Convective Heat Transfer in Micro and Nano Channels: Nusselt Number Beyond Slip Flow

2000 ◽  
Author(s):  
Nicolas G. Hadjiconstantinou
Keyword(s):  
Nusselt Number ◽  
Slip Flow ◽  
Direct Simulation Monte Carlo ◽  
Simulation Technique ◽  
Channel Height ◽  
Transition Flow ◽  
Height Range ◽  
Continuum Analysis ◽  
Wide Range ◽  
Constant Wall Heat Flux

Abstract We present calculations of the constant-wall-heat-flux Nusselt number for fully developed transition flow in two-dimensional microchannels. The Nusselt number cannot be obtained by a continuum analysis since the continuum description breaks down in the transition regime. We have used a molecular simulation technique known as the direct simulation Monte Carlo (DSMC). DSMC is a stochastic simulation technique previously shown to capture the hydrodynamic behavior of hard sphere gases. A wide range of Knudsen numbers is investigated: a channel height range of approximately 50 is analyzed starting from the micrometer scale that corresponds to slip flow. The channels have a length/height ratio of 20 to ensure fully developed flow, and care was taken to ensure that the Brinkman number is always small. The Nusselt number is found to decrease with increasing rarefaction (Knudsen number). The effects of thermal creep are discussed.

scholarly journals Performance of Air-Cooled Heat Exchanger with Laminar, Transitional, and Turbulent Tube Flow

2018 ◽  
Vol 240 ◽  
pp. 02012
Author(s):  
Dawid Taler
Keyword(s):  
Nusselt Number ◽  
Heat Exchanger ◽  
Heat Flow ◽  
Friction Factor ◽  
Flow Rate ◽  
Empirical Relationship ◽  
Heat Flow Rate ◽  
Transition Flow ◽  
Water Side ◽  
Wide Range

Some air-cooled heat exchangers, especially in air conditioning and heating installations, heat pumps, as well as car radiators, work in a wide range of loads when the liquid flow in the tubes can be laminar, transitional or turbulent. In this paper, a semi-empirical and empirical relationship for the Nusselt number on the liquid-side in the transitional and turbulent range was derived. The friction factor in the transition flow range Rew,trb ≤ Rew ≤ Rew,tre was calculated by linear interpolation between the values of the friction factor for Rew,trb =2,100 and Rew,tre =3,000. Based on experimental data for a car radiator, empirical heat transfer relationships for the air and water-side were found by using the least squares method. The water temperature at the outlet of the heat exchanger was calculated using P-NTU (effectiveness-number of transfer units) method. The heat flow rate from water to air was calculated as a function of the water flow rate to compare it with the experimental results. The theoretical and empirical correlation for the water-side Nusselt number developed in the paper were used when determining the heat flow rate. The calculation results agree very well with the results of the measurements.

Direct Simulation Monte Carlo Calculations of Three Dimensional Non-Continuum Gas Flows

2002 ◽  
Author(s):  
Fang Yan ◽  
Bakhtier Farouk ◽  
Jeremy Johnson
Keyword(s):  
Monte Carlo ◽  
Couette Flow ◽  
Three Dimensional ◽  
Direct Simulation Monte Carlo ◽  
Particle Removal ◽  
Direct Simulation ◽  
Transition Flow ◽  
Multiprocessor Computer ◽  
Wide Range ◽  
Simulation Monte Carlo

This paper describes the parallel implementation of a three-dimensional direct simulation Monte Carlo (DSMC) code using the OpenMP procedure on a shared memory multiprocessor computer. A dynamic domain decomposition is performed to maintain load balance among the threads. Performance tests are conducted to evaluate the effect of granularity on efficiency. It is shown that the parallel performance is dependent on the problem size. For larger-scale problems, better efficiency can be expected. Synchronization overhead due to data contention is reduced by re-arranging particle removal procedure. The parallel code is used to simulate flow through a rectangular channel with a high-speed moving wall (Couette flow). For high Knudsen (Kn) numbers, the Couette flow characteristics are found to be very different from their continuum counterparts. ‘Ultimate pressures’ are calculated for a wide range of Kn number flows. The variation of the ultimate pressure with Kn number is computed for given wall speed. Maximum compression ratio is obtained in the transition flow region.

