Comparison between single-phase and two-phases CFD modeling of laminar forced convection flow of nanofluids in a circular tube under constant heat flux

In this article, forced convection heat transfer with laminar and developed flow for water-Al₂O₃ nanofluid inside a circular tube under constant heat flux from the wall was numerically investigated using computational fluid dynamics method. Both single and two-phase models are accomplished for either constant or temperature dependent properties. For this study nanofluids with size particles equal to 100 nm and particle concentrations of 1 and 4 wt% were used. It is observed that the nanoparticles when dispersed in base fluid such as water enhance the convective heat transfer coefficient. The Nusselt number and heat transfer coefficient of nanofluids were obtained for different nanoparticle concentrations and various Reynolds numbers. Heat transfer was enhanced by increasing the concentration of nanoparticles in nanofluid and Reynolds number. Also, a correlation based on the dimensionless numbers was obtained for the prediction the Nusselt number. The modeling results showed that the predicted values were in very good agreement with reference experimental data.     

Coupled FHD–MHD free convection of a hybrid nanoliquid in an inversed T-shaped enclosure occupied by partitioned porous media

The article treats the study on free convection of a hybrid nanoliquid confined within contrariwise T-shaped enclosure saturated by two porous media with different material and structure. Nanocomposite particles of multiwall carbon nanotubes–Fe₃O₄ are dispersed into water. Variable magnetic source located to the bottom wall has been analyzed in terms of heat transport performance and nanofluid motion behavior in the enclosure. The governing equations with boundary conditions formulated using the primitive dimensionless variables have been numerically worked out by the finite element technique. Impacts of the Hartmann number, magnetic number, Rayleigh number, ratio of thermal conductivity, porosity ratio, the Darcy number, and convective heat transfer coefficient at solid–nanofluid interface have been investigated. It has been found that low values of dimensionless convection parameter ratio at the border between solid and nanoliquid phases characterize high values of the nanofluid dimensionless convective heat transfer parameter. The average Nusselt number for the solid state has maximum value for high quantities of ratio of Darcy number and low values of dimensionless convection parameter ratio at the border between solid and nanoliquid phases.     

基于等效比热的MPCMs平板层流传热理论模型

采用边界层的能量积分方程法,基于等效比热模型,对微胶囊相变悬浮液(Microencapsulated Phase Change Materials slurry, MPCMs)的热边界层进行理论建模,推导出了MPCMs外掠平板换热加热等壁温边界条件层流工况下,包含斯蒂芬数的MPCMs的对流换热关联式,然后与数值模拟结果进行比较。结果表明,对流传热系数的解析解与数值模拟结果趋势上相一致,修正后的解析解与数值模拟结果高度吻合。     

Effects of Wall-Located Heat Barrier on Conjugate Conduction/Natural-Convection Heat Transfer and Fluid Flow in Enclosures

The effects of a heat barrier, located in the ceiling wall of an enclosure, on conjugate conduction/natural convection are investigated numerically. The vertical walls of the enclosure are differentially heated and the horizontal walls are adiabatic. Heatline technique is used to visualize heat transport. The variations of average Nusselt number, dimensionless heat transfer rate through the ceiling wall, and dimensionless overall heat transfer rate are studied. Calculations are performed for different Rayleigh numbers (10³ ≤ Ra ≤ 10⁶), thermal conductivity ratios (1 ≤ K ≤ 100), dimensionless locations of the heat barrier (0 < X _h  < 1),and two dimensionless ceiling wall thicknesses (D = 0.05 and D = 0.20). For high thermal conductivity ratio (K = 100), the heat barrier considerably reduces the dimensionless overall heat transfer rate. The effect of the heat barrier on dimensionless heat transfer rate through the enclosure increases as the Rayleigh number decreases. For low Rayleigh number (i.e., Ra = 10³), a location exists in the ceiling wall for which the dimensionless overall heat transfer rate is minimum.     

Coupled heat and mass transfer by natural convection adjacent to a permeable horizontal cylinder in a saturated porous medium

The heat and mass transfer characteristics of free convection about a permeable horizontal cylinder embedded in porous media under the coupled effects of thermal and mass diffusion are numerically analyzed. The surface of the horizontal cylinder is maintained at a uniform wall temperature and uniform wall concentration. The transformed governing equations are obtained and solved by Keller box method. Numerical results for the dimensionless temperature profiles, the dimensionless concentration profiles, the Nusselt number and the Sherwood number are presented. Increasing the buoyancy ratio N and the transpiration parameter f_w increases the Nusselt number and the Sherwood number. For thermally assisting flow, when Lewis number Le increases, the Nusselt (Sherwood) number decreases (increases). Whereas, for thermally opposing flow, both the Nusselt number and the Sherwood number increase with increasing the Lewis number.     

