scholarly journals Continuum and Kinetic Simulations of Heat Transfer Trough Rarefied Gas in Annular and Planar Geometries in the Slip Regime

2017 ◽  
Vol 139 (4) ◽  
Author(s):  
Mustafa Hadj-Nacer ◽  
Dilesh Maharjan ◽  
Minh-Tuan Ho ◽  
Stefan K. Stefanov ◽  
Irina Graur ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Kinetic Equation ◽  
Temperature Jump ◽  
Rarefied Gas ◽  
Large Temperature ◽  
Model Kinetic Equation ◽  
Temperature Ratio ◽  
Slip Regime ◽  
S Model

Steady-state heat transfer through a rarefied gas confined between parallel plates or coaxial cylinders, whose surfaces are maintained at different temperatures, is investigated using the nonlinear Shakhov (S) model kinetic equation and Direct Simulation Monte Carlo (DSMC) technique in the slip regime. The profiles of heat flux and temperature are reported for different values of gas rarefaction parameter δ, ratios of hotter to cooler surface temperatures T, and inner to outer radii ratio R. The results of S-model kinetic equation and DSMC technique are compared to the numerical and analytical solutions of the Fourier equation subjected to the Lin and Willis temperature-jump boundary condition. The analytical expressions are derived for temperature and heat flux for both geometries with hotter and colder surfaces having different values of the thermal accommodation coefficient. The results of the comparison between the kinetic and continuum approaches showed that the Lin and Willis temperature-jump model accurately predicts heat flux and temperature profiles for small temperature ratio T=1.1 and large radius ratios R≥0.5; however, for large temperature ratio, a pronounced disagreement is observed.

Simulation of Heat Transfer Across Rarefied Gas in Annular and Planar Geometries: Comparison of Navier-Stokes, S-Model and DSMC Methods Results

2015 ◽  
Author(s):  
Dilesh Maharjan ◽  
Mustafa Hadj-Nacer ◽  
Minh-Tuan Ho ◽  
Stefan K. Stefanov ◽  
Irina Graur ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Kinetic Equation ◽  
Rarefied Gas ◽  
Model Kinetic Equation ◽  
Parallel Plates ◽  
Coaxial Cylinders ◽  
Aspect Ratios ◽  
S Model ◽  
Analytical Expressions

Steady state heat transfer through a rarefied gas confined between two parallel plates or two coaxial cylinders maintained at different temperatures is investigated using the nonlinear S-model kinetic equation and the DSMC technique for a large range of gas rarefaction. The profiles of heat flux, density and temperature are reported for different values of gas rarefaction parameter and given values of temperature and aspect ratios. In the slip regime the results of the S-model and DSMC technique are compared to the simulations performed using the Lin and Willis temperature jump boundary conditions at the at the solid surface implemented in ANSYS/Fluent CFD simulations. The analytical expressions for density number, temperature and heat flux in the free molecular regimes are obtained for both parallel plates and coaxial cylinders geometries with hot and cold surfaces having different values of the thermal accommodation coefficient. The solutions of these analytical expressions are compared to the S-model kinetic equation and DSMC technique results in the free molecular regime.

Numerical Simulation Of A Microchannel For Microelectronic Cooling

2012 ◽  
Author(s):  
Wai Hing Wong ◽  
Normah Mohd. Ghazali
Keyword(s):  
Heat Transfer ◽  
Numerical Simulation ◽  
Heat Flux ◽  
Aspect Ratio ◽  
Three Dimensional ◽  
Large Temperature ◽  
Rectangular Microchannel ◽  
Numerical Work ◽  
Solid Region ◽  
Wall Interaction

