Analytical Modeling of Gaseous Slip Flow in Parabolic Microchannels

2014 ◽  
Vol 136 (7) ◽  
Author(s):  
Farzad Tahmouresi ◽  
Samir K. Das
Keyword(s):  
Pressure Distribution ◽  
Friction Factor ◽  
Mass Flow Rate ◽  
Mass Flow ◽  
Flow Rate ◽  
Analytical Modeling ◽  
Separation Of Variables ◽  
Slip Flow ◽  
Aspect Ratios ◽  
Gaseous Slip Flow

The paper presents an analytical solution of velocity, mass flow rate, and pressure distribution for fully developed gaseous slip flow in nonsymmetric and symmetric parabolic microchannels. The flow is considered to be steady, laminar, and incompressible with constant fluid properties. Fully developed gaseous slip flow in microchannels of parabolic cross section is solved analytically for various aspect ratios using a parabolic cylindrical coordinate system on applying the method of separation of variables. Prior to apply separation of variables, Arfken transform [Arfken, 1970, Mathematical Methods for Physicists, Academic Press, Orlando, FL, Ch. 2] was used on momentum equations and first-order slip boundary conditions at each channel wall were imposed. A simple model is proposed to predict the friction factor and Reynolds number product fRe for slip flow in parabolic microchannels. Through the selection of a characteristic length scale, the square root of cross-sectional area and the effect of duct shape have been minimized. The results of a normalized Poiseuille number for symmetric parabolic microchannels (ɛ=1) shows good agreement with the previous results [Morini et al., 2004, “The Rarefaction Effect on the Friction Factor of Gas Flow in Micro/Nano-Channels,” Superlattices Microstruct., 35(3–6), pp. 587–599; Khan and Yovanovich, 2008, “Analytical Modeling of Fluid Flow and Heat Transfer in Microchannel/Nanochannel Heat Sinks,” J. Thermophys. Heat Transf., 22(3), pp. 352–359] for rectangular microchannels. The developed model can be used to predict mass flow rate and pressure distribution of slip flow in parabolic microchannels.

Flashing Flow Mechanisms of HFC-134a and HFC-410a Through Short-Tube Orifices

2011 ◽  
Author(s):  
Kitti Nilpueng ◽  
Somchai Wongwises
Keyword(s):  
Temperature Distribution ◽  
Pressure Distribution ◽  
Mass Flow Rate ◽  
Mass Flow ◽  
Flow Rate ◽  
Operating Conditions ◽  
Evaporator Temperature ◽  
Hfc 134A ◽  
Flow Mechanisms ◽  
Short Tube

In this study, the flow mechanisms of HFC-134a and HFC-410A, including flow pattern, pressure distribution, temperature distribution, and mass flow rate inside short-tube orifice are presented and compared under the same working temperature. The test runs are performed at condenser temperature ranging between 35 and 45°C, evaporator temperature ranging between 2 and 12°C, and degree of subcooling ranging between 1 and 12 °C. The results show that the temperature distribution along the short-tube orifice obtained from HFC-410A is slightly higher than that obtained from HFC-134a. On the other hand, the pressure distribution between both refrigerants shows the large difference. It is also found that the tendency of mass flow rate obtained from HFC-134a almost coincides with those obtained HFC-410A as the operating conditions and short-tube orifice size are varied. However, the average mass flow rate of HFC-134a is slightly lower than that of HFC-410A.

scholarly journals Validated Analytical Modeling of Diesel Engines Intake Manifold with a Flexible Crankshaft

Energies ◽  
2021 ◽  
Vol 14 (5) ◽  
pp. 1287
Author(s):  
Salah A.M. Elmoselhy ◽  
Waleed F. Faris ◽  
Hesham A. Rakha
Keyword(s):  
Mass Flow Rate ◽  
Relative Error ◽  
Mass Flow ◽  
Flow Rate ◽  
Diesel Engines ◽  
Analytical Modeling ◽  
Vacuum Pressure ◽  
Analytical Models ◽  
Intake Manifold ◽  
Flow Losses

The flexibility of a crankshaft exhibits significant nonlinearities in the analysis of diesel engines performance, particularly at rotational speeds of around 2000 rpm. Given the explainable mathematical trends of the analytical model and the lack of available analytical modeling of the diesel engines intake manifold with a flexible crankshaft, the present study develops and validates such a model. In the present paper, the mass flow rate of air that goes from intake manifold into all the cylinders of the engine with a flexible crankshaft has been analytically modeled. The analytical models of the mass flow rate of air and gas speed dynamics have been validated using case studies and the ORNL and EPA Freeway standard drive cycles showing a relative error of 7.5% and 11%, respectively. Such values of relative error are on average less than those of widely recognized models in this field, such as the GT-Power and the CMEM, respectively. A simplified version for control applications of the developed models has been developed based on a sensitivity analysis. It has been found that the flexibility of a crankshaft decreases the mass flow rate of air that goes into cylinders, resulting in an unfavorable higher rate of exhaust emissions like CO. It has also been found that the pressure of the gas inside the cylinder during the intake stroke has four elements: a driving element (intake manifold pressure) and draining elements (vacuum pressure and flow losses and inertial effect of rotating mass). The element of the least effect amongst these four elements is the vacuum pressure that results from the piston's inertia and acceleration. The element of the largest effect is the pressure drop that takes place in the cylinder because of the air/gas flow losses. These developed models are explainable and widely valid so that they can help in better analyzing the performance of diesel engines.

