### Abstract

The temperature and pressure jump boundary conditions at the liquid-vapor interfaces, obtained from the kinetic theory, are implemented for the numerical simulation of two-surfaces problem of evaporation and condensation. For a small temperature difference between two interfaces the system of the Navier-Stokes equations (NS) together with the energy conservation equation and the linear approximation of these equations with the same jump boundary conditions are considered in the vapor phase. The numerical and analytical solutions are compared with that obtained previously from the linearized kinetic equation. The analytical temperature profiles derived from the both linearized systems are very close to each other, while the temperature distribution obtained from the full NS and energy equations has an absolutely different character. The velocity and pressure in the vapor phase are found to be constant, though the full NS and energy equations solution gives abrupt change of velocity near the condensation interface. The inverse temperature gradient phenomenon occurs for the considered small temperature difference. The solution in the vapor phase is then applied to a coupled two-phase system problem, which can be realized in a heat-transfer device combining the principles of both thermal conductivity and phase transition. The coupled two-sided (liquid and vapor) model with jump boundary conditions proposed here allows us to estimate the values of the evaporative mass flux and the heat flux, which can be removed from a heat source.

Original language | English |
---|---|

Pages (from-to) | 235-243 |

Number of pages | 9 |

Journal | International Journal of Heat and Mass Transfer |

Volume | 83 |

DOIs | |

Publication status | Published - 1 Jan 2015 |

### Fingerprint

### Keywords

- Cooling system
- Evaporation
- Heat transfer enhancement
- Pressure jump
- Temperature jump
- Vapor-liquid interface

### ASJC Scopus subject areas

- Condensed Matter Physics
- Mechanical Engineering
- Fluid Flow and Transfer Processes

### Cite this

*International Journal of Heat and Mass Transfer*,

*83*, 235-243. https://doi.org/10.1016/j.ijheatmasstransfer.2014.12.003

**The temperature and pressure jumps at the vapor-liquid interface : Application to a two-phase cooling system.** / Gatapova, Elizaveta Ya; Graur, Irina A.; Sharipov, Felix; Kabov, Oleg A.

Research output: Contribution to journal › Article

*International Journal of Heat and Mass Transfer*, vol. 83, pp. 235-243. https://doi.org/10.1016/j.ijheatmasstransfer.2014.12.003

}

TY - JOUR

T1 - The temperature and pressure jumps at the vapor-liquid interface

T2 - Application to a two-phase cooling system

AU - Gatapova, Elizaveta Ya

AU - Graur, Irina A.

AU - Sharipov, Felix

AU - Kabov, Oleg A.

PY - 2015/1/1

Y1 - 2015/1/1

N2 - The temperature and pressure jump boundary conditions at the liquid-vapor interfaces, obtained from the kinetic theory, are implemented for the numerical simulation of two-surfaces problem of evaporation and condensation. For a small temperature difference between two interfaces the system of the Navier-Stokes equations (NS) together with the energy conservation equation and the linear approximation of these equations with the same jump boundary conditions are considered in the vapor phase. The numerical and analytical solutions are compared with that obtained previously from the linearized kinetic equation. The analytical temperature profiles derived from the both linearized systems are very close to each other, while the temperature distribution obtained from the full NS and energy equations has an absolutely different character. The velocity and pressure in the vapor phase are found to be constant, though the full NS and energy equations solution gives abrupt change of velocity near the condensation interface. The inverse temperature gradient phenomenon occurs for the considered small temperature difference. The solution in the vapor phase is then applied to a coupled two-phase system problem, which can be realized in a heat-transfer device combining the principles of both thermal conductivity and phase transition. The coupled two-sided (liquid and vapor) model with jump boundary conditions proposed here allows us to estimate the values of the evaporative mass flux and the heat flux, which can be removed from a heat source.

AB - The temperature and pressure jump boundary conditions at the liquid-vapor interfaces, obtained from the kinetic theory, are implemented for the numerical simulation of two-surfaces problem of evaporation and condensation. For a small temperature difference between two interfaces the system of the Navier-Stokes equations (NS) together with the energy conservation equation and the linear approximation of these equations with the same jump boundary conditions are considered in the vapor phase. The numerical and analytical solutions are compared with that obtained previously from the linearized kinetic equation. The analytical temperature profiles derived from the both linearized systems are very close to each other, while the temperature distribution obtained from the full NS and energy equations has an absolutely different character. The velocity and pressure in the vapor phase are found to be constant, though the full NS and energy equations solution gives abrupt change of velocity near the condensation interface. The inverse temperature gradient phenomenon occurs for the considered small temperature difference. The solution in the vapor phase is then applied to a coupled two-phase system problem, which can be realized in a heat-transfer device combining the principles of both thermal conductivity and phase transition. The coupled two-sided (liquid and vapor) model with jump boundary conditions proposed here allows us to estimate the values of the evaporative mass flux and the heat flux, which can be removed from a heat source.

KW - Cooling system

KW - Evaporation

KW - Heat transfer enhancement

KW - Pressure jump

KW - Temperature jump

KW - Vapor-liquid interface

UR - http://www.scopus.com/inward/record.url?scp=84949115280&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84949115280&partnerID=8YFLogxK

U2 - 10.1016/j.ijheatmasstransfer.2014.12.003

DO - 10.1016/j.ijheatmasstransfer.2014.12.003

M3 - Article

VL - 83

SP - 235

EP - 243

JO - International Journal of Heat and Mass Transfer

JF - International Journal of Heat and Mass Transfer

SN - 0017-9310

ER -