Friction Factor Correlations for Gas Flow in Slip Flow Regime

2007 ◽  
Vol 129 (10) ◽  
pp. 1268-1276 ◽  
Author(s):  
Chungpyo Hong ◽  
Yutaka Asako ◽  
Stephen E. Turner ◽  
Mohammad Faghri
Keyword(s):  
Friction Factor ◽  
Flow Regime ◽  
Gas Flow ◽  
Slip Flow ◽  
Channel Height ◽  
Inlet Temperature ◽  
Arbitrary Lagrangian Eulerian ◽  
Knudsen Numbers ◽  
Wide Range ◽  
Slip Flow Regime

Poiseuille number, the product of friction factor and Reynolds number (fRe) for quasi-fully-developed gas microchannel flow in the slip flow regime, was obtained numerically based on the arbitrary-Lagrangian-Eulerian method. Two-dimensional compressible momentum and energy equations were solved for a wide range of Reynolds and Mach numbers for constant wall temperatures that are lower or higher than the inlet temperature. The channel height ranges from 2 μm to 10 μm and the channel aspect ratio is 200. The stagnation pressure pstg is chosen such that the exit Mach number ranges from 0.1 to 1.0. The outlet pressure is fixed at atmospheric conditon. Mach and Knudsen numbers are systematically varied to determine their effects on fRe. The correlation for fRe for the slip flow is obtained from that of fRe of no-slip flow and incompressible theory as a function of Mach and Knudsen numbers. The results are in excellent agreement with the available experimental measurements. It was found that fRe is a function of Mach and Knudsen numbers and is different from the values by 96/(1+12Kn) obtained from the incompressible flow theory.

scholarly journals Evaluation of Nusselt number for a flow in a microtube using second-order slip model

2011 ◽  
Vol 15 (suppl. 1) ◽  
pp. 103-109 ◽  
Author(s):  
Barbaros Cetin ◽  
Ozgur Bayer
Keyword(s):  
Nusselt Number ◽  
Temperature Jump ◽  
Slip Flow ◽  
Second Order ◽  
Slip Model ◽  
Brinkman Number ◽  
Constant Property ◽  
Axial Conduction ◽  
Closed Form Solutions ◽  
Constant Wall Heat Flux

In this paper, the fully-developed temperature profile and corresponding Nusselt value is determined analytically for a gaseous flow in a microtube with a thermal boundary condition of constant wall heat flux. The flow assumed to be laminar, and hydrodynamically and thermally fully developed. The fluid is assumed to be constant property and incompressible. The effect of rarefaction, viscous dissipation and axial conduction, which are important at the microscale, are included in the analysis. Second-order slip model is used for the slip-flow and temperature jump boundary conditions for the implementation of the rarefaction effect. Closed form solutions for the temperature field and the fully-developed Nusselt number is derived as a function of Knudsen number, Brinkman number and Peclet number.

scholarly journals Evaluation of Nusselt Number for a Flow in a Microtube With Second-Order Model Including Thermal Creep

2012 ◽  
Author(s):  
Barbaros Çetin
Keyword(s):  
Nusselt Number ◽  
Temperature Jump ◽  
Slip Flow ◽  
Second Order ◽  
Thermal Creep ◽  
Brinkman Number ◽  
Order Model ◽  
Closed Form Solutions ◽  
Constant Wall Heat Flux ◽  
Thermo Physical Properties

In this paper, Nusselt number for a flow in a microtube is determined analytically with a constant wall heat flux thermal boundary condition. The flow assumed to be incompressible, laminar, hydrodynamically and thermally fully-developed. The thermo-physical properties of the fluid are assumed to be constant. The effect of rarefaction, viscous dissipation, axial conduction, which are important at the microscale, are included in the analysis. For the implementation of the rarefaction effect, two different second-order slip models are used for the slip-flow and temperature-jump boundary conditions together with the thermal creep at the wall. Closed form solutions for the fully-developed temperature profile and Nusselt number are derived as a function of Knudsen number, Brinkman number and Peclet number.

