Single-Phase Laminar Forced Convection in Microchannels With Rounded Corners

This work investigates the frictional and heat transfer behavior of laminar, fully developed flow in microchannels with trapezoidal and rectangular cross-section and rounded corners under boundary conditions of uniform heat flux along the channel length and perimeter and uniform temperature on the heated perimeter of each cross section. The equations of momentum and energy are solved numerically using the least square method, and the results are validated with analytical data, when available. The runs have been carried out for different aspect ratios and nondimensional radii of curvature, with either all sides or three sides heated, one short side adiabatic for rectangular geometries and three sides heated, the longest one adiabatic for trapezoidal geometries. The Poiseuille and Nusselt numbers are reported and show, for the rectangular cross-section heated on all sides, a maximum increase for the highest value of the aspect ratio with increments in the Poiseuille and Nusselt numbers of about 11% and 16%, respectively, for values of the nondimensional radius of curvature of 0.5, increasing as the geometry approaches the circular duct (12.5% and 21%). The increase is less pronounced as the aspect ratio decreases and also when only three sides are heated (maximum increase of the Nusselt number around 10% for the latter); in the case of trapezoidal geometry the effects of rounding the corners are almost negligible (a maximum increase in the Nusselt number of around 2%).     

An experimental study of convective heat transfer in silicon microchannels with different surface conditions

An experimental investigation has been performed on the laminar convective heat transfer and pressure drop of water in 13 different trapezoidal silicon microchannels. It is found that the values of Nusselt number and apparent friction constant depend greatly on different geometric parameters. The laminar Nusselt number and apparent friction constant increase with the increase of surface roughness and surface hydrophilic property. These increases become more obvious at larger Reynolds numbers. The experimental results also show that the Nusselt number increases almost linearly with the Reynolds number at low Reynolds numbers (Re<100), but increases slowly at a Reynolds number greater than 100. Based on 168 experimental data points, dimensionless correlations for the Nusselt number and the apparent friction constant are obtained for the flow of water in trapezoidal microchannels having different geometric parameters, surface roughnesses and surface hydrophilic properties. Finally, an evaluation of heat flux per pumping power and per temperature difference is given for the microchannels used in this experiment.     

Choked flow and heat transfer of low density gas in a narrow parallel-plate channel with uniformly heating walls

The discharge and heat transfer characteristics of the continuum and slip choked gas flows through a narrow parallel-plate channel with uniform heat flux walls are studied by experimental means, numerical simulation, and analytical approximate solution. The numerical results of the discharge coefficient and the wall surface temperature distributions agree relatively well with the experimental results. The effects of the heat transfer at the walls on the discharge coefficient can be correlated with the dimensionless heat input at the walls. Three kinds of Nusselt numbers which are defined by adiabatic wall, bulk mean, and total temperatures as a reference temperature, respectively, are proposed and the effects of the viscous heating on these Nusselt numbers are clarified.     

Averaging approach for microchannel heat sinks subject to the uniform wall temperature condition

The present paper is devoted to modeling methods for thermal analysis of microchannel heat sinks. The averaging approach presented in earlier works for the case of constant surface heat flux is extended to the problems subject to the uniform wall temperature condition. The solutions for velocity and temperature distributions are obtained by solving one-dimensional averaged governing equations without resorting to a two-dimensional direct numerical simulation. General solutions for both high-aspect-ratio and low-aspect-ratio microchannel heat sinks are presented. Asymptotic solutions in high-aspect-ratio and low-aspect-ratio limits are also given in explicit form. The solutions presented in the paper are validated by comparing them with the results of direct numerical simulation. The friction factors, Nusselt numbers and thermal resistances for microchannel heat sinks with a uniform base temperature are obtained from the presented solutions. The effects of the aspect ratio and the porosity on the friction factor and the Nusselt number are presented. Finally, characteristics of the thermal resistance of the microchannel heat sink are discussed.     

