Analysis and Simulation of Heat Transfer in a Superhydrophobic Microchannel

2010 ◽  
Author(s):  
Ryan Enright ◽  
Marc Hodes ◽  
Todd R. Salamon ◽  
Yuri Muzychka
Keyword(s):  
Thermal Behavior ◽  
Slip Length ◽  
Velocity Slip ◽  
Constant Heat Flux ◽  
Concentration Limit ◽  
Scaling Analysis ◽  
Channel Temperature ◽  
Geometric Scaling ◽  
Flux Boundary Conditions ◽  
Trapped Gas

The transport behavior of a superhydrophobic Hele-Shaw channel subject to arbitrary velocity slip, temperature slip, and constant heat flux boundary conditions is analyzed, resulting in a general expression for the Nusselt number. The results of a scaling analysis and numerical simulation are then presented characterizing the thermal behavior of an idealized pillar-structured superhydrophobic surface in the low pillar concentration limit that treats the trapped gas phase as adiabatic. When thermal behavior is uncoupled from the flow, the temperature slip length is shown to follow the same φs−1/2 dependency on pillar solid fraction as the velocity slip length. Further analysis and simulation including the effects of Marangoni stress, so that the thermal and flow fields are no longer decoupled, yields a further geometric scaling parameter. It is demonstrated that the apparent slip length may be increased against an adverse channel temperature gradient due to the local non-equilibrium of temperature in the vicinity of each pillar.

Effect of thermocapillary stress on slip length for a channel textured with parallel ridges

2017 ◽  
Vol 814 ◽  
pp. 301-324 ◽  
Author(s):  
Marc Hodes ◽  
Toby L. Kirk ◽  
Georgios Karamanis ◽  
Scott MacLachlan
Keyword(s):  
Boundary Conditions ◽  
Slip Length ◽  
Constant Heat Flux ◽  
Matched Asymptotic Expansion ◽  
Channel Height ◽  
Conformal Map ◽  
Adiabatic Flow ◽  
Channel One ◽  
Flux Boundary Conditions ◽  
Thermocapillary Stress

We compute the apparent hydrodynamic slip length for (laminar and fully developed) Poiseuille flow of liquid through a heated parallel-plate channel. One side of the channel is textured with parallel (streamwise) ridges and the opposite one is smooth. On the textured side of the channel, the liquid is in the Cassie state. No-slip and constant heat flux boundary conditions are imposed at the solid–liquid interfaces along the tips of the ridges, and the menisci between ridges are considered to be flat and adiabatic. The smooth side of the channel is subjected to no-slip and adiabatic boundary conditions. We account for the streamwise and transverse thermocapillary stresses along menisci. When the latter is sufficiently small, Stokes flow may be assumed. Then, our solution is based upon a conformal map. When, additionally, the ratio of channel height to half of the ridge pitch is of order 1 or larger, an accurate but less cumbersome solution follows from a matched asymptotic expansion. When inertial effects are relevant, the slip length is numerically computed. Setting the thermocapillary stress equal to zero yields the slip length for an adiabatic flow.

scholarly journals Nusselt numbers for Poiseuille flow over isoflux parallel ridges accounting for meniscus curvature

2016 ◽  
Vol 811 ◽  
pp. 315-349 ◽  
Author(s):  
Toby L. Kirk ◽  
Marc Hodes ◽  
Demetrios T. Papageorgiou
Keyword(s):  
Nusselt Number ◽  
Poiseuille Flow ◽  
Numerical Solutions ◽  
Surface Deformation ◽  
Slip Length ◽  
Constant Heat Flux ◽  
Flux Boundary Condition ◽  
Nusselt Numbers ◽  
Dual Series Equations ◽  
Hydrodynamic Slip

We investigate forced convection in a parallel-plate-geometry microchannel with superhydrophobic walls consisting of a periodic array of ridges aligned parallel to the direction of a Poiseuille flow. In the dewetted (Cassie) state, the liquid contacts the channel walls only at the tips of the ridges, where we apply a constant-heat-flux boundary condition. The subsequent hydrodynamic and thermal problems within the liquid are then analysed accounting for curvature of the liquid–gas interface (meniscus) using boundary perturbation, assuming a small deflection from flat. The effects of this surface deformation on both the effective hydrodynamic slip length and the Nusselt number are computed analytically in the form of eigenfunction expansions, reducing the problem to a set of dual series equations for the expansion coefficients which must, in general, be solved numerically. The Nusselt number quantifies the convective heat transfer, the results for which are completely captured in a single figure, presented as a function of channel geometry at each order in the perturbation. Asymptotic solutions for channel heights large compared with the ridge period are compared with numerical solutions of the dual series equations. The asymptotic slip length expressions are shown to consist of only two terms, with all other terms exponentially small. As a result, these expressions are accurate even for heights as low as half the ridge period, and hence are useful for engineering applications.

Lattice Boltzmann Simulation of Flow and Heat Transfer Characteristics in a Symmetrically Bifurcated Microchannel

2004 ◽  
Author(s):  
Keqiang Xing ◽  
Yong Tao
Keyword(s):  
Heat Transfer ◽  
Lattice Boltzmann ◽  
Constant Heat Flux ◽  
Lattice Boltzmann Model ◽  
Straight Tube ◽  
Lattice Boltzmann Simulation ◽  
Flux Boundary Conditions ◽  
Boltzmann Method ◽  
Thermal Lattice Boltzmann ◽  
Transfer Problems

The lattice Boltzmann method (LBM) as a relatively new numerical scheme has recently achieved considerable success in simulating fluid flows and associated transport phenomena. However, application of this method to heat transfer problems has been at a stage of infancy. In this work, a thermal lattice Boltzmann model is employed to simulate a two-dimensional, steady flow in a symmetric bifurcation under constant temperature and constant heat flux boundary conditions. The bifurcation effects on the heat transfer and fluid flow are investigated and comparisons are made with the straight tube. Also, different bifurcation angles are simulated and the results are compared with the work of the other researchers.

