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.     

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.     

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.     

Burnett simulation of gas flow and heat transfer in micro Poiseuille flow

The Burnett equations with slip boundary conditions are used to simulate the compressible gas flow and heat transfer in micro Poiseuille flow in the slip and transition flow regime. A relaxation method on Burnett terms is proposed in the present study and the thermal creep effect is considered. Convergent results at Knudsen number up to 0.4 are achieved and the results agree very well with experimental data. It is found that with the increase of Knudsen number, the Poiseuille number decreases while Nusselt number increases. The local Poiseuille number decreases along the whole channel while the local Nusselt number decreases rapidly first and then increases slowly afterwards.     

Numerical simulation of roughness effects on flow and heat transfer in microchannels at slip flow regime

A numerical simulation for studying fluid flow and heat transfer characteristics in microchannels at slip flow regime with consideration of slip and temperature jump is studied. The wall roughness is simulated in two cases with periodically distributed triangular microelements and random shaped micro peaks distributed on the wall surfaces. Various Knudsen numbers have used to investigate the effects of rarefaction. The numerical results have also checked with available theoretical and experimental relations and good agreements has achieved. It has been found that rarefaction has more significant effect on flow field in microchannels with higher relative roughness. The negative influence of roughness on fluid flow and heat transfer found to be the friction factor increment and Nusselt number reduction. In addition high influence of roughness distribution and shape has been shown by a comparison of Poiseuille and Nusselt numbers for tow different cases.     

An evaluation of secondary effects on microchannel frictional and convective heat transfer characteristics

The frictional and convective heat transfer characteristics of rarified flows in rectangular microchannels, with either isoflux or isothermal boundary conditions, are evaluated subject to second-order slip boundary conditions, creep flow, viscous dissipation, and axial conduction effects. Numerical results are obtained using a continuum based, three-dimensional, compressible, unsteady computational fluid dynamics algorithm with first- and second-order slip velocity and temperature jump boundary conditions applied to the momentum and energy equations, respectively. The results, reported in the form of Poiseuille and Nusselt numbers, are found to be significant functions of aspect ratio, Knudsen number, slip model parameters, Brinkman number, and Peclet number.     

Poiseuille Number Correlations for Gas Slip Flow in Micro-Tubes

Fundamental research in fluid flow characteristics in micro-tubes are required for designing microfluidic systems. In this study, Poiseuille number, the product of friction factor and Reynolds number (f · Re) for quasi-fully developed micro-tube flows, was obtained for slip flow regime. The numerical methodology was based on the Arbitrary-Lagrangian-Eulerian (ALE) method and the uncertainties of the results were assessed based on the grid convergence index (GCI). The numerical model was validated with the available experimental and numerical results. The compressible momentum and energy equations were solved for a wide range of Reynolds and Mach numbers with two thermal boundary conditions: constant wall temperature (CWT), and constant heat flux (CHF), respectively. The slip boundary conditions and their numerical implementation are appropriately documented. The tube diameter ranged from 3 to 10 μm and the tube aspect ratio was 200. The stagnation pressure was chosen in such a way that the exit Mach number ranged from 0.1–1.0. The outlet pressure was fixed at the atmospheric condition. It was found that for the case of compressible and slip flows, f · Re correlations are functions of the Mach and Knudsen numbers, and are different from the values obtained from the expression, 64/(1 + 8 Kn), available for the incompressible slip flow regime. The f · Re correlations obtained here are applicable to both no-slip and slip conditions, and for both incompressible and compressible flows. The results are in excellent agreement with the available experimental data.     

Slip-flow and heat transfer of gaseous flows in the entrance of a wavy microchannel

The present work investigates the developing fluid flow and heat transfer through a wavy microchannel with numerical methods. Governing equations including continuity, momentum and energy with the velocity slip and temperature jump conditions at the solid walls are discretized using the finite-volume method and solved by SIMPLE algorithm in curvilinear coordinate. The effects of creep flow and viscous dissipation are assumed. The numerical results are obtained for various Knudsen numbers. The results show that Knudsen number has declining effect on both the C_f.Re and Nusselt number on the undeveloped fluid flow. Significant viscous dissipation effects have been observed for large Knudsen number. Also, viscous dissipation causes a singular point in Nusselt profiles.     

