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.

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.

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.

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.

Effect of Constant Heat Flux Boundary Condition on Wall Temperature Fluctuations

2000 ◽  
Vol 123 (2) ◽  
pp. 213-218 ◽  
Author(s):  
A. Mosyak ◽  
E. Pogrebnyak ◽  
G. Hetsroni
Keyword(s):  
Boundary Conditions ◽  
Wall Temperature ◽  
Solid Wall ◽  
Rectangular Channel ◽  
Temperature Fluctuations ◽  
Temperature Fields ◽  
Flux Boundary Condition ◽  
Wall Boundary ◽  
Wall Boundary Conditions ◽  
Thermal Entrance

An experimental study of the wall temperature fluctuations under different thermal-wall boundary conditions was carried out. Statistics obtained from the experiments are compared with existing experimental and numerical data. The wall temperature fields are also examined in terms of the coherent thermal structures. In addition the effect of the thermal entrance region on the wall temperature distribution is also studied. For water flow in a flume and in a rectangular channel, the mean spacing of the thermal streaks does not depend on the thermal entrance length and on the type of thermal-wall boundary conditions. The wall temperature fluctuations depend strongly on the type of wall thermal boundary conditions. Overall, the picture that emerges from this investigation confirms the hypothesis that moderate-Prandtl-number heat transfer at a solid wall is governed by the large-scale coherent flow structures.

The Solution of Temperature Development in the Entrance Region of an MHD Channel by the B. G. Galerkin Method

1969 ◽  
Vol 91 (2) ◽  
pp. 212-220 ◽  
Author(s):  
R. C. LeCroy ◽  
A. H. Eraslan
Keyword(s):  
Eigenvalue Problem ◽  
Galerkin Method ◽  
Wall Temperature ◽  
Mathematical Problem ◽  
Considerable Effect ◽  
Constant Wall Temperature ◽  
Axial Conduction ◽  
Temperature Development ◽  
Constant Wall Heat Flux ◽  
Plate Channel

The general mathematical problem of MHD thermal entrance regions is formulated for a parallel plate channel by including Joule heating, viscous dissipation, and the effect of axial conduction. The associated eigenvalue problem is solved by the B. G. Galerkin method and the results are presented for constant wall temperature and constant wall heat flux conditions. It is shown that the particular method has distinct computational advantages over the classical form of solutions. The constant wall temperature case is investigated by employing the solutions of the eigenvalue problem and it is concluded that the axial conduction has considerable effect on the temperature development for low values of Peclet number.

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.

Convective Heat Transfer in Elliptical Microchannels Under Slip Flow Regime and H1 Boundary Conditions

2015 ◽  
Vol 138 (4) ◽  
Author(s):  
Pamela Vocale ◽  
Gian Luca Morini ◽  
Marco Spiga
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Aspect Ratio ◽  
Boundary Conditions ◽  
Convective Heat Transfer ◽  
Cross Section ◽  
Convective Heat ◽  
Slip Flow ◽  
The Cross ◽  
Cross Section Geometry

In this work, hydrodynamically and thermally fully developed gas flow through elliptical microchannels is numerically investigated. The Navier–Stokes and energy equations are solved by considering the first-order slip flow boundary conditions and by assuming that the wall heat flux is uniform in the axial direction, and the wall temperature is uniform in the peripheral direction (i.e., H1 boundary conditions). To take into account the microfabrication of the elliptical microchannels, different heated perimeter lengths are analyzed along the microchannel wetted perimeter. The influence of the cross section geometry on the convective heat transfer coefficient is also investigated by considering the most common values of the elliptic aspect ratio, from a practical point of view. The numerical results put in evidence that the Nusselt number is a decreasing function of the Knudsen number for all the considered configurations. On the contrary, the role of the cross section geometry in the convective heat transfer depends on the thermal boundary condition and on the rarefaction degree. With the aim to provide a useful tool for the designer, a correlation that allows evaluating the Nusselt number for any value of aspect ratio and for different working gases is proposed.

Laminar Heat Transfer of Gas-Liquid Segmented Flows in Circular Ducts With Constant Wall Temperature

2019 ◽  
Author(s):  
K. Alrbee ◽  
Y. S. Muzychka ◽  
X. Duan
Keyword(s):  
Heat Transfer ◽  
Aspect Ratio ◽  
Wall Temperature ◽  
Silicone Oil ◽  
Liquid Fraction ◽  
Horizontal Tube ◽  
Two Phase ◽  
Constant Wall Temperature ◽  
Transfer Rates ◽  
Taylor Flow

Abstract Laminar heat transfer of gas-liquid Taylor flow in circular tubes is considered. Previous studies have found that introducing a gas phase into a flow stream of a liquid phase significantly increases the heat transfer rate. Other studies considered the effect of slug length on heat transfer rates. The present study’s aim is to demonstrate heat transfer enhancement due to the shortening of liquid slug lengths in a segmented flow and to further validate a model previously developed by the second author. An experimental setup was assembled using mini scale horizontal tube in which the two phase fluid flow is heated under constant wall temperature. New experimental data for gas-liquid Taylor flow in mini scale were carefully obtained using 1 cSt silicone oil which was segmented by air. The experiments were performed with a liquid fraction maintained constant at 0.5 and Reynolds numbers from 50 to 320. In the present work, it is shown that for constant wall temperature, the dimensionless mean wall flux and Nusselt number have been increased by a factor of two at the upper limit of laminar flow which was considered with ReD = 320, when the slug aspect ratio LS/D equal to 10. On other hand the enhancement becomes three times at the same limit of flow when slug aspect ratio has reduced to 1.25 which almost approaches the tube diameter.

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