This paper is aimed at investigating the nanofluid film condensation by mixed convection in the presence of water vapor,

In this work, film condensation of moist air by mixed convection in a vertical channel in the presence of nanoparticles was numerically studied. Condensation of humid air is one of the most applicable phase change processes in various industrial equipment [

The modeling of heat transfer enhancement with or without the addition of nanoparticles is important for several processes; many works in the literature have been focused on the study of the presence of a magnetic field or nanoparticles on heat transfer enhancement, among which are the following.

Mahian et al. [

The subject of film condensation has been widely studied since its first appearance with the work of Nusselt [

In recent times, since 2011, several authors have been interested in the study of condensation under various conditions and different geometries. These studies include the following: Giri et al. [

The number of publications devoted to the study of heat and mass transfer during condensation in the presence of nanoparticles remains rather limited, despite its importance in improving the efficiency of industrial processes. Nanofluids have become a new frontier for scientific research because of the higher thermophysical properties than those of the base fluid. Avramenko et al. [_{2}O_{3}, and TiO_{2}, were considered. These authors showed that nanofluids improve the thermal transfer rate due to their excellent thermal conductivity. In addition, the thickness of the condensate film decreases with increasing heat transfer rate when a larger volume fraction of nanofluids is added. Mghari et al. [

Although recent publications have shown positive impact of nanoparticles on heat transfer, including natural, mixed, or forced convection, for condensation, there are few studies on the impact of nanoparticles on this phase change phenomenon. In this article, the effect of additional nanoparticles in vapor phase on condensation of vapor in the presence of NCG (air) was studied for different volume fractions of nanoparticles, velocities, and relative humidities at the inlet of the vertical channel. The local values of the Nusselt number and the condensate thickness as well as the accumulated rate of condensation were discussed.

We consider a water vapor with nanoparticles in presence of a NCG circulating in a symmetrical vertical channel of length

Scheme of the physical model under study.

Simplifying assumptions were adopted for both phases. These are listed below:

Gas flow is laminar and stationary

Heat and mass transfers are supposed to be two dimensional

Vapor-air mixture is considered an ideal mixture

Radiation heat transfer, the viscous dissipation, and the pressure work terms are neglected in the energy equation

There is a local thermal equilibrium between nanoparticles and main flow

Nanoparticles are distributed evenly in air-vapor mixture and in the liquid film

Liquid film contains the same fraction of the nanoparticles as in the mixture.

Equations used to describe heat and mass transfer phenomenon during condensation are given in the following references [

Mass conservation:

Momentum conservation:

Energy conservation:

The conservation equations in the field of mixture have been formulated taking into consideration the simplifying assumptions mentioned above. Afterwards, the equations of the mixing range can be transcribed as follows:

Mass conservation:

Momentum conservation:

Energy conservation:

Species conservation:

In order to remedy nonuniformity of mesh generated by the profile of the liquid film thickness, we have changed the variables from coordinates

Following the aforementioned change of variables, the governing equations are thus transformed as follows:

Continuity equation in the liquid film:

Momentum equation in the liquid film:

Energy equation in the liquid film:

Continuity equation in the mixture region:

Momentum equation in the mixture region:

Energy equation in the mixture region:

Diffusion equation in the mixture region:

The boundary conditions in the transformed coordinates are prescribed below [

At the entrance of the canal

At the outlet of the canal

On the left wall

At the interface

On the axis of symmetry

The properties of nanofluids (condensate with nanoparticles and air-vapor-nanoparticles) are calculated as a function of the volume fraction; the properties of solid nanoparticles listed in Table

Properties of nanoparticles used in this work [

Density (kg m^{-1}) | 8300 |

Thermal conductivity (J s^{-1} K^{-1}) | 401 |

Heat capacity (J s^{-1} kg K^{-1}) | 420 |

The thermophysical properties of Cu nanoparticles are listed in Table

The local Nusselt number at interface is determined by the following expression:

The bulk temperature is

The accumulated condensation rate at interface is calculated by

The effect of the nanoparticles on the heat and mass transfers is determined by the effective ratio defined as follows:

Based on change in variables mentioned above, the physical domain (Figure

Mesh distribution in the numerical domain.

The study of the influence of different grid on local Nusselt number variation at the interface and the local Sherwood number variation at the interface at various

Grid sensitivity tests.

