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.

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.

Isothermal Microtube Heat Transfer With Second-Order Slip Flow and Temperature Jump Boundary Conditions

2006 ◽  
Author(s):  
Nian Xiao ◽  
John Elsnab ◽  
Susan Thomas ◽  
Tim Ameel
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Nusselt Number ◽  
Boundary Conditions ◽  
Temperature Jump ◽  
Slip Flow ◽  
Second Order ◽  
Order Model ◽  
First Order ◽  
Second Order Model

Two analytical models are presented in which the continuum momentum and energy equations, coupled with second-order slip flow and temperature jump boundary conditions, are solved. An isothermal boundary condition is applied to a microchannel with a circular cross section. The flow is assumed to be hydrodynamically fully developed and thermal field is either fully developed or thermally developing from the tube entrance. A traditional first-order slip boundary condition is found to over predict the slip velocity compared to the second-order model. Heat transfer increases at the upper limit of the slip regime for the second-order model. The maximum second-order correction to the first-order Nusselt number is on the order of 18% for air. The second-order effect is also more significant in the entrance region of the tube. The Nusselt number decreases relative to the no-slip value when slip and temperature jump effects are of the same order or when temperature jump effects dominate. When temperature jump effects are small, the Nusselt number increases relative to the no-slip value. Comparisons to a previously reported model for an isoflux boundary condition indicate that the Nusselt number for the isoflux boundary condition exceeds that for the isothermal case at all axial locations.

Microtube Gas Flows With Second-Order Slip Flow and Temperature Jump Boundary Conditions

2006 ◽  
Author(s):  
Nian Xiao ◽  
John Elsnab ◽  
Tim Ameel
Keyword(s):  
Nusselt Number ◽  
Boundary Conditions ◽  
Temperature Jump ◽  
Order Approximation ◽  
Slip Flow ◽  
Order Effect ◽  
Second Order ◽  
First Order ◽  
Slip Regime ◽  
Energy Equations

Second-order slip flow and temperature jump boundary conditions are applied to solve the momentum and energy equations in a microtube for an isoflux thermal boundary condition. The flow is assumed to be hydrodynamically fully developed, and the thermal field is either fully developed or developing from the tube entrance. In general, first-order boundary conditions are found to over predict the effects of slip and temperature jump, while the effect of the second-order terms is most significant at the upper limit of the slip regime. The second-order terms are found to provide a correction to the first-order approximation. For airflows, the maximum second-order correction to the Nusselt number is on the order of 50%. The second-order effect is also more significant in the entrance region of the tube. Nusselt numbers are found to increase relative to their no-slip values when temperature jump effects are small. In cases where slip and temperature jump effects are of the same order, or where temperature jump effects dominate, the Nusselt number decreases when compared to traditional no-slip conditions.

Rarefaction, Temperature Jump, and Viscous Dissipation Effects on Heat Transfer in Rotating Micro Devices

2006 ◽  
Author(s):  
Latif M. Jiji
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Viscous Dissipation ◽  
Knudsen Number ◽  
Temperature Jump ◽  
Slip Flow ◽  
Fluid Temperature ◽  
Rotating Shaft ◽  
Number Range ◽  
Rotating Surface

This paper examines the effects of rarefaction and dissipation on flow and heat transfer characteristics in rotating micro devices. The housing is assumed to be at uniform temperature while the rotating surface is insulated. Thus heat generation and transfer are due to viscous dissipation only. An analytic solution is obtained for the velocity and temperature distribution in the gas filled concentric clearance between a rotating shaft and its stationary housing. The solution is valid in the slip flow and temperature jump domain defined by the Knudsen number range of Kn < 0.1. The Nusselt number was found to depend on three parameters: the Knudsen number Kn, ratio of housing to shaft radius ro / ri, and Prandtl number-specific heat ratio group γ/(γ + 1) Pr. Results indicate that curvature and Knudsen number have significant effect on the Nusselt number. However, fluid temperature rise due to dissipation is negligible.