Kertas kerja ini membincangkan simulasi berangka ke atas sinki haba saluran mikro dalam penyejukan alatan mikroelektronik. Model Dinamik Bendalir Berkomputer (CFD) tiga dimensi dibina menggunakan pakej komersil, FLUENT, untuk mengkaji fenomenon aliran bendalir dan pemindahan haba konjugat di dalam suatu sinki haba segi empat yang diperbuat daripada silikon. Model ditentusahkan dengan keputusan daripada uji kaji dan pengkajian berangka yang lepas untuk lingkungan nombor Reynolds kurang daripada 400 berdasarkan diameter hidraulik 86 mm. Kajian ini mengambil kira kesan kelikatan bendalir yang bersandaran dengan suhu dan keadaan aliran pra–membangun dari segi hidrodinamik dan haba. Model memberi maklumat tentang taburan suhu dan fluks haba yang terperinci di dalam sinki haba saluran mikro. Kecerunan suhu yang tinggi dicatat pada kawasan pepejal berdekatan dengan sumber. Fluks haba paling tinggi didapati pada dinding tepi saluran mikro diikuti oleh dinding atas dan bawah. Purata pekali pemindahan haba yang lebih tinggi bagi silikon menjadikan ia bahan binaan sinki haba saluran mikro yang lebih baik berbanding dengan kuprum dan aluminium. Peningkatan nisbah aspek saluran mikro yang bersegi empat memberi kecekapan penyejukan yang lebih tinggi kerana kelebaran saluran yang berkurangan memberi kecerunan halaju yang lebih tinggi dalam saluran. Nisbah aspek yang optimum yang diperoleh adalah dalam lingkungan 3.7 – 4.1. Kata kunci: Saluran mikro, CFD, FLUENT, simulasi berangka, penyejukan mikroelektron The paper discusses the numerical simulation of a micro–channel heat sink in microelectronics cooling. A three–dimensional Computational Fluid Dynamics (CFD) model was built using the commercial package, FLUENT, to investigate the conjugate fluid flow and heat transfer phenomena in a silicon–based rectangular microchannel heatsink. The model was validated with past experimental and numerical work for Reynolds numbers less than 400 based on a hydraulic diameter of 86 mm. The investigation was conducted with consideration of temperaturedependent viscosity and developing flow, both hydrodynamically and thermally. The model provided detailed temperature and heat flux distributions in the microchannel heatsink. The results indicate a large temperature gradient in the solid region near the heat source. The highest heat flux is found at the side walls of the microchannel, followed by top wall and bottom wall due to the wall interaction effects. Silicon is proven to be a better microchannel heatsink material compared to copper and aluminum, indicated by a higher average heat transfer. A higher aspect ratio in a rectangular microchannel gives higher cooling capability due to high velocity gradient around the channel when channel width decreases. Optimum aspect ratio obtained is in the range of 3.7 – 4.1. Key words: Microchannel, CFD, FLUENT, numerical simulation, microeletronics cooling

Mixed Convection in a Vertical Parallel Plate Microchannel With Asymmetric Wall Heat Fluxes

2006 ◽  
Vol 129 (8) ◽  
pp. 1091-1095 ◽  
Author(s):  
Mete Avcı ◽  
Orhan Aydın
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Mixed Convection ◽  
Convective Heat Transfer ◽  
Parallel Plate ◽  
Temperature Jump ◽  
Velocity Slip ◽  
Heat Fluxes ◽  
Limiting Case ◽  
Convection Parameter

In this study, exact analytical results are presented for fully developed mixed convective heat transfer of a Newtonian fluid in an open-ended vertical parallel plate microchannel with asymmetric wall heating at uniform heat fluxes. The velocity slip and the temperature jump at the wall are included in the formulation. The effects of the modified mixed convection parameter, Grq∕Re, the Knudsen number, Kn, and the ratio of wall heat flux, rq=q1∕q2, on the microchannel hydrodynamic and thermal behaviors are determined. Finally, a Nu=f(Grq∕Re,Kn,rq) expression is developed. For, the limiting case of Kn=0, the results are found to be in an excellent agreement with those in the existing literature.

Design of an Experiment to Measure the Thermal Accommodation Coefficient Between Helium and Stainless-Steel in Concentric Cylinders

2015 ◽  
Author(s):  
Rachel Green ◽  
Mustafa-Hadj Nacer ◽  
Miles Greiner
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Stainless Steel ◽  
Temperature Difference ◽  
Rarefied Gas ◽  
Accommodation Coefficient ◽  
Theoretical Expression ◽  
Thermal Accommodation ◽  
Concentric Cylinders ◽  
Thermal Accommodation Coefficient

Heat transfer through a 1 mm gap between two concentric cylinders representing the gap between a fuel support basket and a canister is experimentally and numerically investigated. The objective of this work is to study rarefied gas heat transfer in a simple geometry, and to measure the thermal accommodation coefficient at the interface between stainless steel and rarefied helium. The thermal accommodation coefficient is used to characterize the interaction between gas molecules and wall at the molecular level. It is important to determine its value with precision for better determination of heat transfer at low pressure. The experimental procedure consists of measuring the temperature difference between the inner and outer cylinders as the pressure is decreased in the gap. By knowing the heat flux across the gap the thermal accommodation coefficient can be extracted from the theoretical expression relating the temperature difference to the radial heat flux. Three-dimensional simulations using the ANSYS/Fluent commercial code are conducted to assess on the design of the experimental apparatus. These simulations confirmed that the apparatus design is effective to study the heat transfer across rarefied gas and to determine the thermal accommodation coefficient for helium on stainless steel surface.

Rarefied gas flow behavior in micro/nanochannels under specified wall heat flux

2015 ◽  
Vol 26 (08) ◽  
pp. 1550087 ◽  
Author(s):  
Mojtaba Balaj ◽  
Hassan Akhlaghi ◽  
Ehsan Roohi
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Heat Flux ◽  
Gas Flow ◽  
Rarefied Gas ◽  
Flow Behavior ◽  
Direct Simulation Monte Carlo ◽  
Wall Heat Flux ◽  
Linear Distribution ◽  
Thermal Transpiration

In this paper, we investigate the effects of convective heat transfer on the argon gas flow through micro/nanochannels subject to uniform wall heat flux (UWH) boundary condition using the direct simulation Monte Carlo (DSMC) method. Both the hot wall (q wall > 0) and the cold wall (q wall < 0) cases are considered. We consider the effect of wall heat flux on the centerline pressure, velocity profile and mass flow rate through the channel in the slip regime. The effects of rarefaction, property variations and compressibility are considered. We show that UWH boundary condition leads to the thermal transpiration. Our investigations showed that this thermal transpiration enhances the heat transfer rate at the walls in the case of hot walls and decreases it where the walls are being cooled. We also show that the deviation of the centerline pressure distribution from the linear distribution depends on the direction of the wall heat flux.