Laminar Forced Flow and Heat Transfer in Cross-Corrugated Triangular Ducts

The fluid flow and heat transfer characteristics in a cross-corrugated triangular channel are studied under laminar forced flow and uniform wall temperature conditions. Both the local and the periodic mean values of friction factor and wall Nusselt numbers in the hydro and thermally developing entrance region are investigated. It is found that at higher Reynolds numbers, recirculations in the lower wall valleys are a dominant factor for flow and heat transfer, while at lower Reynolds numbers, parallel flows in the upper wall corrugation are the predominant factor. Compared with a parallel flat plates duct, the Nusselt numbers in a cross-corrugated triangular duct can be enhanced, and can be even higher at higher Reynolds numbers. The growth of steady recirculations and the concomitant periodic disruption and thinning of the boundary layer promote enhanced transport of heat as well as momentum. Effects of heat transfer enhancement are more obvious under higher Reynolds numbers. Two correlations are proposed to predict the periodic mean values of Nusselt numbers and friction factors for Reynolds numbers from 10 to 2000.     

Micro-scale thermo-fluidic transport in two immiscible liquid layers subject to combined electroosmotic and pressure-driven transport

A theoretical analysis is presented for fully developed convective heat transfer in two immiscible fluid layers confined within parallel plate microchannels subject to combined effects of axial pressure gradients and imposed electrical fields. Assuming desperate zeta potentials at the interfaces thus formed, closed-form expressions are derived for the velocity and temperature distributions under fully developed conditions, with uniform wall heat flux boundary conditions. For the heat transfer analysis, the viscous dissipation effects are neglected as compared to the Joule heating effects. Results are subsequently obtained for different ranges of the ratios of various electrical properties of the two fluid layers and various relative strengths of the ratios of the electrical fields and the imposed pressure gradients. These results demonstrate the effects of the applied electric fields and pressure gradients, presence of external heat source or sink and interfacial positions on the temperature distributions in the two layers and the corresponding Nusselt numbers.     

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.     

Analysis of flow and heat transfer inside oscillatory squeezed thin films subject to a varying clearance

The flow and heat transfer inside a non-isothermal and incompressible thin film having its upper plate slightly inclined from the horizontal and undergoing an oscillatory squeezing motion is investigated in this work. Two models are analyzed: low and large Reynolds number flow models. The corresponding governing equations for each model are properly non-dimensionalized and solved numerically. The main controlling parameters for the dynamic and thermal behavior of the inclined thin film are found to be the amplitude of the upper plate motion, squeezing Reynolds number, squeezing number, thermal squeezing parameter and the dimensionless slope of the upper plate. It is found that fluctuations in the axial and normal velocities are greater for convergent thin films than for divergent thin films. Furthermore, Nusselt numbers and their amplitudes are found to decrease with an increase in the dimensionless slope of the upper plate. Finally correlations are obtained for Nusselt numbers and their corresponding amplitudes for two different thermal conditions: constant wall temperature and uniform wall heat flux.     

Influences of Boundary Condition on Laminar Natural Convection of Bingham Fluids in Square Cross-Sectioned Cylindrical Annular Enclosures with Differentially Heated Vertical Walls

Numerical simulations have been carried out to analyze steady-state laminar natural convection of yield stress fluids obeying Bingham model in square cross-sectioned cylindrical annular enclosures with differentially heated vertical walls for both constant wall temperature and constant wall heat flux boundary conditions for active walls. The simulations have been performed under the assumption of axisymmetry for a nominal Rayleigh number range of 10³ to 10⁶ and nominal Prandtl number range of 10 to 10³ for different ratio of internal cylinder radius to cylinder height range of 0.125 to 16. The mean Nusselt number on the inner periphery for the constant wall heat flux configuration has been found to be smaller than that in the case of constant wall temperature configuration for a given set of values of nominal Rayleigh and Prandtl numbers for both Newtonian and Bingham fluid cases. The mean Nusselt number normalized by the corresponding value obtained for pure conductive transport increases with increasing internal radius before approaching the corresponding mean Nusselt number for square enclosures regardless of the boundary conditions. Detailed physical explanations have been provided for the effects of the aforementioned parameters on the mean Nusselt number on the inner periphery. Finally, the new Nusselt number correlations have been proposed for laminar natural convection of both Newtonian and Bingham fluids in square cross-sectioned cylindrical annular enclosures for both constant wall temperature and constant wall heat flux boundary conditions.     

