The effect of viscous dissipation and rarefaction on rectangular microchannel convective heat transfer

The effect of viscous dissipation and rarefaction on rectangular microchannel convective heat transfer rates, as given by the Nusselt number, is numerically evaluated subject to constant wall heat flux (H2) and constant wall temperature (T) thermal boundary conditions. Numerical results are obtained using a continuum based, three-dimensional, compressible, unsteady computational fluid dynamics algorithm with slip velocity and temperature jump boundary conditions applied to the momentum and energy equations, respectively. For the limiting case of parallel plate channels, analytic solutions for the thermally and hydrodynamically fully developed momentum and energy equations are derived, subject to both first- and second-order slip velocity and temperature jump boundary conditions, from which analytic Nusselt number solutions are then obtained. Excellent agreement between the analytical and numerical results verifies the accuracy of the numerical algorithm, which is then employed to obtain three-dimensional rectangular channel and thermally/hydrodynamically developing Nusselt numbers. Nusselt number data are presented as functions of Knudsen number, Brinkman number, Peclet number, momentum and thermal accommodation coefficients, and aspect ratio. Rarefaction and viscous dissipation effects are shown to significantly affect the convective heat transfer rate in the slip flow regime.     

Similarity solutions for flows and heat transfer in microchannels between two parallel plates

In this paper we give analytical similarity solutions of the Navier–Stokes equations coupled with energy equation of Newtonian fluid in a microchannel between two parallel plates taking into account the effects of viscous dissipation, the velocity slip and the temperature jump at the wall. Two different thermal boundary conditions are considered: the constant heat flux (CHF) and the constant wall temperature (CWT). We provide new similarity transformations for the governing equations and derive the expressions of Poiseuille number (Po) and Nusselt number (Nu). Then, the homotopy analysis method (HAM) is employed to solve the nonlinear differential equations with related boundary conditions. Both the dimensionless analytical expressions of velocity and temperature are obtained. The rarefaction effects on velocity distribution and flow friction are exhibited. The interactive effects of the Brinkman number (Br) and the Knudsen number (Kn) on Nu are analytically studied for both the CHF and CWT cases.     

Effects of High-Order Slip/Jump,Thermal Creep,and Variable Thermophysical Properties on Natural Convection in Microchannels With Constant Wall Heat Fluxes

Natural convection gaseous slip flows in open-ended vertical parallel-plate microchannels with symmetric wall heat fluxes are numerically investigated. A second-order model, including thermal creep effects, is considered for velocity slip and temperature jump boundary conditions with variable thermophysical properties. Simulations are performed for wide range of Rayleigh numbers from 5 × 10^{? 6} to 5 × 10^{? 3} in the continuum to slip flow regime. The developing and fully developed solutions are examined by solving the Navier–Stokes and energy equations using a control volume technique. It is found that the second-order effects reduce the temperature jump and the slip velocity, whereas thermal creep strongly increases the slip velocity in both developing and fully developed regions. Moreover, the rarefaction effects increase the flow and heat transfer rates considerably, while decreasing the maximum gas temperature and friction coefficient as compared to the continuum limit. It was also shown that the axial temperature variations of the gas layer adjacent to the wall in the modeling of the thermal creep are of paramount importance and neglecting these variations, which is common in literature, leads to unphysical velocity and temperature distributions.     

Fluid flow in microtubes with axial conduction including rarefaction and viscous dissipation

Graetz problem inside the microtube is revisited considering rarefaction effect, viscous dissipation term and axial conduction in the fluid for uniform wall temperature boundary condition in the slip flow regime. The flow is assumed to be hydrodynamically fully developed, thermally developing, and the velocity profile is solved analytically. The temperature field is determined by the numerical solution of the energy equation. The rarefaction effect is imposed to the problem via velocity-slip and temperature jump boundary conditions. The local and fully developed Nu numbers are obtained in terms of dimensionless parameters; Pe, Kn, Br, κ. Fully developed Nu numbers and the thermal entrance length are found to increase by the presence of the finite axial conduction.     