Thermal and Hydraulic Performances of Porous Microchannel Heat Sink using Nanofluids

2021 ◽  
pp. 1-32
Author(s):  
Zahir Uddin Ahmed ◽  
Md. Roni Raihan ◽  
Omidreza Ghaffari ◽  
Muhammad Ikhlaq
Keyword(s):  
Heat Transfer ◽  
Pressure Drop ◽  
Friction Factor ◽  
Mass Flow Rate ◽  
Mass Flow ◽  
Flow Rate ◽  
Heat Sink ◽  
Hydraulic Performance ◽  
Microchannel Heat Sink ◽  
Nanoparticle Concentration

Abstract Microchannel heat sink is an effective method in compact and faster heat transfer applications. This paper numerically investigates thermal and hydraulic characteristics of a porous microchannel heat sink (PMHS) using various nanofluids. The effect of porosity, inlet velocity and nanoparticle concentration on thermal-hydraulic performance is systematically examined. The result shows a significant temperature increase (40°C) of the coolant in the porous zone. The pressure drop reduces by 35% for γ = 0.32 compared to the non-porous counterpart, and this reduction of pressure significantly continues when γ further increases. The pressure drop with win is linear for PMHS with nanofluids, and the change in pressure drop is steeper for nanofluids compared to their base fluids. The average heat transfer coefficients increases about 2.5 times for PMHS, and a further increase of 6% in is predicted with the addition of nanoparticle. The average Nusselt number increases non-linearly with Re for PMHS. The friction factor reduces by 50% when γ increases from 0.32 to 0.60, and the effect of nanofluid on friction factor is insignificant beyond the mass flow rate of 0.0004 kg/s. Whilst Cu and CuO nanoparticles help to dissipate the larger amount of heat from the microchannel, Al2O3 nanoparticle appears to have a detrimental effect on heat transfer. The thermal-hydraulic performance factor strongly depends on the nanoparticles, and it slightly decreases with the mass flow rate. The increase of nanoparticle concentration, in general, enhances both h and ΔP linearly for the range considered.

Gas Mass Flow Rate Measurement in T-Shaped Microchannels in Slip Flow Regime

2011 ◽  
Author(s):  
Yongli Li ◽  
Christine Barrot ◽  
Lucien Baldas ◽  
Ste´phane Colin ◽  
Ju¨rgen J. Brandner ◽  
...  
Keyword(s):  
Flow Regime ◽  
Mass Flow Rate ◽  
Mass Flow ◽  
Flow Rate ◽  
Slip Flow ◽  
Rate Measurement ◽  
Gas Mixing ◽  
Flow Rate Measurement ◽  
Slip Flow Regime ◽  
Good Agreement

A new setup was developed for gas mixing analysis in T-shaped microchannels. The principle of the flow rate measurement was based on the Constant Volume (CV) method [1]. The mass flow rate measurements of two gases N2 / CO2 mixing in a T mixer were carried out in the slip flow regime and followed by a simulation work for comparison. The mass flow rate has a magnitude of 10−8 or 10−7 kg/s and has good agreement with simulation for the lowest inlet over outlet pressures ratios and moderate agreement for the highest inlet over outlet pressures ratios.

Second-Order Gaseous Flow Models in Long Circular and Noncircular Microchannels and Nanochannels

2011 ◽  
Author(s):  
Zhipeng Duan
Keyword(s):  
Boundary Conditions ◽  
Pressure Distribution ◽  
Mass Flow Rate ◽  
Mass Flow ◽  
Flow Rate ◽  
Second Order ◽  
Slip Boundary Conditions ◽  
Gaseous Flow ◽  
Slip Boundary ◽  
Poiseuille Number

