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This article consists of an analytical solution for obtaining the outlet temperatures of the hot and cold fluids in a shell and tube heat exchanger. The system analyzed through the concepts of efficiency, effectiveness (
*ε*-
*NTU*), and irreversibility consisted of a shell and tube heat exchanger, with cold nanofluid flowing in the shell and hot water flowing in the tube. The nanofluid consists of 50% of ethylene glycol and water as the base fluid and copper oxide (CuO) nanoparticles in suspension. The volume fractions of the nanoparticles range from 0.1 to 0.5. The flow rate in the nanofluid ranges from 0.0331 to 0.0568 Kg/s, while two mass flow rates, from 0.0568 and 0.5 Kg/s, for the hot fluid, are used as parameters for analysis. Results for the efficiency, effectiveness, irreversibility, heat transfer rate, and outlet temperatures for cold and hot fluids were obtained graphically. The flow laminarization effect was observed through the results obtained and had significant relevance in the results.

It is an analytical solution to analyze the effects on the outlet temperature of a hot fluid that flows in the tube and exchanging heat with a cold nanofluid that flows in the housing, using concepts of efficiency, effectiveness, and irreversibility.

Equipment that allows heat exchange between two fluids, separated or not by a solid medium, is commonly called heat exchangers. Among the existing heat exchangers, shell and tube heat exchangers stand out.

Heat exchangers shell and tube type usually use baffles. The baffles change the direction of flow on the side of the shell to ensure high heat transfer rates and provide support for the tube bundles. Also, they play an essential role in hydrodynamics and thermal performance.

In this work, the interest is in the heat exchange between fluids consisting of cold water in the tube and hot nanofluid in the shell. The nanofluid consists of 50% of ethylene glycol and water as the base fluid and suspension of copper oxide (CuO) nanoparticles.

Based on the first law and the second law of thermodynamics, the analysis focuses mainly on the outlet temperature of the water to be cooled using the efficiency, effectiveness, and irreversibility concepts.

There are many reports in the specialized literature related to shell and tube type heat exchangers based on the second reading of thermodynamics. The efficiency of a system is based on thermal irreversibility and viscous dissipation.

One of the first authors to use the concept of efficiency and entropy in heat exchanger systems, in a comprehensive and detailed review, was Adrian Bejan [

Ahmad Fakheri [

Roopesh Tiwari and Govind Maheshwari [

Qazizada Mohammad Emal and Pivarciova Elena [

Karthik Silaipillayarputhur and Hassan Khurshid [

Amir Qashqaei and Ramin Ghasemi Asl [

Ms. Sivahari Shankar, P. Immanuel, and M. Eswaran [_{2}O_{3} nanoparticles that flows inside the shell of one shell and tube heat exchanger. The experiments were conducted with the Reynolds number in the tubes varying from 1700-9500. They conclude that the application of nanofluid in the shell, compared to water, improves the overall heat transfer coefficient of the shell and tube heat exchanger.

Rahul Mahajan et al. [_{2}O_{3}/water nanofluid with particle varying in the range of 0.01% - 0.3% in the shell and tube heat exchanger in an experimental procedure. They conclude that the dispersion of nanoparticles into the distilled water increases the thermal conductivity and viscosity of the nanofluids and enhances the conduction as well as convection rate. More considerable temperature differences will occur by using nanofluids.

Priyanka S. Gore and Jagdeep M. Kshirsagar [_{2}O_{3} nanofluid with twisted tapes incorporated in tubes of shell & tube heat exchanger. They conclude that the swirl flow, caused the twisted tape, enhances the heat transfer coefficient considerably, and justify the use because the energy consumption optimization becomes important.

The equations presented below and some demonstrations can be obtained through the following references: Adrian Bejan [

Basic data: L_{S} = 0.762 m; d_{S} = 0.508 m; d_{T} = 0.0127 m; Tc_{i} = 27˚C; Th_{i} = 90˚C; N_{T} = 32; one pass in the tube, one pass in the shell and 3 baffles.

