Huei Chu Weng

Natural Convection in a Vertical Microchannel

It is highly desirable to understand the fluid flow and the heat transfer characteristics of buoyancy-induced micropump and microheat exchanger in microfluidic and thermal systems. In this study, we analytically investigate the fully developed natural convection in an open-ended vertical parallel-plate microchannel with asymmetric wall temperature distributions. Both of the velocity slip and the temperature jump conditions are considered because they have countereffects both on the volume flow rate and the heat transfer rate. Results reveal that in most of the natural convection situations, the volume flow rate at microscale is higher than that at macroscale, while the heat transfer rate is lower. It is, therefore, concluded that the temperature jump condition induced by the effects of rarefaction and fluid-wall interaction plays an important role in slip-flow natural convection.

Developing natural convection with thermal creep in a vertical microchannel

Thermal creep occurs in anisothermal gas microflow. It is highly desirable to understand the creep effect on the flow and heat transfer characteristics for developing natural convective microflow. In this study, we investigate the steady developing natural convective flow in an open-ended vertical parallel-plate microchannel with asymmetric wall temperature distributions. The boundary-layer equations subject to the boundary conditions with respect to dynamic pressure at the channel entry as well as higher-order jump temperature and slip velocity with thermal creep along the channel surface are employed. The mathematical model and the numerical code are validated through available macroscale work. Numerical solutions of high-order slip coefficient, slip/jump, velocity, pressure, temperature, flow rate, flow drag and heat transfer rate are presented for air at the standard reference state with complete accommodation. It is found that thermal creep has significant effect on the high-order slip effect and the flow and thermal fields. The creep effect is to increase the flow rate; moreover, valuable reduced flow drag and enhanced heat transfer are obtained.

On the importance of thermal creep in natural convective gas microflow with wall heat fluxes

Thermal creep occurs in gas microflow with wall heat fluxes. In this study, we investigate the creep effect on the steady natural convection in an open-ended vertical parallel-plate microchannel with asymmetric wall heat fluxes. The fully developed solutions for the velocity, pressure, temperature, flow rate, flow drag and heat transfer rate are derived analytically and presented for air at the standard reference state with complete accommodation. It is found that thermal creep has a significant effect. The effect is to unify the velocity and pressure and to elevate the temperature. Moreover, it tends to enhance the flow rate and heat transfer rate and to reduce the maximum gas temperature and flow drag. Its logarithm can be magnified by the decrease in the channel length and the increase in the Knudsen number.

Variable Physical Properties in Natural Convective Gas Microflow

Anisothermal flow prevails in a heated microchannel. It is desirable to understand the influence of temperature-dependent physical properties on the flow and heat transfer characteristics for natural convective gas microflow. In this study, formulas for the shear viscosity, thermal conductivity, constant-pressure specific heat, density, and molecular mean free path are proposed in power-law form and validated through experimental data. Natural convective gas flow with variable physical properties in a long open-ended vertical parallel-plate microchannel with asymmetric wall temperature distributions is further investigated. The full Navier-Stokes equations and energy equation combined with the first-order slip/jump boundary conditions are employed. Analysis process shows that the compressibility and viscous dissipation terms in balance equations are negligible. Numerical solutions are presented for air at the standard reference state with complete accommodation. It is found that the effect of variable properties should be considered for hotter-wall temperatures greater than 306.88 K. The effect is to advance the velocity slip and temperature jump as well as the velocity symmetry and temperature nonlinearity. Moreover, it tends to reduce the mass flow rate and the local heat transfer rate excluding on the cooler-wall surface where the temperature-jump effect prevails over the temperature-nonlinearity effect. Increasing the cooler-wall temperature magnifies the effect on flow behavior but minifies that on thermal behavior.

A challenge in Navier–Stokes-based continuum modeling: Maxwell–Burnett slip law

In this paper, we provide an analytical solution of the Navier–Stokes equations subject to second-order slip boundary conditions for gas flow in a long open-ended parallel-plate microchannel with variable working temperature. Comparisons with available experimental data show the limits of various slip laws in the experimental setups. It is found that the Maxwell (first-order) slip law can be valid for average Knudsen numbers up to 0.255 and that the Maxwell–Burnett slip law should be preferred and can be valid for values up to 1.60. The influences of working temperature on the appearance of the Knudsen paradox and the change in the centerline pressure curvature for different values of the pressure-drop parameter are further predicted. Results reveal that the value of the Knudsen number where the Knudsen paradox appears is always greater than the value where the pressure curvature changes. When the working temperature rises, both the critical values increase. However, both the corresponding values of the m...