0.01007 | 85.534 | 15.108 | 95.118 | 16.738 | 97.866 | 17.204 | 98.601 | 17.326 | 98.440 | 17.291 |

0.10079 | 37.259 | 6.619 | 37.614 | 6.681 | 37.713 | 6.700 | 37.697 | 6.697 | 37.563 | 6.6712 |

0.20044 | 30.155 | 5.399 | 30.261 | 5.419 | 30.275 | 5.423 | 30.279 | 5.424 | 30.132 | 5.3960 |

0.39945 | 25.487 | 4.627 | 25.465 | 4.625 | 25.520 | 4.637 | 25.526 | 4.638 | 25.378 | 4.6099 |

0.75015 | 23.019 | 4.276 | 22.992 | 4.274 | 23.065 | 4.288 | 23.062 | 4.288 | 22.927 | 4.2622 |

0.99367 | 22.255 | 4.197 | 22.245 | 4.198 | 22.310 | 4.212 | 22.307 | 4.211 | 22.178 | 4.1861 |

Err. Max. | 13.11% | 12.62% | 3.37% | 3.19% | 0.60% | 0.62% | 0.59% | 0.614% | Ref. | Ref. |

Discretization of equations (

Evolution of thickness of liquid film is determined by an iterative procedure using the Newton-Raphson method applied to the equation of the energy balance at the liquid-gas mixture interface.

Validation tests are performed by comparison of our results with the experimental results of Lebedev et al. [

Validation with Lebedev et al. [

Validation with Giri et al. [

Validation of the solution with experimental data of [

Present work | [ | Relative error | Present work | [ | Relative error | |
---|---|---|---|---|---|---|

0.05 | 17.381 | 15.40 | 22.8398 | 23.46 | ||

0.1 | 30.2757 | 31.46 | 39.5541 | 45.38 | ||

0.15 | 42.4438 | 48.4842 | 54.7401 | 68.12723 |

Validation of the solution with numerical data of [

Present work | [ | Relative error | Present work | [ | Relative error | Present work | [ | Relative error | |
---|---|---|---|---|---|---|---|---|---|

0.05 | 0.00361 | 0.00388 | 6.9% | 0.00298 | 0.00329 | 9.4% | 0.00282 | 0.00295 | 4.4% |

0.22 | 0.00515 | 0.00529 | 2.6% | 0.00462 | 0.00487 | 5.1% | 0.00394 | 0.00401 | 1.7% |

0.53 | 0.00611 | 0.00622 | 1.7% | 0.00564 | 0.00593 | 4.8% | 0.00468 | 0.00471 | 0.6% |

1 | 0.00682 | 0.00681 | 0.11% | 0.00651 | 0.00661 | 1.5% | 0.00524 | 0.00521 | 0.5% |

In this article, study of condensation of an air-vapor mixture in the presence of nanoparticles was carried out. The mixture flows downward into a condenser formed by vertical channel with length

Operating conditions.

Parameters | Ranges |
---|---|

Nanoparticles volume fraction, | |

Reynolds number, | |

Inlet relative humidity, | |

Inlet to wall temperature difference, | |

Inlet temperature, | |

Inlet pressure, |

In order to evaluate the influence of the volume fraction of nanoparticles, Figures

Condensate film thickness for different volume fractions of nanoparticles.

Accumulated condensation rate for different volume fractions of nanoparticles.

The local Nusselt number for different volume fractions of nanoparticles.

Figure

The influence of the volume fraction of nanoparticles on the mass transfer is described by the variation in the condensation rate accumulated along the channel (Figure

Figure

The evolution of dimensionless velocity and temperature profiles in the liquid and gas phase regions at different axial cross sections of the channel is presented and analyzed in this section (Figures

Dimensionless velocity profiles in the mixture region at different sections of the channel.

Dimensionless velocity profiles in the liquid region at different sections of the channel.

Dimensionless temperature profiles in the mixture region at different sections of the channel.

Dimensionless temperature profiles in the liquid region at different sections of the channel.

Bulk concentration profiles.

We can observe in Figures

Figures

Figure

The influence of nanoparticles on the process of condensation depends on the inlet conditions, such as inlet velocity, inlet relative humidity, wall temperature, inlet temperature, and inlet pressure. To distinguish the effect of these parameters, the local Nusselt number, the accumulated condensation rate, and the thickness of the liquid film along the channel are plotted and compared with the case of the pure humid air.