Heat transfer characteristics of nanofluids from a sinusoidal corrugated cylinder placed in a square cavity

2021 ◽  
pp. 095440622110272
Author(s):  
Salaika Parvin ◽  
Nepal Chandra Roy ◽  
Litan Kumar Saha ◽  
Sadia Siddiqa
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Rayleigh Number ◽  
Aspect Ratio ◽  
Average Nusselt Number ◽  
Numerical Study ◽  
Heat Transfer Characteristics ◽  
Number Range ◽  
Transfer Characteristics ◽  
Wide Range

A numerical study is performed to investigate nanofluids' flow field and heat transfer characteristics between the domain bounded by a square and a wavy cylinder. The left and right walls of the cavity are at constant low temperature while its other adjacent walls are insulated. The convective phenomena take place due to the higher temperature of the inner corrugated surface. Super elliptic functions are used to transform the governing equations of the classical rectangular enclosure into a system of equations valid for concentric cylinders. The resulting equations are solved iteratively with the implicit finite difference method. Parametric results are presented in terms of streamlines, isotherms, local and average Nusselt numbers for a wide range of scaled parameters such as nanoparticles concentration, Rayleigh number, and aspect ratio. Several correlations have been deduced at the inner and outer surface of the cylinders for the average Nusselt number, which gives a good agreement when compared against the numerical results. The strength of the streamlines increases significantly due to an increase in the aspect ratio of the inner cylinder and the Rayleigh number. As the concentration of nanoparticles increases, the average Nusselt number at the internal and external cylinders becomes stronger. In addition, the average Nusselt number for the entire Rayleigh number range gets enhanced when plotted against the volume fraction of the nanofluid.

Investigation of Coriolis Forces Effect of Flow Structure and Heat Transfer Distribution in a Rotating Dimpled Channel

2011 ◽  
Vol 134 (3) ◽  
Author(s):  
Mohammad A. Elyyan ◽  
Danesh K. Tafti
Keyword(s):  
Heat Transfer ◽  
Flow Structure ◽  
Recirculation Zone ◽  
Channel Height ◽  
Coriolis Forces ◽  
Flow Recirculation ◽  
Heat Transfer Augmentation ◽  
Wide Range ◽  
Large Eddy ◽  
Dimple Surface

Large-eddy simulations are used to investigate Coriolis forces effect on flow structure and heat transfer in a rotating dimpled channel. Two geometries with two dimple depths are considered, δ=0.2 and 0.3 of channel height, for a wide range of rotation number, Rob=0.0–0.70, based on mean bulk velocity and channel height. It is found that the turbulent flow is destabilized near the trailing side and stabilized near the leading side, with secondary flow structures generated in the channel under the effect of Coriolis forces. Higher heat transfer levels are obtained at the trailing surface of the channel, especially in regions of flow reattachment and boundary layer regeneration at the dimple surface. Coriolis forces showed a stronger effect on the flow structure for the shallow dimple geometry (δ=0.2) compared with the deeper dimple where the growth and shrinkage of the flow recirculation zone in the dimple cavity with rotation were more pronounced than the deep dimple geometry (δ=0.3). Under the action of rotation, heat transfer augmentation increased by 57% for δ=0.2 and by 70% for δ=0.3 on the trailing side and dropped by 50% for δ=0.2 and by 45% for δ=0.3 on the leading side from that of the stationary case.

Laminar Forced Convection in Annular Microchannels With Slip Flow Regime

2009 ◽  
Author(s):  
Arman Sadeghi ◽  
Abolhassan Asgarshamsi ◽  
Mohammad Hassan Saidi
Keyword(s):  
Nusselt Number ◽  
Fluid Flow ◽  
Aspect Ratio ◽  
Boundary Conditions ◽  
Knudsen Number ◽  
Gas Flow ◽  
Slip Flow ◽  
Outer Wall ◽  
Graphical Form ◽  
Uniform Temperature

