Constant Wall Temperature Boundary Condition Research Articles

Numerical study of hydrodynamic and heat transfer of nanofluid flow in microchannels containing micromixer

In this study heat transfer and fluid flow of Al2O3/water nanofluid in two dimensional parallel plate microchannel without and with micromixers have been investigated for nanoparticle volume fractions of ϕ=0,ϕ=4% and base fluid Reynolds numbers of Ref=5, 20, 50. One baffle on the bottom wall and another on the top wall work as a micromixer and heat transfer enhancement device. A single-phase finite difference FORTRAN code using Projection method has been written to solve governing equations with constant wall temperature boundary condition. The effect of various parameters such as nanoparticle volume fraction, base fluid Reynolds number, baffle distance, height and order of arrangement have been studied. Results showed that the presence of baffles and also increasing the Re number and nanoparticle volume fraction increase the local and averaged heat transfer and friction coefficients. Also, the effect of nanoparticle volume fraction on heat transfer coefficient is more than the friction coefficient in most of the cases. It was found that the main mechanism of enhancing heat transfer or mixing is the recirculation zones that are created behind the baffles. The size of these zones increases with Reynolds number and baffle height. The fluid pushing toward the wall by the opposed wall baffle and reattaching of separated flow are the locations of local maximum heat transfer and friction coefficients.

Slip flow effect on laminar convection inside micro-tubes with permeable walls

In this study, a two-dimensional steady state simultaneously developing laminar flow along a permeable micro-tube is investigated numerically under slip flow conditions. The constant wall temperature boundary condition and the case of uniform suction at the entire tube wall were considered. The set of governing equations subjected to the appropriate boundary conditions for the hydrodynamic and thermal fields was solved by using the Finite Volume Method. The numerical model was validated using the available data for developing and fully developed continuum flow. The results show that increasing the Knudsen number reduces the axial velocity of the tube center and increases the streamwise fluid velocity at the wall, inducing a flattening of the velocity profiles. This leads to a reduced friction coefficient compared to the continuum case. Furthermore, the study reveals a significant effect on the rarefaction on the hydrodynamic and thermal fields especially for high values of the suction Reynolds number, Rew. In fact, for values of Rew close to zero, the impact on the apparent friction coefficient and Nusselt number was found to be negligible and the behavior of both parameters along the duct remains unchanged compared with the case of Rew = 0 (impermeable tube). The variation of the fully developed Nusselt number with Prandtl number, Knudsen number, and suction Reynolds number is presented and analyzed.

Experimental and numerical study of turbulent flow and heat transfer inside hexagonal duct

Flow and heat transfer characteristics in transition and turbulent regions are studied experimentally and numerically in a horizontal smooth regular hexagonal duct under constant wall temperature boundary condition covering a range of Reynolds number from 2.3 × 103 to 52 × 103. Two types of k-omega (standard and shear stress transport (SST)) and three types of k-e (standard, renormalization (RNG), and realizable) turbulence model are employed for transition and turbulent regions, respectively. Both average and fully developed Darcy friction factor and Nusselt number are presented as a function of Reynolds number. It is seen that k-omega SST and k-e realizable turbulence models gave the best agreement with the experimental data in transition and turbulent regions, respectively. All the experimental results are correlated within an accuracy of ±13 % and ±7 % for Nusselt number and Darcy friction factor, respectively. Results obtained in this study are compared with circular duct results using hydraulic diameter.

Optimization of peripheral finned-tube evaporators using entropy generation minimization

The peripheral finned-tube (PFT) is a new geometry for enhanced air-side heat transfer under moisture condensate blockage (evaporators). It consists of individual hexagonal (peripheral) fin arrangements with radial fins whose bases are attached to the tubes and tips are interconnected with the peripheral fins. In this paper, experimentally validated semi-empirical models for the air-side heat transfer and pressure drop are combined with the entropy generation minimization theory to determine the optimal characteristics of PFT heat exchangers. The analysis is based on three independent parameters, i.e., porosity, equivalent particle diameter and particle-based Reynolds number. The total heat transfer rate is a fixed constraint. The optimal heat exchanger configurations, i.e., those in which the entropy generation number reaches a minimum, are calculated for constant heat flux and constant tube wall temperature boundary conditions. Performance evaluation criteria of fixed geometry, fixed face area and variable geometry were implemented. In all cases, it was possible to determine a combination of independent parameters that provided a minimum entropy generation rate.

