Investigation of fluid flow and heat transfer in rotating microchannels is important for centrifugal microfluidics, which has emerged as an advanced technique in biomedical applications and chemical separations. The pseudo forces namely the centrifugal force and the Coriolis force arising as a consequence of the rotating reference frame change the flow pattern significantly from the parabolic profile in a non-rotating channel. The convective heat transfer process is also influenced by the secondary flow introduced by the rotational effect. Moreover, if the microchannel wall is hydrophobic, slip flow can occur inside the channel when the conventional no slip boundary condition is no longer valid. In this work, we have numerically investigated the flow and heat transfer inside a straight rotating rectangular microchannel in the slip flow regime. A pressure based finite volume technique in a staggered grid was applied to solve the steady incompressible Navier-Stokes and energy equations. It has been observed that, depending on the rotational velocity, different slip velocities are induced at the channel walls. The average fluid temperature increases with the increase of rotation as convective heat transfer mechanism is increased due to the secondary flow. However, the slip boundary condition has a negligible effect on the temperature profiles.

In the present work, the second law of thermodynamics analysis has been carried out for steady state hydrodynamically and thermally fully developed laminar gas flow in annulus microchannels with asymmetrically heated walls. The rarefaction effects are taken into consideration using first order slip velocity and temperature jump boundary conditions. Viscous heating is also included for both the hot wall and the cold wall cases. Using the velocity distribution obtained in earlier works, the energy equation is solved to get analytically the temperature distribution and consequently to compute the entropy generation rate. The effects of rarefaction and the annulus geometrical aspect ratio on velocity distribution are discussed. The complicated interactive effects of rarefaction, viscous dissipation, the ratio of Brinkman number to dimensionless temperature difference, annulus geometrical aspect ratio and asymmetry on entropy generation rate and Bejan number are shown in graphical form and also discussed in details. The analytical results obtained are compared with those available in the literature and an excellent agreement is observed. It is realized that the effect of the wall heat fluxes ratio on entropy generation is negligible at great values of the ratio of Brinkman number to dimensionless temperature difference, while the effect of increasing values of the annulus geometrical aspect ratio is to severely increase entropy generation. The entropy generation decreases as Knudsen number increases, however the effect of increasing values of Brinkman number and the ratio of Brinkman number to dimensionless temperature difference is to increase entropy generation.

Heat transfer characteristics of gaseous flows in concentric micro annular tubes with constant wall temperature whose temperature is lower or higher than the inlet temperature were numerically investigated. The slip velocity, temperature jump and shear stress work were considered on the slip boundary. The numerical methodology was based on the Arbitrary-Lagrangian-Eulerian (ALE) method. The computations were performed for two thermal cases. This is, the wall temperature was constant at the outer wall and inner wall was adiabatic (Case i) and the wall temperature was constant at the inner wall and the outer wall was adiabatic (Case ii). The stagnation temperature was fixed at 300 K and the computations were done for the wall temperature which ranges from 250 K to 350 K. The outer tube radius ranged from 20 to 150 μm with the radius ratio 0.02, 0.05, 0.1, 0.25 and 0.5 and the ratio of length to hydraulic diameter was 100. The stagnation pressure was chosen in such a way that the exit Mach number ranged from 0.1 to 0.8. The outlet pressure was fixed at the atmospheric pressure. The heat transfer characteristics in concentric micro annular tubes were obtained. The bulk temperature and the total temperature are compared with those of both cooled and heated cases and also compared with those of the simultaneously developing incompressible flow obtained by SIMPLE algorithm. The results show that the compressible slip flow static bulk temperature along the length is different from that of incompressible flow. Therefore heat transfer characteristics of the gaseous flow are different from those of the liquid flow and also have different trends whether the wall temperature is lower or higher than the inlet temperature. A correlation for the prediction of the heat transfer rate of gas slip flow in concentric micro annular tubes is proposed.

Micro-scale fluid dynamics has received intensive interest due to the emergence of Micro-Electro-Mechanical Systems (MEMS) technology. Non-circular cross sections are common channel shapes that can be produced through a variety of micro-fabrication techniques. Non-circular microchannels have extensive practical applications in MEMS. Slip flow in noncircular microchannels has been examined by the authors and a review of several new models obtained by the authors is presented. These models are general and robust, and can be used by the research community for practical engineering design of microchannel flow systems. The reviewed models address: (i) fully developed slip flow in non-circular microchannels, (ii) hydrodynamically developing slip flow in non-circular microchannels, (iii) compressibility effects, and (iv) roughness effects. A model is proposed to predict the friction factor and Reynolds product fRe for fully developed and developing slip flow in most non-circular micro-channels. Compressibility effects on slip flow in non-circular microchannels have been examined and simple models are proposed to predict the pressure distribution and mass flow rate for slip flow in most non-circular microchannels. Finally, the effect of corrugated surface roughness on fully developed laminar flow in microtubes is examined. Simple analytical models are developed to predict friction factor and pressure drop in corrugated rough microtubes for continuum flow and slip flow.

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.

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.

Miniaturization of devices has received a rapid expansion in the last years and a great attention of research activities is given to microflow due to its new applications of microfluidic systems and components. In the present paper a transient investigation on natural convection in parallel-plate vertical microchannels is carried out numerically. The vertical microchannel is considered asymmetrically or symmetrically heated at uniform heat flux. The first-order model for slip velocity and jump temperature is assumed in microscale conditions. The analysis is performed in laminar boundary layer assumption for different values for different values of Knudsen number, Rayleigh number and the ratio of wall heat flux in order to evaluate their effects on wall temperatures, mass flow rate and Nusselt number. Wall temperature overshoots are detected for the different conditions. These values increase increasing the Knudsen number, Kn, at high Rayleigh number, Ra, whereas for lower Ra the lowest wall temperature are obtained for Kn = 0.05. Mass flow rate increases increasing Kn whereas Nusselt number decreases increasing Kn.

The frictional windage losses associated with non-ventilated airflows in the air gaps between the rotor and stator of a high speed rotating machine can greatly influence the rotor outer and stator inner surface temperatures. The characteristics of the radial and axial air-gap flows have been of general interest in many engineering applications. A rotating air gap flow is very complex, and in general, can be categorized as a continuum flow, slip flow, and free molecule flow, depending on the ratio of its mean free path to the air gap dimension. For a continuum flow between concentric rotating cylinders, secondary flow of rows of circumferential Taylor vortices in the air gap due to centrifugal flow instability of a curved flow at relatively high rotating speeds will typically be formed. As the air pressure in the air gap drops significantly, rarefied gas flow, departure from continuum flow, occurs when the mean free path becomes relatively large compared to the air gap dimension. This paper has developed and summarized an analytical approach to predict high speed windage losses (rotor tip velocities up to 900 m/s) at low rotor cavity air pressures (0.1 torr to 10 torr). The predicted transient windage losses at various air pressures and high rotor speeds are compared with measured windage losses generated in continuum and slip flow regimes. The agreements between the predicted and measured windage losses are relatively well.