Thermal and hydrodynamic analysis of gaseous flow in trapezoidal silicon microchannels

Thermal and hydrodynamic character of a hydrodynamically developed and thermally developing flow in trapezoidal silicon microchannels is analyzed. The continuum momentum and energy equations, with the velocity slip and temperature jump condition at the solid walls, are solved numerically in a square computational domain obtained by transformation of the trapezoidal geometry. The effects of rarefaction, aspect ratio and a parameter representing the fluid/wall interaction on thermal and hydrodynamic character of flow in trapezoidal microchannels are explored. It is found that the friction factor decreases if rarefaction and/or aspect ratio increase. It is also found that at low rarefactions the very high heat transfer rate at the entrance diminishes rapidly as the thermally developing flow approaches fully developed flow. At high rarefactions, heat transfer rate does not exhibit considerable changes along the microchannel, no matter the flow is developing or not.     

Natural convection slip flow in a vertical microchannel heated at uniform heat flux

Numerical solutions for steady state developing natural convection flow in air, in vertical parallel-plate microchannels are accomplished. An asymmetric heating is considered and the walls are assumed to be at uniform heat flux. A first-order model is used for slip and jump boundary conditions and an analytical solution for the fully developed flow is also given. Results are performed for air, for the heat flux ratio in the 0.0–1.0 range, for Rayleigh, Ra, and Knudsen, Kn, numbers from 10^?1 to 8 × 10³ and from 0.0 to 0.10, respectively. The maximum mass flow rate is always obtained for the highest considered Kn value, whereas the average Nusselt number, Nu, increases for lower Ra (<10) and decreases for Ra > 100. Wall temperature profiles have the lowest values for highest considered Kn value at lower Ra, whereas for the developing flow, they present opposite trends. For developing flow, velocity profiles for asymmetric and symmetric heating are completely different. In developing flow velocity profiles along the wall present the highest increases for asymmetric heating and the highest considered Kn value.     

The effect of creep flow on two-dimensional isoflux microchannels

Microchannel convective heat transfer and friction loss characteristics are numerically evaluated for gaseous, two-dimensional, steady state, laminar, constant wall heat flux flows. The effects of Knudsen number, accommodation coefficients, second-order slip boundary conditions, creep flow, and hydrodynamically/thermally developing flow are considered. These effects are compared through the Poiseuille number and the Nusselt number. Numerical values for the Poiseuille and Nusselt numbers are obtained using a continuum based three-dimensional, unsteady, compressible computational fluid dynamics algorithm that has been modified with slip boundary conditions. To verify the numerical results, analytic solutions of the hydrodynamically and thermally fully developed momentum and energy equations have been derived subject to both first- and second-order slip velocity and temperature jump boundary conditions. The resulting velocity and temperature profiles are then utilized to obtain the microchannel Poiseuille and Nusselt numbers as a function of Knudsen number, first- and second-order velocity slip and temperature jump coefficients, Brinkman number, and the ratio of the thermal creep velocity to the mean velocity. Excellent agreement between the numerical and analytical data is demonstrated. Second-order slip terms and creep velocity are shown to have significant effects on microchannel Poiseuille and Nusselt numbers within the slip flow regime.     

EFFECTS OF RAREFACTION AND COMPRESSIBILITY OF GASEOUS FLOW IN MICROCHANNEL USING DSMC

The direct simulation Monte Carlo (DSMC) is performed for two-dimensional gaseous flow through a microchannel in both slip and transition regimes to understand the effects of compressibility and rarefaction. Results are presented in the form of axial pressure distribution, velocity profile, local friction coefficient, and local Mach number (Ma) and are compared with the available analytical and experimental results. The effect of compressibility is examined for the inlet to outlet pressure ratios ranging from 1.38 to 4.5. Low-pressure drop simulations with Knudsen numbers (Kn) ranging from 0.03 to 0.11 are performed to identify the effect of rarefaction. It was found that compressibility makes the axial pressure variation nonlinear and enhances the local friction coefficient. On the other hand, rarefaction does not affect pressure distribution but causes the flow to slip at the wall and reduces the local friction coefficient. In addition, it was found that the locally fully developed (LFD) assumption is valid for low Ma flows by comparison with DSMC results.     