An analytical study of pulsating laminar heat convection in a circular tube with constant heat flux

Pulsating laminar convection heat transfer in a circular tube with constant wall heat flux is investigated analytically. The results show that both the temperature profile and the Nusselt number fluctuate periodically about the solution for steady laminar convection, with the fluctuation amplitude depending on the dimensionless pulsation frequency, ω*, the amplitude, γ, and the Prandtl number, Pr. It is also shown that pulsation has no effect on the time-average Nusselt numbers for pulsating convection heat transfer in a circular tube with constant wall heat flux.     

Laminar heat transfer and friction characteristics of microencapsulated phase change material slurry in a circular tube with twisted tape inserts

It is novel and better method that microencapsulated phase change material (MPCM) slurry and the tube with twisted tape inserts are adopted together to enhance convective heat transfer. In this paper, numerical analyses were carried out to study laminar heat transfer and friction characteristics of MPCM slurry in a circular tube with twisted tape inserts. It is found that the MPCM slurry in the tube with twisted tape insert leads to the best performance of convective heat transfer for the bigger apparent specific heat and the intensive swirl flow. Furthermore, the modified average Nusselt number increases with decreasing bulk Stefan number, twisted ratio and increasing Re, while the friction factor increases with increasing Re and decreasing twisted ratio. It is also found that the heat transfer enhanced efficiency increases with increasing Re and decreasing Ste_b, and the heat transfer enhancement effects of twisted tape for low Ste_b slurry are better than that for high Ste_b slurry. Moreover, the thermal-hydraulic performance ratios increase to a peak, then decrease gradually with increasing Re for different twist ratio. The performance ratio increases with decreasing the twist ratio only in a definite Re range, and the Re range decreases with decreasing twist ratio.     

Numerical Investigation of Unsteady Natural Convection in an Inclined Square Enclosure With Heat-Generating Porous Medium

The unsteady laminar natural convection in an inclined square enclosure with heat-generating porous medium whose heat varies by a cosine function is investigated by a thermal equilibrium model and the Brinkman–Darcy–Forchheimer model numerically, with the four cooled walls of closure as isothermal. The numerical code based on the finite-volume method has been validated by reference data before it was adopted. Influence of dimensionless frequency and inclination angle on heat transfer characteristics in a square enclosure, such as flow distribution, isotherm, averaged Nusselt number on each wall, and time-averaged Nusselt number, are discussed, with specified value for Rayleigh number = 10⁸, Darcy number = 10^?4, Prandtl number = 7, porosity = 0.4, and specific heat ratio = 1. It is found that when the internal heat source varies by cosine, the Nusselt numbers of the four walls oscillate with the same frequency as the internal heat source; however, phase difference occurs. Moreover, frequency has little impact on time-averaged Nusselt number of the four walls, which is different from the phenomenon discovered in natural convection with suitable periodic varying wall temperature boundary condition. Moreover, inclination angle plays an important role in the heat transfer characteristics of the walls studied.     

Natural Convection Heat Transfer in a Nanofluid Filled U-Shaped Enclosures: Numerical Investigations

In the present work, enhancement of convective heat transfer rate in three-dimensional U-shaped enclosures using nanofluids is numerically investigated. Two different types of nanoparticles, namely, Cu, and Al₂O₃, with pure water, are the considered single-phase nanofluids. Natural convection and geometric parameter effects on the averaged Nusselt numbers are investigated. Velocity vectors and isotherm fields for the Al₂O₃/H₂O nanofluid are presented at various Rayleigh numbers. The governing dimensionless equations are solved using the commercial finite-volume-based computational fluid dynamics code, FLUENT. Our results are consistent with previously published predictions. In particular, heat transfer enhancement is found to increase with increasing nanoparticles volume fractions, Rayleigh numbers, as well as cooled wall length extensions.     

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In this study, fully developed laminar flow and convective heat transfer in an internally finned tube heat exchanger are investigated numerically. The flow is assumed to be both hydrodynamically and thermally developed with uniform outside wall temperature. Parameters of the thickness, length, and number of fins and thermal conductivity ratio between fin and working fluid are varied to obtain the friction factor as well as Nusselt number. The results show that the heat transfer improves significantly if more fins are used; however, the pressure drop turns out to be large in this heat exchanger. In addition, it is found that the emergence of closed-loop isotherms between the areas of two neighboring fins leads to heat transfer enhancement in the internally finned tube. When the fin number is smaller than 14, there appears a maximum Nusselt number at about 0.8 of the dimensionless fin length. Finally, an experiment is conducted to verify the numerical results.     