Viscous dissipation effects on the asymptotic behaviour of laminar forced convection for Bingham plastics in circular ducts

The present study concentrates on the effects of viscous dissipation and the yield shear stress on the asymptotic behaviour of the laminar forced convection in a circular duct for a Bingham fluid. It is supposed that the physical properties are constant and the axial conduction is negligible. The asymptotic temperature profile and the asymptotic Nusselt number are determined for various axial distributions of wall heat flux which yield a thermally developed region. It is shown that if the asymptotic value of wall heat flux distribution is vanishes, the asymptotic value of the Nusselt number is zero. The case of the asymptotic wall heat flux distribution non-vanishing giving a value of the Nusselt number dependent on the Brinkman number and on the dimensionless radius of the plug flow region was also analysed. For an infinite asymptotic value of wall heat flux distributions, the asymptotic value of the Nusselt number depends on the dimensionless radius of the plug flow region and on the dimensionless parameter which depends on the asymptotic behaviour of the wall heat flux. The condition of uniform wall temperature and convection with an external isothermal fluid were also considered. The comparison with other existing solutions in the literature in the Newtonian case is analysed.     

Experimental investigation of forced and mixed convection heat transfer in a foam-filled horizontal rectangular channel

An experimental study was performed to investigate the heat transfer characteristics of the mixed convection flow through a horizontal rectangular channel where open-cell metal foams of different pore densities (10, 20 and 30 PPI) were situated. A uniform heat flux was applied at all of the bounding walls of the channel. For each of three values of the uniform heat flux, temperatures were measured on the entire surfaces of the walls. Results for the average and local Nusselt numbers are presented as functions of the Reynolds and Richardson numbers. The Reynolds number based on the channel height of the rectangular channel was varied from 600 to 33000, while the Richardson number ranged from 0.02 to 103, extending over forced, mixed and natural convection. Second important parameter that influences the heat transfer is the aspect ratio of the foams. Three different aspect ratios (AR) as 0.25, 0.5 and 1 are tested. Based on the experimental data, new empirical correlations have been constructed to link the Nusselt number. The results of all cases were compared to that of the empty channel and the literature. We found that our results were in agreement with those that are mentioned in the literature.     

An analytical solution for thermally fully developed combined pressure – electroosmotically driven flow in microchannels

An analytical solution is presented to study the heat transfer characteristics of the combined pressure – electroosmotically driven flow in planar microchannels. The physical model includes the Joule heating effect to predict the convective heat transfer coefficient in two dimensional microchannels. The velocity field, which is a function of external electrical field, electroosmotic mobility, fluid viscosity and the pressure gradient, is obtained by solving the hydrodynamically fully-developed laminar Navier–Stokes equations considering the electrokinetic body force for low wall zeta potentials. Then, assuming a thermally fully-developed flow, the temperature distribution and the Nusselt number is obtained for a constant wall heat flux boundary condition. The fully-developed temperature profile and the Nusselt number depend on velocity field, channel height, solid/liquid interface properties and the imposed wall heat flux. A parametric study is presented to evaluate the significance of various parameters and in each case, the maximum heat transfer rate is obtained.     

Natural convection measurements in a mercury-filled rectangular plenum

Experiments have been carried out using a rectangular plenum containing mercury, heated at the roof and one wall and cooled at the floor. The interaction between the internal stratification and the natural convection at the wall of the plenum has been measured for several different boundary conditions. Nusselt numbers at the plenum floor, when a uniform wall heat flux was applied, were found to be nearly 2; whereas a value of approximately 5 was observed for the uniform wall temperature case, indicating strong internal convection. The results confirm earlier water tests which showed strong unidimensional behaviour of the plenum temperature. Measured Nusselt numbers were found to agree well with predictions from a 1-D analysis.     

Laminar Flow and Heat Transfer to a Non-Newtonian Fluid in an Entrance Region of a Square Duct with Prescribed Constant Axial Wall Heat Flux

Abstract

Forced-convection heat transfer information as a function of the pertinent nondimensional numbers is obtained numerically for laminar incompressible non-Newtonian fluid flow in the entrance region of a square duct with simultaneously developing temperature and velocity profiles for constant axial wall heat flux with uniform peripheral wall temperature. The power-law model characterizes the non-Newtonian behavior.

