On Temperature Jump Condition for Slip Flow in a Microchannel With Constant Wall Temperature

2017 ◽  
Vol 139 (7) ◽  
Author(s):  
Yutaka Asako ◽  
Chungpyo Hong
Keyword(s):  
Boundary Condition ◽  
Viscous Dissipation ◽  
Wall Temperature ◽  
Energy Equation ◽  
Temperature Jump ◽  
Slip Flow ◽  
Jump Condition ◽  
Constant Wall Temperature ◽  
Maximum Heat ◽  
Maximum Heat Transfer

The analytical solution in the fully developed region of a slip flow in a circular microtube with constant wall temperature is obtained to verify the conventional temperature jump boundary condition when both viscous dissipation (VD) and substantial derivative of pressure (SDP) terms are included in the energy equation. Although the shear work term is not included in the conventional temperature jump boundary condition explicitly, it is verified that the conventional temperature jump boundary condition is valid for a slip flow in a microchannel with constant wall temperature when both viscous dissipation and substantial derivative of pressure terms are included in the energy equation. Numerical results are also obtained for a slip flow in a developing region of a circular tube. The results showed that the maximum heat transfer rate decreases with increasing Mach number.

Three Dimensional Numerical Analysis of Laminar Slip-Flow Heat Transfer in Rectangular Microchannels

2008 ◽  
Author(s):  
H. D. Madhawa Hettiarachchi ◽  
Mihajlo Golubovic ◽  
William M. Worek
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Temperature Jump ◽  
Slip Flow ◽  
Three Dimensional ◽  
Velocity Slip ◽  
Thermal Boundary Condition ◽  
Navier Stokes ◽  
Constant Wall Temperature ◽  
Rectangular Microchannels

Slip-flow and heat transfer in rectangular microchannels are studied numerically for constant wall temperature (T) and constant wall heat flux (H2) boundary conditions under thermally developing flow. Navier-Stokes and energy equations with velocity slip and temperature jump at the boundary are solved using finite volume method in a three dimensional cartesian coordinate system. A modified convection-diffusion coefficient at the wall-fluid interface is defined to incorporate the temperature-jump boundary condition. Validity of the numerical simulation procedure is stabilized. The effect of rarefaction on heat transfer in the entrance region is analyzed in detail. The velocity slip has an increasing effect on the Nusselt (Nu) number whereas temperature jump has a decreasing effect, and the combined effect could result increase or decrease in the Nu number. For the range of parameters considered, there could be high as 15% increase or low as 50% decrease in fully developed Nu is plausible for T thermal boundary condition while it could be high as 20% or low as 35% for H2 thermal boundary condition.

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.

Analytical Solution of the Graetz Problem Extended to Slip-Flow in Microtube

2012 ◽  
Vol 134 (10) ◽  
Author(s):  
Fayao Xu ◽  
Hugen Ma
Keyword(s):  
Analytical Solution ◽  
Energy Equation ◽  
Temperature Jump ◽  
Separation Of Variables ◽  
Slip Flow ◽  
Power Series Expansion ◽  
Velocity Slip ◽  
Jump Condition ◽  
Dimensionless Temperature ◽  
Graetz Problem

The original Graetz problem is extended to slip-flow in microtube. The extended Graetz problem in slip-flow with the isothermal boundary condition on the wall was solved using conventional energy equation with both the velocity slip and the temperature jump condition of slip-flow. The analytical solution was obtained by solving the energy equation with the method of separation of variables. The accurate eigenvalues were obtained by solving the eigenfunction with the method of power series expansion. In the end, temperature distributions, local Nusselt number Nux, and dimensionless temperature jump θs were obtained. In addition, the influences of Knudsen number Kn on Nux, Nu∞, and θs were discussed.