The effect of the Reynolds number is presented in Figures

Effect of the inlet Reynolds number on the liquid film thickness.

Effect of the inlet Reynolds number on accumulated condensation rate.

Effect of the input Reynolds number on the local Nusselt number.

Figure

Figure

The effect of the Reynolds number with or without nanoparticles on the Nusselt number is shown in Figure

The influence of the inlet temperature on the performance of the condensation process of humid air with and without nanoparticles is shown in Figures

Effect of inlet temperature on liquid film thickness.

Effect of inlet temperature on accumulated condensation rate.

Effect of input temperature on the local Nusselt number.

From Figure

The amount of steam condensed along the channel, with and without nanoparticles, is significantly improved by increasing the inlet temperature. Figure

Figure

The variation of the liquid film thickness, the accumulated condensation rate, and the Nusselt number at the interface, in both cases with and without the nanoparticles and for three input relative humidity values, are shown in Figures

Effect of the inlet relative humidity on liquid film thickness.

Effect of the inlet relative humidity on the accumulated condensation rate.

Effect of the inlet relative humidity on the local Nusselt number.

From Figure

Figure

Figure

Figures

Effect of inlet pressure on liquid film thickness.

Effect of inlet pressure on accumulated condensation rate.

Effect of the inlet pressure on the local Nusselt number.

The variation of the liquid film thickness for three values of the inlet pressure (

Figure

The heat transfer results mainly from the latent heat released by the condensation of the steam. Indeed, Figures

The numerical analysis presented in this article is aimed at studying the condensation of nanofluid film with air as a noncondensable gas through a vertical channel. The effects of adding nanoparticles in the inlet flow on improvement of film condensation and on combined heat and mass transfers were analyzed. The governing equations for the two dimensional, stationary, and laminar flow in both phases have been numerically modeled with different inlet conditions using the finite volume method. Findings of this investigation include the following:

Use of nanoparticles during condensation results in improving the process of heat and mass transfer. The results obtained affirm that the volume fraction of the nanoparticles is an essential factor for the improvement of the thermal and mass transfer compared to the case of the base fluid

The ratio of heat and mass transfer enhancement in the presence of nanoparticles increases with increasing the Reynolds number

Increase in the volume fraction of the nanofluid further promotes heat and mass transfer. The maximum improvement of

Thickness of condensate film in the presence of nanoparticles increases with the increase in

Convective heat transfers improved by an effective ratio of

The phenomenon of condensation of humid air is a process often experienced in many industrial installations. Hence, providing more effort to better comprehend the mechanisms of this phase change process is important. According to the results of this study, the use of suspended nanoparticles improves heat and mass transfer processes during condensation, and the results detailed above could be useful in finding the optimal conditions for using nanoparticles to improve heat and mass transfer during condensation processes.

Specific heat (J kg+ K^{-1})

Mass diffusivity (m^{2} s^{-1})

Moisture content (kg/kg of dry air)

Gravitational acceleration (m s^{-2})

Half of plate spacing (m)

Latent heat (J kg^{-1})

Condensation mass flux (kg m^{-2} s^{-1})

Length of plate (m)

Molar mass of air (kg mol^{-1} K^{-1})

Accumulated condensation rate

Noncondensable gas

Pressure (atm)

Saturate pressure (atm)

Reynolds number of the gas stream (

Relative humidity

Temperature (°C)

Bulk temperature

Liquid velocity components in

Axial and cross-stream coordinates correspondingly

Vapor mass fraction

Bulk concentration of water vapor (

Density (kg m^{-3})

Dynamic viscosity (kg m^{-1} s^{-1})

Thermal conductivity (W m^{-1} K^{-1})

Condensate layer thickness (m)

Dimensionless condensate layer thickness

Dimensionless condensate layer thickness

Axial and cross-stream transformed coordinates, respectively.

Air

Inlet

Interface liquid-vapor

Liquid

Mixture

Vapor

Saturate

Wall

Nanofluid

Base fluid (water vapor-air)

Nanoparticles.

The data used to support the findings of this study are included within the article.

The authors declare that they have no conflicts of interest.