Comparative Numerical Investigation on TiO2/Water Nanofluid Turbulent Flow by Implementation of Single Phase and Two Phase Approaches

In this article, turbulent TiO₂/water nanofluid flow and convective heat transfer in a horizontal tube is numerically investigated. Four computer codes were developed for each model (single phase, volume of fluid, mixture, and Eulerian) to simulate this problem. The Finite volume method is applied to solve the two-dimensional steady state governing equations. The results are compared with each other and an experimental work. A model with the most similar results to those of the experimental data and less amount of time for the CPU usage is chosen to develop two correlations for Nusselt number and friction factor based on dimensionless numbers.     

Heat transfer enhancement for combined convection flow of nanofluids in a vertical rectangular duct considering radiation effects

In this paper, combined convective heat transfer and nanofluids flow characteristics in a vertical rectangular duct are numerically investigated. This investigation covers Rayleigh numbers in the range of 2 × 10⁶ ≤ Ra ≤ 2 × 10⁷ and Reynolds numbers in the range of 200 ≤ Re ≤ 1000. Pure water and five different types of nanofluids such as Ag, Au, CuO, diamond, and SiO₂ with a volume fraction range of 0.5% ≤ φ ≤ 3% are used. The three‐dimensional steady, laminar flow, and heat transfer governing equations are solved using finite volume method (FVM). The effects of Rayleigh number, Reynolds number, nanofluids type, nanoparticle volume fraction of nano‐ fluids, and effect of radiation on the thermal and flow fields are examined. It is found that the heat transfer is enhanced using nanofluids by 47% when compared with water. The Nusselt number increases as the Reynolds number and Rayleigh number increase and aspect ratio decreases. A SiO₂ nanofluid has the highest Nusselt number and highest wall shear stress while the Au nanofluid has the lowest Nusselt number and lowest wall shear stress. The results also revealed that the wall shear stress increases as Reynolds number increases, aspect ratio decreases, and nanoparticle volume fraction increases. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20354     

Theoretical research of convective condensation heat transfer for mixture gas on a horizontal tube

The mechanism of convective condensation heat transfer of moist mixed gas across a horizontal tube was studied in this paper. The models referring to how the liquid film flows and the heat transfers on the tube are set up by combining modified film model and Nusselt condensation theory. The effects of Re number, wall temperature, and water vapor concentration on condensation heat transfer are discussed. Results predict that the film thickness profile on the tube is influenced greatly by vapor shear force on liquid film. Local Nusselt number depends remarkably on gas phase heat resistance, which is different from pure vapor and very similar to single‐phase gas. © 2007 Wiley Periodicals, Inc. Heat Trans Asian Res, 36(6): 324–333, 2007; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20169     

Thermal performance of various cross-sectioned rectangular minichannels with water-based phase change nano-suspensions

A numerical study is performed to investigate the influence of geometrical factors on the performance characteristics of a laminar thermally developing flow of phase change nano-suspensions in a rectangular minichannel considering axial wall conduction effects. The phase change material dispersed in the pure water is considered N-eicosane with the onset point of melting of 34.7°C, latent heat of fusion of 243 J/g, and particle size of 200 nm. The volume fractions of the phase change nano-suspensions are 2% and 10%, and the Reynolds number is in the range of 200 to 1500. To evaluate the influences of geometrical parameters on the cooling performance of the minichannel heat sinks, five minichannels are investigated, with aspect ratios (ration between channel height and width) AR_ch of 1, 1.25, and 1.5 and bottom wall thicknesses H_bw of 0.5, 1, and 1.5. The results reveal that the axial wall conduction significantly affects the heat transfer process of a flow in a minichannel at a low Reynolds number, and this effect is more remarkable with a shallower channel and a thicker bottom wall. Five performance indicators are used to systematically evaluate the heat transfer characteristics of the minichannels, including dimensionless heat flux at the bottom wall, temperature suppression, heat transfer effective ratio, heat dissipation of the extended wall, and figure of merit.     

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 study of developing laminar forced convection of a nanofluid in an annulus

Laminar forced convection of a nanofluid consisting of Al₂O₃ and water has been studied numerically. Two dimensional elliptical governing equations have been solved to investigate the hydrodynamics and thermal behaviors of the fluid flow throughout an annulus. Single phase approach is used for the nanofluid modeling. The velocity and temperature profiles are presented in the fully developed region. The axial evolution of temperature, convective heat transfer coefficient and the friction coefficient at the inner and outer walls' region are shown and discussed. It is shown that the dimensionless axial velocity profile does not significantly change with the nanoparticle volume fraction. But, the temperature profiles are affected by the nanoparticle concentration. In general convective heat transfer coefficient increases with nanoparticle concentration. However, when the order of magnitude of heating energy is much higher than the momentum energy the friction coefficient depends on the nanoparticle concentration. At higher Reynolds numbers for which the momentum energy increases, this dependency on the nanoparticle volume fraction decreases.     