Thermally fully developed electroosmotic flow through a rectangular microchannel

This study investigates the velocity and temperature distributions of the thermally fully developed electroosmotic flow through a rectangular microchannel. Based on linearized Poisson–Boltzmann (PB) equation, Navier–Stokes equation and thermally fully developed energy equation, analytical solutions of normalized velocity, temperature and Nusselt number are derived. They greatly depend on the ratio K of characteristic scale of the rectangular microchannel to Debye length, width to height ratio α and Joule heating to heat flux ratio S. By numerical computation, we found that for prescribed electrokinetic width K, increased S yields greater temperature. For small K, the variations of the temperature θ are larger than those of large K. The dependence of temperature on S is more significant for a small K, while at a larger K the temperature profiles are almost identical. In addition, we illustrate the Nusselt number Nu variations with S, α and K.     

UNIQUE BEHAVIORS OF A BACKWARD-FACINGSTEP FLOW AT MICROSCALE

ABSTRACT

The direct simulation Monte Carlo (DSMC) method is used to simulate micro backward-facing step flows in both slip and transition flow regimes. The effects of rarefaction on flow characteristics are analyzed and discussed. It is found that flow separation, recirculation, and reattachment will disappear as Knudsen number Kn exceeds 0.1. The stability of the vortex behind the step relies on the magnitudes of mean and thermal velocities in the region, which are closely related to the Kn number, local temperature, and driving pressure ratio. A highly intensified pressure and velocity region behind the step is identified in the transition flow regime. The mechanism leading to the significant increase of velocity and pressure is discussed. The effect of rarefaction on the surface shear stress and friction coefficient is also studied.     

Laminar forced convection slip-flow in a micro-annulus between two concentric cylinders

Forced convection heat transfer in hydrodynamically and thermally fully developed flows of viscous dissipating gases in annular microducts between two concentric micro cylinders is analyzed analytically. The viscous dissipation effect, the velocity slip and the temperature jump at the wall are taken into consideration. Two different cases of the thermal boundary conditions are considered: uniform heat flux at the outer wall and adiabatic inner wall (Case A) and uniform heat flux at the inner wall and adiabatic outer wall (Case B). Solutions for the velocity and temperature distributions and the Nusselt number are obtained for different values of the aspect ratio, the Knudsen number and the Brinkman number. The analytical results obtained are compared with those available in the literature and an excellent agreement is observed.     

Flow and heat transfer characteristics in pulsating pipe flows (effects of pulsation on internal heat transfer in a circular pipe flow)

Effects of pulsation on flow and heat transfer characteristics are experimentally examined in the pulsating pipe flows having sinusoidal velocity fluctuations around a nonzero mean. By systematically varying three pulsation parameters (the amplitude, frequency, and mean velocity), time-averaged and fluctuating temperature profiles are measured under the heating condition of constant wall temperature using saturated vapor. The mean Nusselt number, Nu_p, is calculated, and compared with that in ordinary turbulent pipe flows without pulsation. The results show that Nu_p, decreases initially as the pulsation amplitude increases, then recovers gradually, and finally becomes much greater than the original value. In pulsating pipe flows with a nonzero mean velocity, therefore, pulsation cannot always promote heat transfer, but sometimes suppresses it, depending mainly on the pulsation amplitude and mean velocity. It is also found that these heat transfer characteristics of a pulsating pipe flow are controlled by the transition of flow patterns with pulsation amplitude from a fully turbulent flow to a conditionally turbulent flow via a transitional flow. © 1997 Scripta Technica, Inc. Heat Trans Jpn Res, 25(5): 323–341, 1996     