Gaseous flow in circular and noncircular microchannels has been examined and a simple analytical model with second-order slip boundary conditions for normalized Poiseuille number is proposed. The model is applicable to arbitrary length scale. It extends previous studies to the transition regime by employing the second-order slip boundary conditions. The effects of the second-order slip boundary conditions are analyzed. As in slip and transition regimes, no solutions or graphical and tabulated data exist for most geometries, the developed simple model can be used to predict friction factor, mass flow rate, tangential momentum accommodation coefficient, pressure distribution of gaseous flow in noncircular microchannels by the research community for the practical engineering design of microchannels such as rectangular, trapezoidal, double-trapezoidal, triangular, rhombic, hexagonal, octagonal, elliptical, semielliptical, parabolic, circular sector, circular segment, annular sector, rectangular duct with unilateral elliptical or circular end, annular, and even comparatively complex doubly-connected microducts. The developed second-order models are preferable since the difficulty and “investment” is negligible compared with the cost of alternative methods such as molecular simulations or solutions of Boltzmann equation. Navier-Stokes equations with second-order slip models can be used to predict quantities of engineering interest such as Poiseuille number, tangential momentum accommodation coefficient, mass flow rate, pressure distribution, and pressure drop beyond its typically acknowledged limit of application. The appropriate or effective second-order slip coefficients include the contribution of the Knudsen layers in order to capture the complete solution of the Boltzmann equation for the Poiseuille number, mass flow rate, and pressure distribution. It could be reasonable that various researchers proposed different second-order slip coefficients because the values are naturally different in different Knudsen number regimes. The transition regime is a varying mixture of different transport mechanisms and the mixed degree relies on the magnitude of the Knudsen number. It is analytically shown that the Knudsen’s minimum can be predicted with the second-order model and the Knudsen value of the occurrence of Knudsen’s minimum depends on inlet and outlet pressure ratio. The compressibility and rarefaction effects on mass flow rate and the curvature of the pressure distribution by employing first-order and second-order slip flow models are analyzed and compared. The condition of linear pressure distribution is given. This paper demonstrates that with some relatively simple ideas from knowledge, observation, and intuition, one can predict some fairly complex flows.

On the thermally-driven gas flow through divergent micro/nanochannels

2017 ◽  
Vol 28 (12) ◽  
pp. 1750143 ◽  
Author(s):  
Mohammad Sajjad Mozaffari ◽  
Ehsan Roohi
Keyword(s):  
Mass Flow Rate ◽  
Mass Flow ◽  
Flow Rate ◽  
Gas Flow ◽  
Constitutive Law ◽  
Thermal Mass ◽  
Transition Regime ◽  
Aspect Ratios ◽  
Wide Range ◽  
Thermally Driven

A detailed study on thermally driven flows through divergent micro/nanochannels is presented. Rarefied gas flow behavior and thermal mass flow rate were investigated with different divergence angles ranging between 0[Formula: see text] and 7[Formula: see text] at two aspect ratios ([Formula: see text]) using particle-based direct simulation Monte-Carlo (DSMC) method. We compare our DSMC solutions for normalized thermal mass flow rate with the numerical solution of the Boltzmann–Krook–Walender (BKW) model and Bhatnagar–Gross–Krook (BGK) model and asymptotic theory over a wide range of Knudsen number in the transition regime. The flow field properties including Mach number, pressure, overall temperature and magnitude of shear stress are examined in detail. Based on our analysis, we observed an approximately constant velocity and pressure distribution at a microchannel with a small opening angle. Our results also demonstrate that the heat lines from weakly nonlinear form of Sone constitutive law and DSMC show good agreement at low Knudsen numbers. Moreover, we show that the effect of divergence angle is influential in increasing normalized thermal mass flow rate at early transition regime.

scholarly journals Mass flow rate measurement of thermal creep flow from transitional to slip flow regime

2016 ◽  
Vol 795 ◽  
pp. 690-707 ◽  
Author(s):  
Hiroki Yamaguchi ◽  
Pierre Perrier ◽  
Minh Tuan Ho ◽  
J. Gilbert Méolans ◽  
Tomohide Niimi ◽  
...  
Keyword(s):  
Flow Regime ◽  
Mass Flow Rate ◽  
Mass Flow ◽  
Flow Rate ◽  
Slip Flow ◽  
Thermal Creep ◽  
Creep Flow ◽  
Slip Flow Regime ◽  
Thermal Creep Flow ◽  
Good Agreement

Measurements of the thermal creep flow through a single rectangular microchannel connected to two tanks maintained initially at the same pressure, but at different temperatures, are carried out for five noble gas species, over a large range of pressure and for two temperature differences between the tanks. The time-dependent pressure variations in both cold and hot tanks are investigated, and the temperature-driven (thermal creep) mass flow rate between two tanks is calculated from these data for the rarefaction parameter ranging from the transitional to slip flow regime. The measured mass flow rate is compared with the numerical solution of the S-model kinetic equation, and they show good agreement. A novel approximate expression to calculate the temperature-driven mass flow rate in the transitional and slip flow regimes is proposed. This expression provides results in good agreement with the measured values of the mass flow rate. In the slip flow regime, the thermal slip coefficient is calculated by employing the previously reported methodology, and the influence of the nature of the gas on this coefficient is investigated. The measured values of the thermal slip coefficient agree well with the values available in the literature, indicating that this coefficient is independent of the shape of a channel.

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