Theoretical Two-Dimensional Modeling of Gas Conduction Between Finite Parallel Plates in High Vacuum

2012 ◽  
Vol 134 (5) ◽  
Author(s):  
Taishan Zhu ◽  
Wenjing Ye
Keyword(s):  
Heat Transfer ◽  
High Vacuum ◽  
Finite Size ◽  
Direct Simulation Monte Carlo ◽  
Free Molecule ◽  
Mems Devices ◽  
Parallel Plates ◽  
Thermal Accommodation ◽  
Representative Model ◽  
Gas Conduction

A theoretical approach based on gaskinetic theory is described and applied for the modeling of steady-state free-molecule gaseous heat conduction within a diffusive enclosure. With a representative model of microelectromechanical system (MEMS) devices with integrated heaters, the heat transfer between the heated component and its gaseous ambient enclosed in a high vacuum is studied in detail. A molecular simulation based on the direct simulation Monte Carlo (DSMC) method is also employed to validate the theoretical solutions and to study the effects of incomplete thermal accommodation. The impacts of the finite size of the heated beam as well as the gap between the beam and a substrate on the heat transfer are investigated to examine the appropriateness of the common assumptions employed in the modeling of Pirani sensors. Interesting phenomena that are unique in the free-molecule regime are observed and discussed. These studies are valuable to the design of MEMS devices with microheaters.

Gas-Phase Heat Transfer From a Heated Microcantilever Inside a Vacuum Enclosure

2009 ◽  
Author(s):  
Taishan Zhu ◽  
Wenjing Ye
Keyword(s):  
Heat Transfer ◽  
Monte Carlo ◽  
Analytical Approach ◽  
Rectangular Cross Section ◽  
High Vacuum ◽  
Direct Simulation Monte Carlo ◽  
Mems Devices ◽  
Simulation Code ◽  
Atomic Force ◽  
Thermal Sensing

The modeling of heat transfer inside a vacuum packaged MEMS devices has been performed by several researchers mostly through Monte Carlo simulations. In this work, we employ an analytical approach to study the heat transport of gas inside a high vacuum enclosure. In this pressure range, the interaction between gas molecules is negligible compared to their interaction with the walls, and hence the gas is treated as the free-molecule gas. The heated cantilever is modeled as a uniform beam with a rectangular cross section located at a certain distance away from the bottom wall which could represent a substrate in the real device. To account for various situations, the temperatures of the surrounding walls are allowed to be different from each other and different from that of the beam and the substrate. The temperature contour and the heat flux are obtained from the analytical approach. A molecular simulation code based on the direct simulation Monte Carlo (DSMC) has been developed and employed to validate the analytical results and excellent agreements have been obtained. The effects of incomplete thermal accommodation are also investigated. It is anticipated that the developed analytical solutions would be very valuable to the design of Pirani sensors and other MEMS devices utilizing micro heaters, for example, the thermal sensing atomic force microscope.

Free Molecule Heat Transfer between Parallel Plates

1964 ◽  
Vol 7 (3) ◽  
pp. 473 ◽  
Author(s):  
E. M. Sparrow ◽  
R. B. Kinney
Keyword(s):  
Heat Transfer ◽  
Free Molecule ◽  
Parallel Plates

Numerical Calculations of Heat Conduction Between Soot Aggregates and the Surrounding Gas in the Free-Molecular Regime Using the DSMC Method

2005 ◽  
Author(s):  
Fengshan Liu ◽  
Min Yang ◽  
David R. Snelling ◽  
Gregory J. Smallwood
Keyword(s):  
Heat Transfer ◽  
Heat Conduction ◽  
Direct Simulation Monte Carlo ◽  
Interaction Model ◽  
Numerical Calculations ◽  
Hard Sphere Model ◽  
Sphere Diameter ◽  
Free Molecular Regime ◽  
Thermal Accommodation ◽  
Maxwell Gas