Effects of entrance region transport processes on free convection slip flow in vertical microchannels with isothermally heated walls

Natural convection gaseous slip flows in vertical microchannels with isothermal wall conditions are numerically investigated, in order to analyze the influence of the entrance (developing) region on the overall heat transfer characteristics. A long channel aspect ratio is considered, so as to achieve both hydrodynamically and thermally fully developed conditions at the channel exit. In other words, the flow-field within the microchannel consists of both developing and fully developed regimes. A wide range of Rayleigh number is covered, so that the cases of very short and relatively large entrance lengths can be analyzed in the same unified mathematical framework. With first order velocity and temperature jump conditions at the microchannel walls, local and average Nusselt number values are computed, by invoking the Navier Stokes equation and the energy conservation equation. It is recognized that the micro-scale effects, being associated with the velocity slip and temperature jump conditions, exhibit enhancements in the rate of heat transfer, as compared to the similar macro-scale geometries. The relative enhancements in the average Nusselt number become more prominent for higher values of Knudsen number, whereas this augmentation effect is found to be somewhat arrested at higher values of Rayleigh number. Contrasting features in the heat transfer rate predictions with and without the considerations of the entrance region effects are also carefully noted.     

Forced convective heat transfer in a microtube including rarefaction,viscous dissipation and axial conduction effects

Subsonic gas convective heat transfer in a microtube with a constant cross-sectional area and uniform wall temperature is investigated both analytically and numerically. First, the effect of rarefaction on heat transfer characteristics, at a distance from the inlet where Nu becomes constant, is analytically investigated for two cases: (i) including and (ii) neglecting the viscous dissipation effect. An exact solution for Nu in fully developed flow is presented for the case without viscous dissipation, while a closed-form solution for the asymptotic Nu is also provided for the case with viscous dissipation. Next, a numerical model is employed to investigate the simultaneous effects of rarefaction, viscous dissipation, and axial conduction for developing hydrodynamic and temperature conditions. The Nusselt number is substantially affected by viscous dissipation, rarefaction and axial conduction.     

Wind Effect on Combined Convection and Surface Radiation Heat Losses of a Fully Open Cylindrical Cavity With Insulation

Wind effect, of both the wind incidence angle and the wind speed, on convection and surface radiation heat losses of a fully open cylindrical cavity with constant bottom wall temperature was numerically investigated. The impacts of cavity tilt angle and wall temperature were also considered. Temperature contours, velocity contours, and vectors inside and around the cavity were presented. The variations of average convection and radiation heat loss Nusselt numbers Nu_c and Nu_r and percentages of heat losses with related parameters (wind speed, wind incidence angle, tilt angle, and bottom wall temperature) were also shown. In the end, correlations about Nu_c and Nu_r for practical applications were proposed. Results show that compared with no-wind condition, Nu_c under a wind condition is almost always higher except for head-on wind with velocity of 1.5 m/s, while Nu_r is always lower. Nu_c varies slightly, while Nu_r increases rapidly as the bottom wall temperature increases. With the existence of wind, the effect of tilt angle on heat transfer becomes more complex. A critical wind direction close to 30° is detected, which maximizes Nu_c and percentage of convective heat loss. The results also demonstrate that wind speed, wind incidence angle, and tilt angle should be considered simultaneously when analyzing heat transfer inside the cavity under a wind condition.     

Thermally developing flow in elliptic ducts with axially variable wall temperature distribution

The laminar, incompressible, hydrodynamically fully developed and thermally developed and developing flow is studied in straight elliptic ducts with aspect ratio a^* varying from 0.25 to 0.99 (which is an almost circular duct). The duct wall is subjected successively to constant temperature, to circumferential uniform and axially linearly or exponentially varying temperature. Numerical results obtained with the ADI scheme indicate that the friction factor increases as aspect ratio a^* decreases. In the thermally developing flow a high Nusselt number decreases as a^* decreases. In the thermally developed limit as a^* decreases, the Nusselt number increases for small axial wall temperature distributions, while decreases for large axial wall temperature values.     