Momentum and heat transfer from a square cylinder in power-law fluids

Numerical solutions are sought, using FLUENT, to the mass, momentum and thermal energy equations for the 2-D flow of power-law fluids over a cylinder of square cross-section. The major thrust of this work is to delineate the values of the Reynolds number denoting the onset of flow separation and the limits of the steady flow regime for both shear-thinning and shear-thickening type fluids. Extensive results are reported on streamline and vorticity contours over wide ranges of power-law index (0.2–1.4) corroborating the occurrence of these two transitions. Having established the limits of the steady flow regime, drag and Nusselt number results are obtained in this regime as functions of the Reynolds number (0.1–40), of Prandtl number (0.7–100) for highly shear-thinning fluids (power-law index < 0.5) thereby extending the range of currently available results to that encountered in practical applications. The Nusselt number shows positive dependence on both the Reynolds and Prandtl numbers. Also, shear-thinning characteristics can augment the rate of heat transfer by up to 100% under appropriate conditions.     

Heat transfer,pressure drop,and fluid flow patterns in yawed tube banks

Complementary heat transfer, pressure distribution, and flow visualization experiments were performed to investigate the effect of yaw on both staggered and in-line tube tanks. The heat transfer measurements were carried out on a row-by-row basis, and pressures were measured internal to the tube banks as well as upstream and downstream. Air was the heat transfer fluid. The visualization experiments revealed that yaw markedly affected the manner in which the flow impinged on the tubes of the in-line array, with a lesser effect of yaw on the flow field in the staggered array. At a given freestream Reynolds number, the Nusselt number generally decreased as the angle of yaw increased. The yaw effect was well correlated for the staggered array, but not so well for the in-line array because of the aforementioned flow field modifications. The in-line-array Nusselt numbers generally exceeded those for the staggered array, a trend which was accentuated at larger yaw. The pressure drop decreased with increasing yaw. In the present operating range, the in-line-array pressure drops were smaller than the corresponding staggered-array values.     

MIXED-CONVECTIVE COOLING OF AN ISOTHERMAL HOT SURFACE BY CONFINED SLOT JET IMPINGEMENT

The flow and heat transfer characteristics in the cooling of a heated surface by impinging slot jets have been investigated numerically. Computations are done for vertically downward-directed two-dimensional slot jets impinging on a hot isothermal surface at the bottom and confined by a parallel adiabatic surface on top. Some computations are also performed where the jet is vertically upward, with an impingement plate at the top. The principal objective of this study is to investigate the associated heat transfer process in the mixed-convective regime. The computed flow patterns and isotherms for various domain aspect ratios (4–10) and for a range of jet exit Reynolds numbers (100–500) and Richardson numbers (0–10) are analyzed to understand the mixed-convection heat transfer phenomena. The local and average Nusselt numbers and skin friction coefficients at the hot surface for various conditions are presented. It is observed that for a given domain aspect ratio and Richardson number, the average Nusselt number at the hot surface increases with increasing jet exit Reynolds number. On the other hand, for a given aspect ratio and Reynolds number, the average Nusselt number does not change significantly with Richardson number, indicating that the buoyancy effects are not very significant in the overall heat transfer process for the range of jet Reynolds number considered in this study. Also, for the same problem configuration, the average Nusselt number does not change significantly when the jet is moving upward or downward.     

Three-dimensional numerical simulation of the slip flow through triangular microchannels

Three-dimensional numerical analysis for fully developed incompressible fluid flow and heat transfer through triangular microchannels over the slip flow regime is simulated in this paper. In order to study the flow through the channel, the Navier–Stokes equations are solved in conjunction with slip/jump boundary conditions. The influences of Knudsen number (0.001 < Kn < 0.1), aspect ratio (0.2 < A < 4.5), and Reynolds number (1 < Re < 15) on the fluid flow and heat transfer characteristics are extensively investigated in the paper. The numerical results reveal that the rarefaction decreases the Poiseuille number, while its effect on the Nusselt number completely depends on the interaction between velocity slip and temperature jump. It is also found that the aspect ratio has an important role in the analysis, but the variation of Reynolds number is less remarkable.     