Slip-Flow and Conjugate Heat Transfer in Rectangular Microchannels

2008 ◽  
Author(s):  
H. D. Madhawa Hettiarachchi ◽  
Mihajlo Golubovic ◽  
William M. Worek ◽  
W. J. Minkowycz
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Nusselt Number ◽  
Conjugate Heat Transfer ◽  
Temperature Jump ◽  
Slip Flow ◽  
Numerical Code ◽  
Published Data ◽  
Rectangular Microchannels ◽  
Knudsen Numbers

Slip-flow and conjugate heat transfer in rectangular microchannels are studied numerically for thermally developing laminar flow subjected to constant wall temperature (T) and constant wall heat flux (H2) boundary conditions. A three-dimensional numerical code based on finite volume method is developed to solve the coupled energy equations in the wall and fluid regions together with temperature jump at the wall-fluid boundary. A modified convection-diffusion coefficient at the wall-fluid interface is defined to incorporate the temperature-jump boundary condition. The numerical code is validated by comparing the present results with the published data. The effect of rarefaction and wall conduction on the heat transfer in the entrance region is analyzed in detail. Results show that the wall conduction has a considerable influence on the developing Nusselt number along the channel for the H2 boundary condition, particularly at low Knudsen numbers. In the case of the T thermal boundary condition, negligible influence of wall conduction on the Nusselt number is observed for all Knudsen numbers considered.

Evaluation of Nusselt Number for a Flow in a Parallel Plates Using MHD Second Order Slip Model

2021 ◽  
Author(s):  
Hatice Simsek
Keyword(s):  
Magnetic Field ◽  
Boundary Condition ◽  
Nusselt Number ◽  
Slip Flow ◽  
Mhd Flow ◽  
Second Order ◽  
Parallel Plates ◽  
First Order ◽  
Condition Model ◽  
Boundary Condition Model

Abstract In this study, two separate boundary condition models, as proposed by Beskok and Karniadakis [1] and Deissler [2], widely preferred for the second order boundary condition, were used. These two proposed boundary condition models were solved in the presence of a magnetic field moving normal to the plate surface in magneto-hydrodynamic (MHD) flow between micro-parallel plates with constant wall heat flux. The energy equation for the second-order temperature jump boundary condition, taking into account the momentum and viscous dissipation, as well as the corresponding Nusselt value were solved analytically in slip flow regime.The flow of an incompressible viscous flow between fixed micro-parallel plates with electrical conductivity is assumed to be constant, laminar, hydrodynamically and thermally developed. The closed form solutions for the temperature field and the fully developed Nusselt number are derived as a function of the Magnetic parameter (MHD), Knudsen number and Brinkman number and shown graphically and in a tabular form. The second order boundary condition model proposed by Deissler [2] predicts the Nusselt number to be at lower values when compared to the first order boundary condition model, and the second order boundary condition model proposed by Beskok and Karniadakis [1] predicts the Nusselt number to be at higher values than that of the first order boundary condition model. Moreover, increasing the magnetic field parameter M, led to higher Nusselt values in the slip flow model proposed by both Deissler [2] and Beskok and Karniadakis [1] compared to that when M = 0.

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.

High Order Slip and Thermal Creep Effects in Micro Channel Natural Convection

2010 ◽  
Author(s):  
Hamid Niazmand ◽  
Behnam Rahimi
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Temperature Jump ◽  
Slip Flow ◽  
Velocity Slip ◽  
Thermal Creep ◽  
Transfer Rates ◽  
Thermal Fields ◽  
Slip Flow Regime ◽  
Rarefaction Effects

Developing natural convection gaseous flows in an open-ended parallel plate vertical microchannel with isothermal wall conditions are numerically investigated to analyze the rarefaction effects on heat transfer and flow characteristics in slip flow regime. The Navier-Stokes and energy equations are solve by a control volume technique subject to higher-order temperature jump and velocity slip conditions including thermal creep effects. The flow and thermal fields in the entrance and fully developed regions along with the axial variations of velocity slip, temperature jump, and heat transfer rates are examined in detail. It is found that rarefaction effects significantly influence the flow and thermal fields such that mass flow and heat transfer rates are increased considerably as compared to the continuum regime. Furthermore, thermal creep contribution to the velocity slip is found to be dominant close to the channel inlet and vanishes in the fully developed region, while velocity slip approaches a finite value there. Both Mass flow rate and thermal entrance length increase with increasing Knudsen number in slip flow regime.

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