Experimental study of forced convective heat transfer of nanofluids in a microchannel

The forced convective heat transfer for flow of water and aqueous nanofluids (containing colloidal suspension of silica nanoparticles) inside a microchannel was studied experimentally for the constant wall temperature boundary condition. Applications of nanofluids have been explored in the literature for cooling of micro-devices due to the anomalous enhancements in their thermo-physical properties as well as due to their lower susceptibility to clogging. The effect of flow rate on thermal performance of nanofluid is analyzed in this study. Variations of thermo-physical properties of the nanofluid samples were also measured. The experimental results show that heat transfer increases with flow rate for both water and nanofluid samples; however, for the nanofluid samples, heat transfer enhancements occur at lower flow rates and heat transfer degradation occurs at higher flow rates (compared to that of water). Electron microscopy of the heat-exchanging surface revealed that surface modification of the microchannel flow surface occurred due to nanoparticle precipitation from the nanofluid. Hence, the fouling of the microchannels by the nanofluid samples is believed to be responsible for the progressive degradation in the thermal performance, especially at higher flow rates. Hence, these results are observed to be consistent with previous experimental studies reported in the literature.

Bubble coalescence at constant wall temperatures during subcooled nucleate pool boiling

Bubble coalescence during subcooled nucleate pool boiling was investigated experimentally using constant wall temperature boundary conditions while the wall heat flux was measured at various locations to understand the effects of coalescence on the heat transfer. The effects of the subcooling on the coalesced bubble shape, size and departure time were also investigated. The observations showed that the coalesced bubble moved and oscillated on the heater surface with significant heat transfer variations prior to departure. The coalesced (or departure) bubble size and departure frequency decreased as the subcooling increased. The heat flux for boiling with coalescence fluctuated much more than for single bubble boiling with the heat flux fluctuations due to oscillations of the coalesced bubble on the heater surface resulting in frequent rewetting of the heated surfaces. In some cases, many additional small bubbles nucleated very near a larger bubble and then rapidly coalesced with the larger bubble which enhanced the overall heat transfer. The observations also showed coalescence with no increase in the heat transfer rate for very fast bubble coalescence such as would occur for large surface superheats as the boiling conditions approach CHF. A mechanistic model comparing the inertia and heat flux controlled bubble growth phases for inhomogeneous bubble growth shows that this coalescence without increased heat transfer corresponds to the inertial growth phase.

Rarefaction and dissipation effects on transport phenomena associated with an immiscible two-phase flow within a shaft-housing micro configuration

A parametric analytical study is performed to investigate the mechanism of fluid flow and heat transfer associated with an immiscible gas–liquid flow within a shaft-housing micro configuration. The incompressible Navier–Stokes–Fourier (NSF) equations in the cylindrical polar coordinate reference frame are employed, while simultaneous effects of viscous dissipation and rarefaction phenomenon are taken into account. Two different classical thermal boundary conditions, namely, the Uniform Heat Flux (UHF) and the Constant Wall Temperature (CWT) boundary conditions are considered. Throughout a combination of these boundary conditions three thermal case studies are constructed and then treated separately. Solutions for the velocity and temperature distributions for both liquid and gas phases of each thermal case are obtained. Employing these solutions, major quantities such as shear and temperature reductions at the shaft due to the gas layer and the Nusselt number pertained to the gas and liquid phases are evaluated. Effects of parameters such as the Knudsen and Brinkman numbers as well as the aspect ratio of the annuli on the aforementioned major variables are examined. The results indicate that introducing a gas layer into the micro domain always contributes to decreasing the shear stress at the shaft and consequently, reducing the torque required to initiate the flow, which is absolutely desirable. However, depending on the thermal case considered, this may be accompanied by serious thermal drawbacks like higher temperatures at the shaft surface. It is also found that increasing values of the Knudsen and Brinkman numbers may even deteriorate the situation.