Stability of micropolar fluid flow between concentric rotating cylinders

In this study, the theory of micropolar fluids is employed to study the stability problem of flow between two concentric rotating cylinders. The field equations subject to no-slip conditions (non-zero velocity and microrotation velocity components) at the wall surfaces are solved. The analytical solutions of the velocity and microrotation velocity fields as well as the shear stress difference, couple stress and strain rate for basic flow are obtained. The equations with respect to non-axisymmetric disturbances are derived and solved by a direct numerical procedure. It is found that non-zero wall-surface microrotation velocity makes the flow faster and more unstable. Moreover, it tends to reduce the limits of critical non-axisymmetric disturbances. The effect on the stability characteristics can be magnified by increasing the microstructure or couple-stress parameter or the microinertia parameter for the cases of corotating cylinders and a stationary outer cylinder or by decreasing the radius ratio or the microinertia parameter for the case of counterrotating cylinders.

STABILITY OF FERROFLUID FLOW BETWEEN CONCENTRIC ROTATING CYLINDERS WITH AN AXIAL MAGNETIC FIELD

Abstract A linear stability analysis for the ferrofluid flow between two concentric rotating cylinders in the presence of an axial magnetic field is implemented in this study. Both of the wide-gap and small-gap cases are considered and the governing equations with respect to three-dimensional disturbances including axisymmetric and non-axisymmetric modes are derived and solved by a direct numerical procedure. A parametric study covering wide ranges of ϕ, the volume fraction of colloidal particles; ξ, the strength of axial magnetic field; μ, the ratio of angular velocity of the outer cylinder to that of the inner cylinder; and e, the ratio of radius of the inner cylinder to that of the outer cylinder, is conducted. Results show that the stability characteristics depend heavily on these factors. It is found that the increases of ϕ and ξ, and decrease of e tend to stabilize the basic flow for an assigned value of μ. The variations of the onset mode with these parameters are discussed in detail. An example for the practical application of present results is given to help the understanding of stability behaviour of this flow.

Fully developed thermocreep-driven gas microflow

In this study, we develop the mathematical model of thermocreep-driven gas flow in an unheated parallel-plate microchannel with discrepant temperatures at both ends. The fully developed solutions for flow and thermal fields as well as the corresponding characteristics are derived analytically and presented for air. Results reveal that the velocity and temperature distributions are uniform. This means that the local flow drag and the local heat transfer rate are zero and that the influence of fluid-wall interaction is negligible. In addition, the velocity slip induced by gas rarefaction is shown to increase the flow rate and the average heat transfer rate. Such effect can be magnified by the decreases of the channel width and the channel length.

The Effect of a Magnetic Field on the Profile of Sessile Magnetic Nanofluid Droplets

Abstract Surface wettability plays an important role in droplet formation, removal, and resistance to fouling. The sessile droplet profile is one of the most important parameters characterizing surface wettability. In this study, an investigation was carried out into the effects of a magnetic field on the profile of sessile droplets of magnetic nanofluid. We started with a revision of the classic Young–Laplace equation according to normal stress balance principles by considering a magnetic nanofluid droplet in an applied magnetic field gradient. The secant method was then used to solve the non-linear differential equation and predict the sessile droplet profile. The results showed that a downward magnetic force caused an expansion of the profile and an upwards magnetic force caused contraction. In other words, droplets on an hydrophilic or hydrophobic surface could be tuned by magnetic field gradients of different strength and direction. This magnetowetting effect could be further adjusted by selection of different fluid, material, and particle concentration.

Second-order slip flow and heat transfer in a microchannel

The present numerical investigation is concerned with the role of second-order slip and jump in the steady incompressible slip flow and heat transfer in an isothermally heated horizontal planar microchannel. The field equations subject to the second-order boundary conditions are numerically solved by using a marching implicit procedure. Results are presented for air from a reservoir in the standard reference state into the microchannel with complete accommodation. It is found that the second-order slip and jump have a significant effect on flow and thermal characteristics. The effect is to decrease the outlet pressure required and to increase the average flow drag and average heat transfer rate obtained. Decreasing the channel length or flow speed enhances it.