Numerical simulation of slip flow through rhombus microchannels

Microgeometry fluid dynamics has gotten a lot interest due to the arrival of Micro-Electro-Mechanical systems (MEMS). When the mean free path of a gas and characteristic length of the channel are in the same order, continuum assumption is no longer valid. In this situation velocity slip and temperature jump occur in the duct walls. Fully developed numerical analysis for characteristic laminar slip flow and heat transfer in rhombus microchannels are performed with slip velocity, and temperature-jump boundary condition at walls. The impacts of Reynolds number (0.1 < Re < 40), velocity slip, and temperature-jump on Poiseuille number, and Nusselt number for different aspect ratio (0.15 < A < 1.0), and Knudsen number are studied in detail. The contours of non-dimensional velocity for some cases are examined as well. The results show that aspect ratio and Knudsen number have important impact on Poiseuille number, and Nusselt number in rhombus microchannels. Reynolds number has considerable influence on Nusselt number at low Reynolds number, but its influence on Poiseuille number is not very important at the studied range.     

Numerical simulation of wall roughness on gaseous flow and heat transfer in a microchannel

A flow and heat transfer numerical simulation was performed for a 2D compressible gas flow through a microchannel in the slip regime to investigate the effects of wall roughness. The wall roughness is simulated by rectangular microelements. This effect is examined for gas flows under inlet Mach number ranging from 0.0055 to 0.202. The numerical results demonstrate that the roughness elements have a significant impact on the flow characteristics. For rarefied gases, it is found that roughness effect leads to an increase in the Poiseuille number with increasing roughness height and decreasing element spacing. The surface roughness has a more significant effect on the flow with a lower inlet Kn. Compressible gas flow is also sensitive to the height of the wall roughness elements. In addition, an increase of the relative roughness height leads to a pronounced decrease in the local heat flux for both rarefied and compressible flow. The average Nusselt numbers have a much more significant reduction for a rarefied flow than a compressible flow. The influence of wall roughness on the average heat transfer rate is smaller than that on the Poiseuille number.     

Heat transfer of rectangular narrow channel with two opposite scale-roughened walls

An experimental study of heat transfer and pressure drop in a rectangular channel roughened by scaled surfaces on two opposite walls with flows directed in the forward and downward directions for Reynolds numbers (Re) in the range of 1500 ⩽ Re ⩽ 15,000 was performed. Nusselt number ratios between the scale-roughened and smooth-walled ducted flows (Nu/Nu_∞) were in the range of 7.4–9.2 and 6.2–7.4 for laminar forward and downward flows respectively. The Nu/Nu_∞ values for turbulent developed flows in the scale-roughened channel with forward and downward flows were about 4.5 and 3 respectively. A comparison of present data with reported results using different types of surface roughness demonstrated the better thermal performances of present scale-roughened channel with forward flow at conditions of Re > 10,000. Experimental correlations of heat transfer and friction coefficient were derived for the present scale-roughened rectangular channel.     

Analysis of heat transfer in simultaneously developing pulsating laminar flow in a pipe with constant wall temperature

Numerical studies of flow and heat transfer in a circular tube under pulsating flow condition were carried out in the laminar regime. The flow at the inlet consists of a fixed part and a pulsating component, which varies sinusoidally in time. The flow was both thermally and hydrodynamically developing while the tube wall was kept at a uniform temperature. The solution of two-dimensional Navier–Stokes equation was performed using the SIMPLE algorithm with the momentum interpolation technique of Rhie and Chow. By analysing the data generated from the simulation, it is observed that in the range of present study (frequency: 0–20 Hz; amplitude: < 1.0), pulsation has no effect on time-averaged heat transfer, although the Nu distribution varies in time in the near-entry region of the pipe.