Heat Transfer and Pressure Drop Characteristics of Nanofluid Flows Inside Corrugated Tubes

An experimental investigation is carried out to study the heat transfer and pressure drop characteristics of multiwalled carbon nanotubes (MWCNTs)/heat transfer oil nanofluid flows inside horizontal corrugated tubes under uniform wall temperature condition. To provide the applied nanafluids, MWCNTs are dispersed in heat transfer oil with mass concentrations of 0.05, 0.1, and 0.2 wt%. The Reynolds number varies between 100 and 4,000. Three tubes with hydraulic diameters of 11.9, 13.2, and 15.5 mm are applied as the test section in the experimental setup. Tubes are corrugated four times on the cross section; that is, there are four different helices around the tube. Depths of the corrugations are chosen as 0.9, 1.1, and 1.3 mm, and pitch of corrugation is 14 mm. The acquired data confirm the increase of heat transfer rate as a result of utilizing nanofluids in comparison with the base fluid flow. However, corrugating the tubes decreases the heat transfer rate at low Reynolds numbers. The highest increase in heat transfer rate is observed for the Reynolds numbers for which the smooth tube is in the transition regime and the corrugated tube reaches the turbulent flow, that is, Reynolds number in the range of 1,000 to 3,000. Rough correlations are proposed to predict the Nusselt number and friction factor.     

Modeling of Navier–Stokes equations for high Knudsen number gas flows

The possibility of modeling the Navier–Stokes equations and together with the conventional second order slip boundary condition at high Knudsen numbers is explored in this paper by incorporating the Knudsen diffusion phenomenon in rarefied gases. An effective mean free path (MFP) model is augmented to the governing equation and the slip boundary condition, as gas transport properties can be related to the MFP. This simple modification is shown to implicitly take care of the complexities associated in the transitional flow regime, without necessitating dependency of the slip coefficients on the Knudsen number. Unique analytical model with fixed values of slip coefficients is proposed and rigorous comparisons with the experimental and simulation data for pressure driven and thermally driven rarefied gas flows support this conjecture. First and second order slip coefficients have been proposed as 1.1466 and 0.9756 for rectangular channels and 1.1466 and 0.14 for the capillaries, from the continuum to the transition flow regime. The current work is significant from the numerical simulation point of view because simulation tools are better developed for Navier–Stokes equations.     

HEAT AND FLUID FLOW ACROSS A SQUARE CYLINDER IN THE TWO-DIMENSIONAL LAMINAR FLOW REGIME

The flow structure and heat transfer characteristics of an isolated square cylinder in cross flow are investigated numerically for both steady and unsteady periodic laminar flow in the two-dimensional regime, for Reynolds numbers of 1 to 160 and a Prandtl number of 0.7. The effect of vortex shedding on the isotherm patterns and heat transfer from the cylinder is discussed. Heat transfer correlations between Nusselt number and Reynolds number are presented for uniform heat flux and constant cylinder temperature boundary conditions.     

Heat and fluid flow across a rotating cylinder dissipating uniform heat flux in 2D laminar flow regime

Free-stream flow and forced convection heat transfer across a rotating cylinder, dissipating uniform heat flux, are investigated numerically for Reynolds numbers of 20–160 and a Prandtl number of 0.7. The non-dimensional rotational velocity (α) is varied from 0 to 6. Finite volume based transient heatline formulation is proposed. For Re = 100, the reasons for the onset/suppression of vortex shedding at a critical rotational velocity is investigated using vorticity dynamics. At higher rotational velocity, the Nusselt number is almost independent of Reynolds number and thermal boundary conditions. Finally, a heat transfer correlation is proposed in the 2D laminar flow regime. Cylinder rotation is an efficient Nusselt number reduction or cylinder-surface temperature enhancement technique.     