Slip-Flow and Heat Transfer of a Non-Newtonian Nanofluid in a Microtube

The slip-flow and heat transfer of a non-Newtonian nanofluid in a microtube is theoretically studied. The power-law rheology is adopted to describe the non-Newtonian characteristics of the flow, in which the fluid consistency coefficient and the flow behavior index depend on the nanoparticle volume fraction. The velocity profile, volumetric flow rate and local Nusselt number are calculated for different values of nanoparticle volume fraction and slip length. The results show that the influence of nanoparticle volume fraction on the flow of the nanofluid depends on the pressure gradient, which is quite different from that of the Newtonian nanofluid. Increase of the nanoparticle volume fraction has the effect to impede the flow at a small pressure gradient, but it changes to facilitate the flow when the pressure gradient is large enough. This remarkable phenomenon is observed when the tube radius shrinks to micrometer scale. On the other hand, we find that increase of the slip length always results in larger flow rate of the nanofluid. Furthermore, the heat transfer rate of the nanofluid in the microtube can be enhanced due to the non-Newtonian rheology and slip boundary effects. The thermally fully developed heat transfer rate under constant wall temperature and constant heat flux boundary conditions is also compared.

BOUNDARY CONDITION EFFECTS ON NATURAL CONVECTION OF BINGHAM FLUIDS IN A SQUARE ENCLOSURE WITH DIFFERENTIALLY HEATED HORIZONTAL WALLS

Natural convection of Bingham fluids in square enclosures with differentially heated horizontal walls has been numerically analyzed for both constant wall temperature (CWT) and constant wall heat flux (CWHF) boundary conditions for different values of Bingham number Bn (i.e., nondimensional yield stress) for nominal Rayleigh and Prandtl numbers ranging from 10 to 10 and from 0.1 to 100, respectively. A semi-implicit pressure-based algorithm is used to solve the steady-state governing equations in the context of the finite-volume methodology in two dimensions. It has been found that the mean Nusselt number Nu increases with increasing Rayleigh number, but Nu is found to be smaller in Bingham fluids than in Newtonian fluids (for the same nominal values of Rayleigh and Prandtl numbers) due to augmented flow resistance in Bingham fluids. Moreover, Nu monotonically decreases with increasing Bingham number irrespective of the boundary condition. Bingham fluids exhibit nonmonotonic Prandtl number Pr dependence on Nu and a detailed physical explanation has been provided for this behavior. Although variation of Nu in response to changes in Rayleigh, Prandtl, and Bingham numbers remains qualitatively similar for both CWT and CWHF boundary conditions, Nu for the CWHF boundary condition for high values of Rayleigh number is found to be smaller than the value obtained for the corresponding CWT configuration for a given set of values of Prandtl and Bingham numbers. The physical reasons for the weaker convective effects in the CWHF boundary condition than in the CWT boundary condition, especially for high values of Rayleigh number, have been explained through a detailed scaling analysis. The scaling relations are used to propose correlations for Nu for both CWT and CWHF boundary conditions and the correlations are shown to capture Nu satisfactorily for the range of Rayleigh, Prandtl, and Bingham numbers considered in this analysis.

