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.

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.

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.

Roughness Effect on the Heat Transfer Coefficient for Gaseous Flow in Microchannels

2010 ◽  
Author(s):  
Metin B. Turgay ◽  
Almila G. Yazicioglu ◽  
Sadik Kakac
Keyword(s):  
Heat Transfer ◽  
Surface Roughness ◽  
Nusselt Number ◽  
Flow Regime ◽  
Viscous Dissipation ◽  
Slip Flow ◽  
Roughness Height ◽  
Working Fluid ◽  
Axial Conduction ◽  
Slip Flow Regime

Effects of surface roughness, axial conduction, viscous dissipation, and rarefaction on heat transfer in a two–dimensional parallel plate microchannel with constant wall temperature are investigated numerically. Roughness is simulated by adding equilateral triangular obstructions with various heights on one of the plates. Air, with constant thermophysical properties, is chosen as the working fluid, and laminar, single-phase, developing flow in the slip flow regime at steady state is analyzed. Governing equations are solved by finite element method with tangential slip velocity and temperature jump boundary conditions to observe the rarefaction effect in the microchannel. Viscous dissipation effect is analyzed by changing the Brinkman number, and the axial conduction effect is analyzed by neglecting and including the corresponding term in the energy equation separately. Then, the effect of surface roughness on the Nusselt number is observed by comparing with the corresponding smooth channel results. It is found that Nusselt number decreases in the continuum case with the presence of surface roughness, while it increases with increasing roughness height in the slip flow regime, which is also more pronounced at low-rarefied flows (i.e., around Kn = 0.02). Moreover, the presence of axial conduction and viscous dissipation has increasing effects on heat transfer with increasing roughness height. Even in low velocity flows, roughness increases Nusselt number up to 33% when viscous dissipation is considered.

Constant Wall Temperature Nusselt and Poiseuille Numbers in Rectangular Microchannels

2007 ◽  
Author(s):  
Jennifer van Rij ◽  
Tim Ameel ◽  
Todd Harman
Keyword(s):  
Aspect Ratio ◽  
Boundary Conditions ◽  
Viscous Dissipation ◽  
Wall Temperature ◽  
Rectangular Channel ◽  
Slip Flow ◽  
Second Order ◽  
Constant Wall Temperature ◽  
Axial Conduction ◽  
Accommodation Coefficients

Slip flow convective heat transfer and friction loss characteristics are numerically evaluated for constant wall temperature rectangular microchannels. The effects of rarefaction, accommodation coefficients, aspect ratio, second-order slip boundary conditions, axial conduction, and viscous dissipation with flow work are each considered. Second-order slip boundary conditions, axial conduction, and viscous dissipation with flow work effects have not been studied previously for rectangular channel slip flows. The effects of each of these parameters on the numerically computed convective heat transfer rate and friction loss are evaluated through the Nusselt number and Poiseuille number respectively. The numerical results are obtained using a continuum-based computational fluid dynamics algorithm that includes second-order slip flow and temperature jump boundary conditions. Numerical results for the three-dimensional, fully developed Nusselt and Poiseuille numbers are presented as functions of Knudsen number, first- and second-order velocity slip and temperature jump coefficients, aspect ratio, Brinkman number, and Peclet number. Effects of rarefaction, accommodation coefficients, and aspect ratio are consistent with previously reported analytical results for rectangular channel constant wall temperature flows. The effects of second-order slip terms, axial conduction and viscous dissipation are also shown to significantly affect the Nusselt and Poiseuille numbers.

The Effect of Viscous Dissipation on Two-Dimensional Microchannel Heat Transfer

2006 ◽  
Author(s):  
Jennifer van Rij ◽  
Tim Ameel ◽  
Todd Harman
Keyword(s):  
Heat Transfer ◽  
Viscous Dissipation ◽  
Slip Flow ◽  
Second Order ◽  
Slip Boundary Conditions ◽  
Pressure Work ◽  
Axial Conduction ◽  
Slip Boundary ◽  
Nusselt Numbers ◽  
Slip Flow Regime

Microchannel convective heat transfer characteristics in the slip flow regime are numerically evaluated for two-dimensional, steady state, laminar, constant wall heat flux and constant wall temperature flows. The effects of Knudsen number, accommodation coefficients, viscous dissipation, pressure work, second-order slip boundary conditions, axial conduction, and thermally/hydrodynamically developing flow are considered. The effects of these parameters on microchannel convective heat transfer are compared through the Nusselt number. Numerical values for the Nusselt number are obtained using a continuum based three-dimensional, unsteady, compressible computational fluid dynamics algorithm that has been modified with slip boundary conditions. Numerical results are verified using analytic solutions for thermally and hydrodynamically fully developed flows. The resulting analytical and numerical Nusselt numbers are given as a function of Knudsen number, the first- and second-order velocity slip and temperature jump coefficients, the Peclet number, and the Brinkman number. Excellent agreement between numerical and analytical data is demonstrated. Viscous dissipation, pressure work, second-order slip terms, and axial conduction are all shown to have significant effects on Nusselt numbers in the slip flow regime.

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.

Sign in / Sign up

Export Citation Format

Share Document