Numerical calculations were conducted to calculate the heat conduction rate between soot (carbon) aggregates of different sizes and the surrounding gas in the free-molecular regime using the direct simulation Monte Carlo method. This method is based on simulation of the trajectories of individual molecules and calculation of the heat transfer at each of the molecule/molecule collisions and the molecule/particle collisions. Soot aggregates of known fractal dimension and pre-factor are first numerically generated using a cluster-cluster aggregation algorithm. Effect of incomplete thermal accommodation was accounted for by employing the Maxwell gas-surface interaction model. Gas collisions were treated using the simple hard sphere model. Numerical results were obtained for aggregate sizes between 10 and 228 primary particles and the thermal accommodation coefficient between 0.1 and 1. A simple scaling for the heat transfer equivalent sphere diameter was also presented for incorporation into a laser-induced incandescence model.

Heat Conduction From Circular Cylinders in Rarefied Gases

1965 ◽  
Vol 87 (4) ◽  
pp. 493-498 ◽  
Author(s):  
G. S. Springer ◽  
R. Ratonyi
Keyword(s):  
Heat Transfer ◽  
Heat Conduction ◽  
Transition Temperature ◽  
Cylindrical Surface ◽  
Temperature Jump ◽  
Circular Cylinders ◽  
Conductive Heat ◽  
Free Molecule ◽  
Thermal Accommodation ◽  
Concentric Cylinders

A method is presented for calculating the conductive heat transfer through gases contained between two concentric cylinders. The method of Lees and Liu is extended to include incomplete thermal accommodation at the inner cylindrical surface, and a comparison is made between the two methods. These results are then compared to those of the low pressure and temperature jump methods. On the basis of this analysis, limits are obtained for the free-molecule, transition, temperature jump, and continuum regimes.

Comparison of DSMC and CFD Models of Heat Transfer in a Rarefied Two-Dimensional Geometry

2018 ◽  
Author(s):  
Dilesh Maharjan ◽  
Mustafa Hadj-Nacer ◽  
Miles Greiner ◽  
Stefan K. Stefanov
Keyword(s):  
Heat Transfer ◽  
Rarefied Gas ◽  
Complex Geometry ◽  
Direct Simulation Monte Carlo ◽  
Accurate Method ◽  
Vacuum Drying ◽  
Helium Pressure ◽  
Two Dimensional ◽  
Dsmc Method ◽  
Cfd Simulations

During vacuum drying of used nuclear fuel (UNF) canisters, helium pressure is reduced to as low as 67 Pa to promote evaporation and removal of remaining water after draining process. At such low pressure, and considering the dimensions of the system, helium is mildly rarefied, which induces a thermal-resistance temperature-jump at gas–solid interfaces that contributes to the increase of cladding temperature. It is important to maintain the temperature of the cladding below roughly 400 °C to avoid radial hydride formation, which may cause cladding embrittlement during transportation and long-term storage. Direct Simulation Monte Carlo (DSMC) method is an accurate method to predict heat transfer and temperature under rarefied condition. However, it is not convenient for complex geometry like a UNF canister. Computational Fluid Dynamics (CFD) simulations are more convenient to apply but their accuracy for rarefied condition are not well established. This work seeks to validate the use of CFD simulations to model heat transfer through rarefied gas in simple two-dimensional geometry by comparing the results to the more accurate DSMC method. The geometry consists of a circular fuel rod centered inside a square cross-section enclosure filled with rarefied helium. The validated CFD model will be used later to accurately estimate the temperature of an UNF canister subjected to vacuum drying condition.

scholarly journals Effects of hybrid nanofluid on novel fractional model of heat transfer flow between two parallel plates

2021 ◽  
Vol 60 (4) ◽  
pp. 3593-3604
Author(s):  
Muhammad Danish Ikram ◽  
Muhammad Imran Asjad ◽  
Ali Akgül ◽  
Dumitru Baleanu
Keyword(s):  
Heat Transfer ◽  
Hybrid Nanofluid ◽  
Parallel Plates ◽  
Fractional Model ◽  
Transfer Flow
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