Effects of rarefaction, viscous dissipation and rotation mode on the first and second law analyses of rarefied gaseous slip flows confined between a rotating shaft and its concentric housing

A parametric analytical study is carried out to scrutinize the mechanism of fluid flow, heat transfer and entropy generation in a low-speed rarefied gaseous flow confined between a shaft and its concentric housing, i.e., the cylindrical Couette flow. In the first law analysis, closed form solutions for the radial temperature profiles are obtained by incorporating the calculated velocity distribution into the energy equation. The derivations for three thermal cases, which are founded on imposing different thermal conditions, namely, the Uniform Heat Flux (UHF) and the Constant Wall Temperature (CWT) boundary conditions, are presented. In the second law analysis, the contributions of thermal diffusion and fluid friction irreversibility to the total entropy generation in the micro domain are illustrated, and the relevant expressions for the Bejan number and the entropy generation number as well as the average entropy generation rate are derived. Finally, the variations of major variables with influential parameters such as the Knudsen number, the Brinkman number and rotation mode are investigated to elucidate the associated effects of rarefaction phenomenon, viscous dissipation and geometric condition on the characteristics of the flow.

The effect of temperature-dependent viscosity on entropy generation in curved square microchannel

The effect of temperature-dependent viscosity on the thermodynamic performance of the curved square microchannel in laminar flow is numerically investigated in terms of entropy generation. The classical Navier–Stokes equations and constant wall temperature boundary conditions are adopted; aniline and ethylene glycol are selected as the working fluids. The results show that the Nusselt number, heat transfer entropy generation number and frictional entropy generation number are less for the temperature-dependent viscosity than for the constant viscosity when aniline is heated. However, the opposite conclusions can be drawn when aniline is cooled. The total entropy generation number extrema exist for the cases of aniline heated and cooled. The differences between the results obtained with and without considering temperature-dependent viscosity is more obvious when aniline is cooled than when aniline is heated. The difference between the Brinkman numbers obtained with and without considering temperature-dependent viscosity grows as the mass flow rate increases when ethylene glycol is heated. The temperature-dependent effect on entropy generation is more pronounced for ethylene glycol than for aniline, since the former has larger viscosity than the latter.

Influences of boundary conditions on laminar natural convection in rectangular enclosures with differentially heated side walls

In this study, two-dimensional steady-state simulations of laminar natural convection of Newtonian fluids in rectangular enclosures with differentially heated side walls have been conducted. Two Prandtl numbers Pr=0.71 and 7.0 – typical values for air and water – and a range of different aspect ratios AR(=H/L where H is the enclosure depth and L is the enclosure width) ranging from 1/8 to 8 for constant heat flux boundary conditions are investigated for Rayleigh numbers in the range 104–106. To demonstrate the difference between the aspect ratio effects between the constant wall temperature and constant wall heat flux boundary conditions, simulations have also been carried out for the same range of numerical values of Rayleigh number for the constant wall temperature boundary condition. It is found that the mean Nusselt number Nu¯ increases with increasing values of Rayleigh number for both constant wall temperature and constant heat flux boundary conditions. The effects of aspect ratio AR have also been investigated in detail and it has been found that the effects of thermal convection (diffusion) strengthens (weakens) with increasing aspect ratio and vice versa, for a given set of nominal values of Rayleigh number and Prandtl number for both types of boundary conditions. In the case of constant wall temperature boundary condition, the mean Nusselt number increases up to a certain value of the aspect ratio ARmax but for AR>ARmax the mean Nusselt number starts to decrease with increasing AR. In contrast, the mean Nusselt number is found to increase monotonically with increasing AR for the constant wall heat flux boundary condition in the range of values of aspect ratio, Rayleigh number and Prandtl number considered in this study. Detailed physical explanations are provided for the observed phenomenon. Suitable correlations are proposed for the mean Nusselt number Nu¯ for both constant wall temperature and wall heat flux boundary conditions which are shown to satisfactorily capture the correct qualitative and quantitative behaviour of Nu¯ for the range of Rayleigh number and aspect ratio considered here.