Synthetic and Continuous Jets Impinging on a Circular Cylinder

Synthetic and continuous water jets impinging onto an electrically heated circular cylinder were experimentally investigated. The slot nozzle width was 0.36 mm, the cylinder diameter was 1.2 mm, and the cylinder-to-nozzle spacing related to the slot width was 5–21. Two optical methods were used: qualitative laser-induced fluorescence (LIF) visualization and laser Doppler vibrometry (LDV) measurements. Simultaneously with the optical experiments, the overall convective heat transfer from the circular cylinder was evaluated. The LDV quantified the velocity of the oscillating piezo-driven diaphragm at frequencies from 30 to 68 Hz. A majority of the study was performed at the near-resonant frequencies from 46 to 49 Hz. For all investigated jets, the Reynolds numbers based on the nozzle width ranged from 36 to 171. The LIF visualization revealed a dominant flow separation occurring on the windward cylinder side. This result is attributed to the effect of the miniscales, a relatively small ratio of the nozzle width to the cylinder diameter, and low Reynolds numbers. An increase in the Reynolds number changes the flow pattern from a steady jet-flow separation to a vortex shedding wake-flow regime. The heat transfer experiments were validated in a natural convection regime. An enhancement of the average Nusselt numbers by 4.2–6.2 times by means of the synthetic jets was quantified by comparison with the natural convection regime. A correlation for the average Nusselt number was proposed for both the continuous and synthetic jets.     

A numerical study of single-phase convective heat transfer in microtubes for slip flow

The steady-state convective heat transfer for laminar, two-dimensional, incompressible rarefied gas flow in the thermal entrance region of a tube under constant wall temperature, constant wall heat flux, and linear variation of wall temperature boundary conditions are investigated by the finite-volume finite difference scheme with slip flow and temperature jump conditions. Viscous heating is also included, and the solutions are compared with theoretical results where viscous heating has been neglected. For these three boundary conditions for a given Brinkman number, viscous effects are presented in the thermal entrance region along the channel. The effects of Knudsen and Brinkman numbers on Nusselt number are presented in graphical and tabular forms in the thermal entrance region and under fully developed conditions.     

Heat transfer from a nano-sphere with temperature and velocity discontinuities at the interface

A singular perturbation method has been used to derive a general equation for the rate of heat transfer from a sphere at low Knudsen number. The final expression includes both velocity slip and temperature slip at the interface and applies to a general Stokesian flow regime. The asymptotic analysis was carried up to the order Pe³ln(Pe). By choosing an expression for the drag multiplier, the derived expression for the Nusselt number may be applied to solid, fluid as well as porous spheres, which are special cases of the general solutions. Comparisons with known results for these special cases indicate the accuracy and wide range of applicability of the derived general expression. The inclusion of the temperature slip at the interface makes this equation applicable to particles, bubbles and drops of nanometer sizes, in the continuum or the slip-flow regime, that is for Knudsen number Kn < 0.1. Our results show that the velocity slip at the interface does not affect significantly the overall Nusselt number, Nu. However, the temperature slip affects the heat transfer significantly. If the temperature discontinuity becomes large, the sphere becomes almost adiabatic. This indicates that, if a temperature slip is possible at the interface of nanospheres, it must be taken into account by using the derived expression for Nu. Our results at the limit of Pe = 0 are compared very well with experimental results found in the literature.     

Experimental Study on Air Cooling Via a Multiport Mesochannel Cross-Flow Heat Exchanger

The air-side heat transfer and flow characteristics of cross-flow multiport slab mesochannel heat exchanger are investigated experimentally in this article. The multiport slab mesochannel heat exchanger consists of 15 finned aluminum slabs; each slab contains 68 flow channels of 1 mm circular diameter. The cold deionized water at a constant mass flow rate was forced to flow through the mesochannels, whereas the hot air at different velocities was allowed to pass through the finned passages of the heat exchanger core in cross-flow orientation. The heat transfer and fluid flow key parameters were examined in the region of the air-side Reynolds number in the range of 972–2758, with a constant water-side Reynolds number of 135. The effect of air-side Reynolds number on air-side Nusselt number was examined and a general correlation of Nusselt number with Reynolds number was obtained. The Nusselt number value was found to be higher in comparison with other research works for the corresponding Reynolds number range. The multiport mesochannel flat slab geometry has offered uniform temperature distribution into the core. This uniform temperature distribution leads to higher heat transfer over stand-alone inline flow tube bank.