If the volume fraction (V_{EG}) of ethylene glycol is provided, the properties of the base fluid can be obtained through the equations below:

μ solution = μ E G V E G + ( 1 − V E G ) μ w c (1)

ρ solution = ρ E G V E G + ( 1 − V E G ) ρ w c (2)

k solution = k E G V E G + ( 1 − V E G ) k w c (3)

Shell Cold Fluid | Tube Hot Fluid | CuO | EG50% | |
---|---|---|---|---|

k W/(m ˚C) | 0.60 | 0.67 | 400 | 1830.4223 |

Cp J/(kg ˚C) | 4180 | 4216 | 8933 | 3878.9317 |

µ kg/(m s) | 0.758 10^{−3 } | 0.3031 10^{−3 } | - | 5.277983 10^{−4 } |

ρ kg/m^{3 } | 997 | 970 | 385 | 1058.33 |

ν m^{2}/s | 0.8 10-6 | 0.334 10^{−6 } | - | 4.987 10^{−7 } |

α m^{2}/s | 1.430 10^{−7 } | 1.680 10^{−7 } | 1.163 10^{−4 } | 4.865 10^{−4 } |

Pr | 5.68 | 1.98 | - | 975.49 |

C p solution = C p E G V E G + ( 1 − V E G ) C p w c (4)

The properties of the nanofluid, for volume fraction ( ϕ ) of the Copper Oxide (CuO), is given by the following equations:

ρ c = ϕ ρ solution + ( 1 − ϕ ) ρ solution (5)

μ c = μ solution ( 1 − 0.19 ϕ + 306 ϕ 2 ) (6)

C p c = ( ϕ ρ particle C p particle + ( 1 − ϕ ) ρ solution C p solution ) / ρ (7)

k c = [ k particle + 2 k solution + 2 ( k particle − k solution ) ( 1 − 0.1 ) 3 ϕ k particle + 2 k solution + 2 ( k particle − k solution ) ( 1 + 0.1 ) 2 ϕ ] k solution (8)

The heat exchange area is obtained by:

A h = π d T L S N T _{} (9)

R e h = 4 ( m ˙ h / N T ) / π d T μ h (10)

R e h is the Reynolds number in the tube, and

N u h = 4.364 + 0.0722 R e h P r h d T L S for R e h < 2100 (11)

or

N u h = 0.023 R e h 0.8 P r h 0.4 (12)

are the Nusselt number in the tube.

Then the convective heat transfer coefficient in the tube is given by:

h h = N u h k h d T (13)

R e c = 4 m c ̇ π d e μ c (14)

R e h is the Reynolds number in the shell, and

N u c = 4.364 + 0.0722 R e c P r c d e L S for R e c < 2100 (15)

or

N u c = 0.023 R e c 0.8 P r c 0.3 (16)

are the Nusselt number in the shell.

At where, d e is the shell equivalent diameter:

d e = 1.27 d T ( P T 2 − 0.785 d T 2 ) (17)

Then, the convection heat transfer coefficient in the shell is:

h c = N u c K c d e (18)

P T = 1.25 d T (19)

P T is the tube pitch, for square pitch.D B = d S ( N T 0.125 ) 1 2.207 (20)

B S = 0.4 D B (21)

D B and B S are, respectively, the bundle diameter and baffles space.

The number of baffles is given by:

B B = L S B S (22)

The overall convection heat transfer coefficient:

U O = 1 1 h h + 1 h c (23)

The thermal capacities of both fluids are given by:

C c = m ˙ c C p c and C h = m ˙ h C p h (24)

NTU = A h U O C min (25)

NTU is the Number of Thermal Units,

at where, C_{min} is the lowest value among thermal capacities.