Turbine Heat Flux Measurements: Influence of Slot Injection on Vane Trailing Edge Heat Transfer and Influence of Rotor on Vane Heat Transfer

1985 ◽  
Vol 107 (1) ◽  
pp. 76-83 ◽  
Author(s):  
M. G. Dunn
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Leading Edge ◽  
Temperature Ratio ◽  
Trailing Edge ◽  
Heated Air ◽  
Flux Measurements ◽  
Nozzle Guide ◽  
Nozzle Guide Vanes ◽  
Blowing Parameter

This paper describes the measurement of heat flux distributions obtained for a Garrett TFE 731-2 hp turbine. Measurements were obtained for a full turbine both with and without injection and for the nozzle guide vanes with and without a rotor. A shock tube is used as a short-duration source of heated air and miniature thin-film gages are used to obtain the heat flux measurements. Results are presented for values of the blowing parameter (ρcVc/ρ∞V∞)at SLOT, in the range of 0.8–1.3. The injection gas (air) as a percentage of turbine weight flow, Wc/Wo, was in the range of 2.1–3.5 percent. A comparison is presented between results obtained with the rotor operating at 100 percent of corrected speed and those obtained with the rotor replaced by a row of flow straighteners. The results suggest that: (i) the reduction of heat flux due to injection is a function of the blowing parameter, the temperature ratio, and the physical location relative to the tip or hub endwall and (ii) the presence of the rotor has a significant affect on the vane trailing edge Stanton number, increasing it by 15 to 25 percent. The vane leading edge and midchord regions were generally unaffected.

Heat Transfer From a Small Heated Region to R-113 and FC-72

1989 ◽  
Vol 111 (4) ◽  
pp. 1053-1059 ◽  
Author(s):  
K. R. Samant ◽  
T. W. Simon
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Quartz Substrate ◽  
Rectangular Channel ◽  
Nucleate Boiling ◽  
Decomposition Temperature ◽  
Large Temperature ◽  
Resistance Thermometer ◽  
Maximum Heat ◽  
Heater Element

An experimental investigation of heat transfer from a small heated patch to a subcooled, fully developed turbulent flow is conducted. The test patch, approximately 0.25 mm long and 2.0 mm wide, is located on the floor of a small rectangular channel through which a coolant (R-113 or FC-72) is circulated. A thin film of Nichrome deposited on a quartz substrate serves as an integrated heater element and resistance thermometer. The maximum achievable heat flux with R-113, limited by the thermal decomposition temperature of the fluid, is 2.04 MW/m2 at a bulk velocity of 1.8 m/s and a high wall superheat of 80° C. The results obtained with FC-72 show large temperature excursions at the onset of nucleate boiling and a boiling hysteresis near the onset of nucleate boiling. These effects decrease with increasing velocity and/or subcooling. The heat flux at departure from nucleate boiling increases with increasing velocity and/or subcooling. A maximum heat flux of 4.26 MW/m2 at departure from nucleate boiling is observed.

scholarly journals Rarefied Poiseuille Flow in a Circular Tube

2019 ◽  
Vol 224 ◽  
pp. 02001
Author(s):  
Oksana Germider ◽  
Vasily Popov
Keyword(s):  
Kinetic Equation ◽  
Chebyshev Polynomials ◽  
Gas Flow ◽  
Rarefied Gas ◽  
Circular Tube ◽  
Three Dimensional ◽  
Heat Fluxes ◽  
Model Kinetic Equation ◽  
Algebraic Equations ◽  
Rarefied Gas Flows

An isothermal rarefied gas flow through a long circular tube due to longitudinal pressure gradient (a three-dimensional Poiseuille problem) was studied using the linearized Bhatnagar-Gross-Krook model kinetic equation over the whole range of the Knudsen numbers covering both free molecular and hydrodynamic regimes. The solution of the model kinetic equation with the diffuse boundary condition is obtained by the collocation method. This approach is based on the Chebyshev polynomials and rational Chebyshev functions. Choosing the zeros of Chebyshev polynomials in the multivariate range of integration for the collocation points, we reduce this problem to a set of algebraic equations. Based on the proposed approach, we have calculated the mass and the heat fluxes through the tube. The obtained results have also been compared with other studies. The developed approach may also be applied to a more general class of problems of rarefied gas flows in microand nanotubes.

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