nanofluid has a thermal performance slightly superior to that of water, due to its more excellent thermal conductivity and diffusivity, since its outlet temperature is higher than water.

Efficiency is high in all cases, with a negligible difference between fluids. However, the effectiveness is significantly higher for the nanofluid, which corroborates the fact that there is greater heat exchange with the refrigerant.

The most critical Region, concerning the highest temperature output in the tube, is Region I, saturated steam. The fluid’s outlet temperature in the tube is higher for the lowest flow, i.e., 0.05 Kg/s. In this case, the water leaves with a temperature close to 50˚C and the nanofluid with a temperature above one degree, that is, close to 51 ˚C.

The most critical region, concerning the refrigerant’s lower temperature output, is Region III, subcooled liquid. The refrigerant outlet temperature is higher for the greatest flow, i.e., 0.40 Kg/s. In this case, the 134a refrigerant leaves with a temperature close to 39˚C.

The most important parameter for measuring thermal performance, when efficiency is high, is effectiveness. A process that produces good thermal performance is an efficient one, works, and is effective.

There are two ways to improve thermal performance: maintaining the heat exchanger’s physical configuration: decreasing the flow in the tube or decreasing the shell’s flow. The latter case, seen through

One of the hypotheses to be considered and analyzed in future works is that variations in the refrigerant inlet pressure, with higher working pressures, can increase the process’s effectiveness, maintaining the same physical configuration as the heat exchanger. Another one is the increasing the number pass of tubes in each region. An increase in the exchange area, with a more significant number of tubes in each region, or an increase in the heat exchanger length, should enable better performance in the outlet temperatures.

The author declares no conflicts of interest regarding the publication of this paper.

Nogueira, É. (2020) Theoretical Analysis of a Shell and Tubes Condenser with R134a Working Refrigerant and Water-Based Oxide of Aluminum Nanofluid (Al_{2}O_{3}). Journal of Materials Science and Chemical Engineering, 8, 1-22. https://doi.org/10.4236/msce.2020.811001