ε = 1 1 η NTU + 1 + C * 2 (26)

(ε) is the effectiveness of the shell and tube heat exchanger [

η = Tanh ( F a ) F a (27)

(η) is the efficiency of the heat exchanger is [

at where,

F a = NTU ( 1 − C * ) 2 (28)

and

C * = C max C min (29)

The heat transfer rate, depending on the efficiency and temperature of the fluids, is obtained by [

Q Actual = ( T h i − T c i ) C min 1 η NTU + 1 + C * 2 (30)

The maximum heat transfer rate is,

Q max = C min ( T h i − T c i ) (31)

T h O = T h i − Q Actual m ˙ h C p h (32)

and

T c O = T c i + Q A c t u a l m ˙ c C p c (33)

T h O and T c O are the outlet temperatures,

Finally, the thermal irreversibility is given by [

σ T = C h C min ln ( T h O T h i ) + C c C min ln ( T c O T c i ) (34)

Fluid enters the tube at 90˚C and the shell at 27˚C. The flow in the shell varies from 0.0331 kg/s to 0.2324 kg/s. Two flow rates in the tube, 0.0568 kg/s and 0.5 kg/s, and fractions in the volume of copper oxide ranging from 0.1 to 0.5 were considered for analysis.

The phenomenon of flow laminarization, as already observed by Nogueira E. (2020), is shown in

The fraction in a volume equal to 0.1 stands out. In this situation, the efficiency presents high values in all Reynolds number range, and for the two hot fluid flow rates considered. For fraction in a volume equal to 0.5 and the flow rate in the tube corresponding to 0.5 kg/s, the efficiency drops significantly in the low number of Reynolds.

Two aspects must be considered for high efficiency for the low value of the volume fraction of copper oxide and low flow rate for the hot fluid: the increased diffusivity of the nanofluid, associated with the most prominent Brownian movement, and the longer time of the heated fluid in the tube. These two aspects contribute to the heat exchange to approach the maximum possible for the conditions imposed on the flow rate in the shell and tube.

As the flow rate of the cold fluid increases, its thermal capacity also increases until it overlaps the value of the thermal capacity of the hot fluid in the pipe. The phenomenon is not observed for the high flow rate of the heated fluid since within the range of flow values of the cold fluid, considering there is no alternation of the minimum thermal capacity.

The irreversibility related to the thermal exchange,

The heat transfer rate,

Through

The outlet temperature of the cold fluid is high when the heat transfer rate, the effectiveness, and the irreversibility are high.

The outlet temperature of the hot fluid is lower when the efficiency is higher, the heat transfer rate and effectiveness are the maximum possible, that is, for the lowest flow rates in the tube, equal to 0.0568 kg/s. Also, the lowest outlet temperature is obtained when the copper oxide fraction is the highest within the range of values analyzed. It can be seen, through

For the higher mass flow rate of the hot fluid, the outlet temperatures of the hot fluid are not favorable for the entire range of fractions in the volume of the nanoparticles analyzed. In this case, thermal irreversibility, which is a measure of heat dissipation, is high, as is the rate of heat transfer, but not equal to the maximum.

High efficiency occurs for low mass flow of the hot fluid and smaller volume fraction for the nanoparticles. On the other hand, for the same situation, we have low effectiveness and irreversibility, and consequently, a higher outlet temperature of the hot fluid

The results show that it is not enough to have high effectiveness, which represents a more significant rate of heat exchange if the efficiency is low when the desired result is the smallest possible outlet temperature.

The most favorable result for the hot fluid outlet temperature occurs when the process is efficient and effective, however, with high efficiency assuming a more significant effect on the outcome for the outlet temperature of the hot fluid.

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

Nogueira, É. (2020) Efficiency and Effectiveness Concepts Applied in Shell and Tube Heat Exchanger Using Ethylene Glycol-Water Based Fluid in the Shell with Nanoparticles of Copper Oxide (CuO). Journal of Materials Science and Chemical Engineering, 8, 1-12. https://doi.org/10.4236/msce.2020.88001