Fluid flow and heat transfer at microscale have attracted an important research interest in recent years due to the rapid development of microelectromechanical systems (MEMS). Fluid flow in microdevices has some characteristics which one of them is rarefaction effect related with gas flow. In this research, hydrodynamically and thermally fully developed laminar rarefied gas flow in annular microducts is studied using slip flow boundary conditions. Two different cases of the thermal boundary conditions are considered, namely: uniform temperature at the outer wall and adiabatic inner wall (Case A) and uniform temperature at the inner wall and adiabatic outer wall (Case B). Using the previously obtained velocity distribution, energy conservation equation subjected to relevant boundary conditions is numerically solved using fourth order Runge-Kutta method. The Nusselt number values are presented in graphical form as well as tabular form. It is realized that for the case A increasing aspect ratio results in increasing the Nusselt number, while the opposite is true for the case B. The effect of aspect ratio on Nusselt number is more notable at smaller values of Knudsen number, while its effect becomes slighter at large Knudsen numbers. Also increasing Knudsen number leads to smaller values of Nusselt number for the both cases.

Investigation of Coriolis Forces Effect of Flow Structure and Heat Transfer Distribution in a Rotating Dimpled Channel

2010 ◽  
Author(s):  
Mohammad A. Elyyan ◽  
Danesh K. Tafti
Keyword(s):  
Heat Transfer ◽  
Flow Structure ◽  
Recirculation Zone ◽  
Channel Height ◽  
Coriolis Forces ◽  
Flow Recirculation ◽  
Heat Transfer Augmentation ◽  
Wide Range ◽  
Large Eddy ◽  
Dimple Surface

Large-eddy simulations are used to investigate Coriolis forces effect on flow structure and heat transfer in a rotating dimpled channel. Two geometries with two dimple depths are considered, δ = 0.2 and 0.3 of channel height, for a wide range of rotation number, Rob = 0.0–0.70, based on mean bulk velocity and channel height. It is found that the turbulent flow is destabilized near the trailing side and stabilized near the leading side, with secondary flow structures generated in the channel under the effect of Coriolis forces. Higher heat transfer levels are obtained at the trailing surface of the channel, especially in regions of flow reattachment and boundary layer regeneration at the dimple surface. Coriolis forces showed a stronger effect on the flow structure for the shallow dimple geometry (δ = 0.2) compared to the deeper dimple where the growth and shrinkage of the flow recirculation zone in the dimple cavity with rotation were more pronounced than the deep dimple geometry (δ = 0.3). Under the action of rotation, heat transfer augmentation increased by 57% for δ = 0.2 and by 70% for δ = 0.3 on the trailing side and dropped by 50% for δ = 0.2 and by 45% for δ = 0.3 on the leading side from that of the stationary case.

Extreme Response Prediction for Fixed Offshore Structures by Monte Carlo Time Simulation Technique

2016 ◽  
Author(s):  
M. K. Abu Husain ◽  
N. I. Mohd Zaki ◽  
M. B. Johari ◽  
G. Najafian
Keyword(s):  
Monte Carlo ◽  
Statistical Properties ◽  
Simulation Technique ◽  
Random Wave ◽  
Wave Loading ◽  
Offshore Structure ◽  
Sampling Variability ◽  
Time Simulation ◽  
Wide Range ◽  
Extreme Response

For an offshore structure, wind, wave, current, tide, ice and gravitational forces are all important sources of loading which exhibit a high degree of statistical uncertainty. The capability to predict the probability distribution of the response extreme values during the service life of the structure is essential for safe and economical design of these structures. Many different techniques have been introduced for evaluation of statistical properties of response. In each case, sea-states are characterised by an appropriate water surface elevation spectrum, covering a wide range of frequencies. In reality, the most versatile and reliable technique for predicting the statistical properties of the response of an offshore structure to random wave loading is the time domain simulation technique. To this end, conventional time simulation (CTS) procedure or commonly called Monte Carlo time simulation method is the best known technique for predicting the short-term and long-term statistical properties of the response of an offshore structure to random wave loading due to its capability of accounting for various nonlinearities. However, this technique requires very long simulations in order to reduce the sampling variability to acceptable levels. In this paper, the effect of sampling variability of a Monte Carlo technique is investigated.

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