HYDRAULIC AND THERMAL PERFORMANCES OF LAMINAR FLOW IN FRACTAL TREELIKE BRANCHING MICROCHANNEL NETWORK WITH WALL VELOCITY SLIP

Fractals ◽  
2020 ◽  
Vol 28 (02) ◽  
pp. 2050022 ◽  
Author(s):  
DALEI JING ◽  
JIAN SONG ◽  
YI SUI
Keyword(s):  
Heat Transfer ◽  
Laminar Flow ◽  
Convective Heat Transfer ◽  
Hydraulic Resistance ◽  
Convective Heat ◽  
Slip Length ◽  
Velocity Slip ◽  
Diameter Ratio ◽  
Slip Condition ◽  
Wall Velocity

This work theoretically studies the effects of wall velocity slip on the hydraulic resistance and convective heat transfer of laminar flow in a microchannel network with symmetric fractal treelike branching layout. It is found that the slip can reduce the hydraulic resistance and enhance the Nusselt number of laminar flow in the network; furthermore, the slip can also affect the optimal structure of the fractal treelike microchannel network with minimum hydraulic resistance and maximum convective heat transfer. Under the size constraint of constant total channel surface area, the optimal diameter ratio of microchannels at two successive branching levels of the symmetric fractal treelike microchannel network with a minimized hydraulic resistance is only dependent on branching number [Formula: see text] in the manner of [Formula: see text] for no slip condition, but decreases with the increasing slip length, the increasing branching number and the increasing length ratio of microchannels at two successive branching levels for slip condition. The convective heat transfer of the treelike microchannel network is independent on the diameter ratio for no slip condition, but displays an increasing after decreasing trend with the increasing diameter ratio for slip condition. The symmetric treelike microchannel network with the worst convective heat transfer performance is the network with diameter ratio equaling one for slip condition.

Scaling Analysis of Liquid Lead–Bismuth Eutectic Thermal Stratification in ADS Facility Under LOCA

2013 ◽  
Author(s):  
Ziwei Su ◽  
Tao Zhou ◽  
Yunbo Li ◽  
Yican Wu
Keyword(s):  
Thermal Stratification ◽  
Fluid Velocity ◽  
Distribution Model ◽  
Process Time ◽  
Liquid Lead ◽  
Scaling Analysis ◽  
Testing Facility ◽  
Geometric Scaling ◽  
Speed Change ◽  
Lead Bismuth Eutectic

In paper the thermal stratification of liquid lead–bismuth eutectic in accelerator driven subcritical system (ADS) under LOCA is investigated. By means of establishing the space geometric distribution model of thermal stratification which produced in ADS interspace as well as using H2TS scaling analysis to simulate the phenomenon, the main parameters of model facility can be calculated and discussed. When the geometric scaling ratio is chosen be 1/10, by analyzing the Ri number, we can get scaling ratio of leak fluid velocity U0 and process time τ in model is 1/3.16 of the prototype, leak fluid flow Q0 and power q is 1/316.23 of the prototype in the formation process of thermal stratification. Moreover, scaling distortion quantitative analysis for the scaling simulation results be made. So the law related to the time, speed change and so on can be researched, all these work would provide reference and theory for testing facility constructing and ADS safety analysis.

Laminar and Turbulent Free Convection From Elliptic Cylinders, With a Vertical Plate and Horizontal Circular Cylinder as Special Cases

1976 ◽  
Vol 98 (1) ◽  
pp. 72-80 ◽  
Author(s):  
G. D. Raithby ◽  
K. G. T. Hollands
Keyword(s):  
Heat Transfer ◽  
Circular Cylinder ◽  
Free Convection ◽  
Vertical Plate ◽  
Constant Heat Flux ◽  
Special Cases ◽  
Flux Boundary Conditions ◽  
Large Eccentricity ◽  
Rayleigh Numbers ◽  
Horizontal Circular Cylinder

Heat transfer by free convection from thin elliptic cylinders is predicted, accounting for both the effect of thick boundary layers at low Rayleigh numbers and the influence of turbulence at higher Rayleigh numbers. Isothermal and constant heat flux boundary conditions are treated. The results are compared with experimental data, which are available for the limiting cases of large eccentricity (vertical plate) and small eccentricity (horizontal circular cylinder); the agreement is excellent. Accurate correlation equations, from which the average heat transfer can be calculated, are given.

Laminar Convective Heat Transfer in a Microchannel With Internal Fins

2008 ◽  
Author(s):  
Ramesh Narayanaswamy ◽  
Tilak T. Chandratilleke ◽  
Andrew J. L. Foong
Keyword(s):  
Heat Transfer ◽  
Numerical Study ◽  
Three Dimensional ◽  
Constant Heat Flux ◽  
Channel Length ◽  
Height Ratio ◽  
Flux Boundary Conditions ◽  
Nusselt Number Distribution ◽  
Internal Fins ◽  
Square Microchannel

A numerical study was conducted to investigate the fluid flow and heat transfer characteristics of a square microchannel with four longitudinal internal fins. Three-dimensional numerical simulations were performed on the microchannel with variable fin height ratio in the presence of a hydrodynamically developed, thermally developing laminar flow. Constant heat flux boundary conditions were assumed on the external walls of the square microchannel. Results of local Nusselt number distribution along the channel length were obtained as a function of the fin height ratio. The analysis was carried out for different fin heights and flow parameters. Interesting observations that provide more physical insight on this passive enhancement technique, and the existence of an optimum fin height is brought out in the present study.

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