Numerical analysis of laminar forced convection with temperature-dependent thermal conductivity of nanofluids and thermal dispersion

Nanofluids are promising heat transfer fluids due to their high thermal conductivity. In order to utilize nanofluids in practical applications, accurate prediction of forced convection heat transfer of nanofluids is necessary. In the first part of the present study, we consider the application of some classical correlations of forced convection heat transfer developed for the flow of pure fluids to the case of nanofluids by the use of nanofluid thermophysical properties. The results are compared with experimental data available in the literature, and it is shown that this approach underestimates the heat transfer enhancement. Furthermore, predictions of a recent correlation based on a thermal dispersion model are also examined, and good agreement with the experimental data is observed. The thermal dispersion model is further investigated through a single-phase, temperature-dependent thermal conductivity approach. Numerical analysis of hydrodynamically fully developed laminar forced convection of Al2O3(20 nm)/water nanofluid inside a circular tube under constant wall temperature and constant wall heat flux boundary conditions has been carried out. Results of the numerical solution are compared with the experimental data available in the literature. The results show that the single-phase assumption with temperature-dependent thermal conductivity and thermal dispersion is an accurate way of heat transfer enhancement analysis of nanofluids in convective heat transfer.

Turbulent convective heat transfer of nanofluids through a square channel

This paper reports the results of experimental investigation on the heat transfer performance of Al2O3/H2O and TiO2/H2O nanofluids through square channel with constant wall temperature boundary condition. The flow regime through channel is turbulent. The nanofluids used in this research are Al2O3/H2O and TiO2/H2O with different nanoparticle concentrations. Based on the results of the present investigation, for specific Peclet number, convective heat transfer coefficient and Nusselt number of nanofluids are higher than those of distilled water. The enhancement increases with increasing nanoparticle concentration. The results also reveal that the convective heat transfer coefficient for Al2O3/H2O nanofluid is relatively the same as that of TiO2/H2O nanofluid.

Two-dimensional computational fluid dynamics simulation of nitrogen and sulfur oxides emissions in a circulating fluidized bed combustor

Based on the previously established two-dimensional computational fluid dynamics (CFD) model which described processes of coal devolatilization, volatile combustion and char combustion in circulating fluidized bed (CFB) combustors, nitrogen and sulfur oxides emissions are numerically simulated and investigated in the present paper. First of all, a more accurate heat transfer model was established by applying energy conservation equations to gas and solid phases separately, rather than one conservation equation of the mixture enthalpy in our previous model. Interphase heat transfer mechanism was considered as well as bed-to-wall heat transfer. For the constant wall temperature boundary condition, proportional heat sinks were adopted in the furnace to compensate the missing heat transfer surfaces from 3-D cylinder riser to 2-D planar model. Results of temperature distributions agreed well with the experimental data. Secondly, processes related to nitrogen and sulfur oxides emissions are included. Results from our previous studies showed that, no NH 3 was detected during pyrolysis of this bituminous coal by TG-FTIR (Thermogravimetry coupled with Fourier Transform Infrared) analysis. So it was assumed that fuel N and S partially released to the volatile as HCN and SO 2, and partially retained in the char. HCN converted to NO and N 2O quickly through homogenous reactions. Char N and S converted to NO and SO 2 during char combustion. NO x was reduced to N 2 by char carbon or CO. SO 2 was retained by CaO calcined from CaCO 3. By converting reaction rate expressions to suitable forms for Eulerian–Eulerian modeling, sulfation reaction rates from two different literatures were compared. Performances of SO 2 emission were evaluated for conditions with/without considering sulfur self-retention. Distributions of gas components in the furnace were predicted and the outlet gas concentrations were validated by the experimental data. Distributions of certain reaction rates in the riser were also illustrated.

Experimental heat transfer of nanofluid through an annular duct

This paper is related to heat transfer performance of Al 2O 3/H 2O and TiO 2/H 2O nonofluids through an annular channel with constant wall temperature boundary condition under turbulent flow regime. The constant temperature is applied on the outer wall of the channel. Experimental investigation was done for a wide range of Al 2O 3 and TiO 2 nanoparticle concentrations and Reynolds number. Based on the experimental results, for specific Peclet number, Nusselt number of nanofluids is higher than that of the base fluid. The enhancement increases with increase of nanparticle concentration for both employed nanofluids. Based on the results of this investigation there is no significant difference on the heat transfer enhancement associated with two employed nanofluids.