Finite-difference representations are developed for the equations of the mathematical model, and numerical solutions are obtained assuming uniform inlet velocity and temperature distributions. Results are presented for local and mean Nusselt numbers as functions of the Graetz number and the Prandtl number in the entrance region. Comparisons are made with previous analytical work for Newtonian fluids. The results show a strong effect of the Prandtl number on the Nusselt numbers with fully developed and uniform velocity profiles representing the lower and upper limits, respectively. The results provide a new insight into the true three-dimensional character of the pseudoplastlc fluid flow in the entrance region of a square duct and are accurate.     

The development of laminar natural-convective flow in a vertical uniform heat flux duct

An account of a theoretical and experimental study of laminar natural-convective flow in heated vertical ducts is presented. The ducts are open-ended and circular in cross-section and their internal surfaces dissipate heat uniformly.

Temperature and velocity fields and the relationship between Nusselt and Rayleigh numbers were obtained by solving the governing equations by a step-by-step numerical technique. Two Rayleigh numbers are introduced, one expressed in terms of the uniform heat flux and the other in terms of the mean wall temperature. The influence that the Prandtl number has on the relationship between the Nusselt and Rayleigh numbers is discussed. Three inlet conditions were examined; they all gave the same Nusselt relationship at small Rayleigh numbers and the differences between the Nusselt relationships obtained at large Rayleigh numbers were only small.

Experimentally determined Nusselt numbers, with air as the convected fluid, agreed satisfactorily with the theoretical relationship.     

Heat Flux Correlation for Spray Cooling in the Nonboiling Regime

An experimental facility was developed to investigate the nonboiling heat transfer performance of water spray cooling. The effects of mass flux and wall temperature on heat transfer coefficient and heat flux were experimentally studied. It was found that heat transfer coefficient increased with the increasing of mass flux and wall temperature. Generalized correlations were developed for the Nusselt number related to wall temperature and the average Nusselt number as a function of the spray Reynolds number and the nondimensional temperature with an absolute error of 4% and 15% when the Reynolds number is more than 440. Compared with the data of Oliphant et al., it was observed that the usage field of the correlations could be extended to Reynolds number greater than 240.     

Thermal Design of Uniformly Heated Inclined Channels in Natural Convection with and without Radiative Effects

Dimensional charts for the design of inclined single channels in air natural convection with symmetrical and asymmetrical uniform wall heat flux are proposed on the basis of correlations between the significant dimensionless process parameters derived from previous articles. The radiative contribution to heat transfer is taken into account. The design charts are obtained for two values of surface emissivity, 0.05 and 0.8, and the thermophysical properties are evaluated at the reference temperature equal to 40 ° C. The optimal spacing value for inclined single channels, in terms of thermal performance, is obtained from composite correlations between average Nusselt and Rayleigh numbers as functions of the angle. The estimated values of optimal spacing for vertical single channels correspond well with the results obtained by Bar-Cohen and Rohsenow [14]. A simple estimation procedure is proposed to evaluate the error in the relevant geometric and thermal parameters due to a different value of the reference temperature. The estimated error, however, is less than the uncertainty of the experimental data employed. Worked examples are carried out in order to show how simple and quick it is to use the proposed graphical procedure.     

Fully developed laminar flow and heat transfer in smooth trapezoidal microchannel

Numerical analysis of fully developed laminar slip flow and heat transfer in trapezoidal micro-channels has been studied with uniform wall heat flux boundary conditions. Through coordinate transformation, the governing equations are transformed from physical plane to computational domain, and the resulting equations are solved by a finite-difference scheme. The influences of velocity slip and temperature jump on friction coefficient and Nusselt number are investigated in detail. The calculation also shows that the aspect ratio and base angle have significant effect on flow and heat transfer in trapezoidal micro-channel.     

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.     

Convective heat transfer for laminar flows in a multi-passage circular pipe subjected to an external uniform heat flux

Convective heat transfer properties of an hydrodynamically and thermally fully-developed flow in a multi-passage circular tube subjected to an external uniform heat flux are analyzed. The significant dimensionless parameters affecting the problem have been determined. The expressions of Nusselt numbers on the inner and the outer wall are obtained. The limiting cases are correlated with the existing values. The representative curves illustrating the variation of Nusselt numbers with the pertinent parameters are plotted.