Shear work, viscous dissipation and axial conduction effects on microchannel heat transfer with a constant wall temperature

2015 ◽  
Vol 230 (14) ◽  
pp. 2496-2507 ◽  
Author(s):  
K Ramadan ◽  
Iskander Tlili
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Wall Temperature ◽  
Slip Flow ◽  
Brinkman Number ◽  
Constant Wall Temperature ◽  
Fully Developed Flow ◽  
Boundary Shear ◽  
Temperature Boundary ◽  
Temperature Boundary Condition

Convective heat transfer in a microchannel rarefied gas flow with a constant wall temperature boundary condition is investigated numerically. The boundary shear work, viscous dissipation and axial conduction are all included in the study. An analytical solution is also derived for the fully developed flow condition including the boundary shear work. The proper thermal boundary condition considering the sliding friction at the wall is implemented. A comparative study is performed to quantify the effect of the shear work on heat transfer in the entrance – and the fully developed – regions of the microchannel for both gas cooling and heating. The results demonstrate that the effect of shear work on heat transfer is significant and it increases with increasing both the Knudsen number and Brinkman number. Neglecting the shear work in a microchannel slip flow leads to over- or under estimation of the Nusselt number considerably. For a fully developed flow in a microchannel with constant wall temperature boundary condition, the contribution of the shear work to heat transfer can be around 55% in the vicinity of the upper limit of the slip flow regime, regardless of how small the non-zero Brinkman number can be. Including the shear work is therefore crucial in the analysis of microchannel heat transfer and should not be neglected.

EFFECTS OF THERMAL CREEP ON COOLING OF MICROFLOWS IN SHORT MICROCHANNELS WITH CONSTANT WALL TEMPERATURE

2012 ◽  
Vol 23 (11) ◽  
pp. 1250072 ◽  
Author(s):  
ALI AMIRI-JAGHARGH ◽  
HAMID NIAZMAND ◽  
METIN RENKSIZBULUT
Keyword(s):  
Wall Temperature ◽  
Temperature Jump ◽  
Control Volume ◽  
Velocity Slip ◽  
Temperature Gradients ◽  
Thermal Creep ◽  
Inlet Temperature ◽  
Constant Wall Temperature ◽  
Aspect Ratios ◽  
Wide Range

Fluid flow and heat transfer in the entrance region of rectangular microchannels of various aspect ratios are numerically investigated in the slip-flow regime with particular attention to thermal creep effects. Uniform inlet velocity and temperature profiles are prescribed in microchannels with constant wall temperature. An adiabatic section is also employed at the inlet of the channel in order to prevent unrealistically large axial temperature gradients due to the prescribed uniform inlet temperature as well as upstream diffusion associated with low Reynolds number flows. A control-volume technique is used to solve the Navier–Stokes and energy equations which are accompanied with appropriate velocity slip and temperature jump boundary conditions at the walls. Despite the constant wall temperature, axial and peripheral temperature gradients form in the gas layer adjacent to the wall due to temperature jump. The simultaneous effects of velocity slip, temperature jump and thermal creep on the flow and thermal patterns along with the key flow parameters are examined in detail for a wide range of cross-sectional aspect ratios, and Knudsen and Reynolds numbers. Present results indicate that thermal creep effects influence the flow field and the temperature distribution significantly in the early section of the channel.

scholarly journals Gas Microflows in the Slip Flow Regime: A Critical Review on Convective Heat Transfer

2011 ◽  
Vol 134 (2) ◽  
Author(s):  
Stéphane Colin
Keyword(s):  
Heat Transfer ◽  
Convective Heat Transfer ◽  
Flow Regime ◽  
Convective Heat ◽  
Temperature Jump ◽  
Numerical Models ◽  
Slip Flow ◽  
Velocity Slip ◽  
Constant Wall Temperature ◽  
Slip Flow Regime

Accurate modeling of gas microvection is crucial for a lot of MEMS applications (microheat exchangers, pressure gauges, fluidic microactuators for active control of aerodynamic flows, mass flow and temperature microsensors, micropumps, and microsystems for mixing or separation for local gas analysis, mass spectrometers, vacuum, and dosing valves…). Gas flows in microsystems are often in the slip flow regime, characterized by a moderate rarefaction with a Knudsen number of the order of 10−2–10−1. In this regime, velocity slip and temperature jump at the walls play a major role in heat transfer. This paper presents a state of the art review on convective heat transfer in microchannels, focusing on rarefaction effects in the slip flow regime. Analytical and numerical models are compared for various microchannel geometries and heat transfer conditions (constant heat flux or constant wall temperature). The validity of simplifying assumptions is detailed and the role played by the kind of velocity slip and temperature jump boundary conditions is shown. The influence of specific effects, such as viscous dissipation, axial conduction and variable fluid properties is also discussed.

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