Experimental Studies on Heat Transfer and Friction Factor Through Isothermal Square Duct with Twisted Tape Inserts

This work addresses Experimental investigations of heat transfer and friction factor characteristics in a concentric double pipe heat exchanger (square duct inner and circular tube outer) using full length twisted tapes of different twist ratios. The data were taken for Reynolds number well in the laminar region (Re =30-1100) with twisted tapes of twist ratios (y=2.66 and y=3.55). Experiments were carried out for constant wall temperature boundary condition using Ethylene glycol as working fluid; the results demonstrate that as twist ratio decreases, the twisted tape gives better heat transfer enhancement. Isothermal friction factors were found to be 6 to13 times the plain duct values. Mean Nusselt number for the twisted tapes are higher than those for the plain duct around 6.0 and 5.30 times for y=2.55 and y=3.66 respectively. The experimental result shows that Nusselt numbers are found to be 5.44 -7.49 and 2.46- 4.88 times the plain square duct forced convection values based on constant flow rate and constant pumping power criteria respectively, for y =2.66.

Numerical analysis of entropy generation in concentric curved annular ducts

The entropy generation has been numerically investigated in concentric curved annular square ducts under constant wall temperature boundary condition. The problem has been assumed to be steady, hydrodynamically and thermally fully developed and incompressible laminar flow with constant physical properties. The solutions of discretized equations for continuity, momentum and energy have been obtained by using an elliptic Fortran Program based on the SIMPLE algorithm. Solutions have been achieved for i) Dean numbers ranging from 3.6 to 207.1, ii) Annulus dimension ratios of 5.5, 3.8, 2.9 and 2.36, and iii) Prandtl number of 0.7. In this regard, local entropy generation as well as overall entropy generation in the whole flow field has been analyzed in detail. Moreover, the effects of Dean number and annulus dimension ratio on entropy generation arising from the friction and heat transfer have been investigated. Accordingly, it is concluded that the effect of volumetric entropy generation that is a result of fluid frictional irreversibility can be neglected as compared with volumetric entropy generation due to heat transfer irreversibility. As Dean number increases, the distribution of volumetric entropy generation coming out from the heat transfer irreversibility is formed by the temperature field, which is depending on the curvature.

Simple Models for Laminar Thermally Developing Slug Flow in Noncircular Ducts and Channels

Solutions to the classical Graetz slug flow problem (uniform velocity distribution) in noncircular ducts are examined. These solutions have applications where a constant uniform velocity distribution exists across a channel or duct. These are most often realized in the laminar flow of low Prandtl number liquids, such as liquid metals, and low Reynolds number flows through porous media. Expressions are developed for a number of applications using the asymptotic correlation method of Churchill and Usagi. These expressions vary depending on the definition used for the dimensionless heat transfer coefficient, in the case of constant wall temperature boundary condition (T), and the dimensionless wall temperature for the constant flux boundary conditions (H) and (H1). Finally, simple expressions are developed for predicting the thermal entrance length and fully developed flow Nu values for noncircular ducts.

Computation of heat transfer enhancement in a plate‐fin heat exchanger with triangular inserts and delta wing vortex generator

AbstractLongitudinal vortices disrupt the growth of the thermal boundary layer, thereby the vortex generators producing the longitudinal vortices are well known for the enhancement of heat transfer in compact heat exchangers. The present investigation determines the heat transfer characteristics with secondary flow analysis in plate fin triangular ducts with delta wing vortex generators. This geometrical configuration is investigated for various angles of attack of the wing i.e. 15°, 20°, 26° and 37° and Reynolds numbers 100 and 200. The constant wall temperature boundary condition is used. The solution of the complete Navier Stokes equation and the energy equation is carried out using the staggered grid arrangement. The performance of the combination of triangular secondary fins and delta wing with stamping on slant surfaces has also been studied. Copyright © 2009 John Wiley & Sons, Ltd.