Modeling of convective heat transfer of a nanofluid in the developing region of tube flow with computational fluid dynamics

In this article, convective heat transfer effect on the nanofluid flow in the developing region of a tube with constant heat flux was investigated using computational fluid dynamics (CFD). For this purpose, nanofluid containing Al₂O₃ and water as a liquid single phase with two average particle sizes of 45 and 150 nm and four particle concentrations of 1, 2, 4 and 6 wt.% were used. Effect of particle size on convective heat transfer coefficient was investigated in different Reynolds numbers (500 < Re < 2500) for various axial locations of tube. According to the modeling results, an equation was obtained for Nusselt number prediction using the dimensionless numbers. The results showed that the predicted data were in very good agreement with experimental data obtained from the literature. The maximum error was around 10%.     

An experimental study of heat transfer in oscillating flow through a channel filled with an aluminum foam

An experimental study has been conducted on the heat transfer of oscillating flow through a channel filled with aluminum foam subjected to a constant wall heat flux. The surface temperature distribution on the wall, velocity of flow through porous channel and pressure drop across the test section were measured. The characteristics of pressure drop, the effects of the dimensionless amplitude of displacement and dimensionless frequency of oscillating flow on heat transfer in porous channel were analyzed. The results revealed that the heat transfer in oscillating flow is significantly enhanced by employing porous media in a plate channel. The cycle-averaged local Nusselt number increases with both the kinetic Reynolds number Re_ω and the dimensionless amplitude of flow displacement A₀. The length-averaged Nusselt number is effectively increased by increasing the kinetic Reynolds number from 178 to 874 for A₀ = 3.1-4.1. Based on the experimental data, a correlation equation of the length-averaged Nusselt number with the dimensionless parameters of Re_ω and A₀ is obtained for a porous channel with L/D_h = 3.     

Correlations for Natural Convective Heat Transfer from Isothermal Surface of Octagonal and Hexagonal Shapes of Different Aspect Ratios

The effect of surface shape on laminar natural convective heat transfer from vertical isothermal hexagonal and octagonal flat plates embedded in a plane adiabatic surface, the adiabatic surface being in the same plane as the surface of the heated plate, has been numerically investigated. Results for the hexagonal and octagonal surface shapes with different aspect ratios have been obtained. It has been assumed that the fluid properties are constant except for the density change with temperature which gives rise to the buoyancy forces, this having been treated using the Boussinesq approach. The solution has been obtained by numerically solving the full three‐dimensional form of governing equations, these equations being written in dimensionless form. The solution was obtained using the commercial finite volume method based cfd code, FLUENT^©14.5. The solution has the surface shape, the Rayleigh number, the dimensionless plate width and the Prandtl number as parameters. Results have only been obtained for a Prandtl number of 0.7 for Rayleigh numbers between 10³ and 10⁸ for various surface shapes with width‐to‐height ratios between 0 and 0.6. The effect of these parameters on the mean Nusselt number has been studied and empirical correlation equations for the mean heat transfer rate have been derived.     

Conjugate Wall Conduction-Fluid Natural Convection in a Three-Dimensional Inclined Enclosure

Laminar conjugate conduction-natural convection heat transfer in a 3-D inclined cubic enclosure comprised of finite thickness conductive walls and central cavity is numerically investigated. The dimensionless governing equations describing the convective flow and wall heat conduction are solved by the high accuracy multidomain pseudospectral method. Computations are performed for different Rayleigh numbers (10³ ≤ Ra* ≤ 10⁶), thermal conductivity ratios (1 ≤ k ≤ 100), dimensionless wall thickness (0 ≤ s ≤ 0.25), and enclosure inclinations (?30° ≤ α ₁ ≤ 30°, 0° ≤ α ₂ ≤ 45°). The effects of the above controlling parameters on the heat transfer performances of the enclosure system are investigated in detail, with emphases on the variations of wall conduction and fluid convection heat transfer, and the interactive heat transfer conditions between solid walls and fluid in the central cavity. Numerical results reveal that the existence of enclosure walls reduces the temperature gradient across the cavity and alters the temperature distribution within the solid walls; thus, the fluid convection is complexly determined by the combined effects of k and s, and is greatly affected by enclosure inclinations at high Rayleigh numbers. Moreover, the temperature distributions and solid-fluid interactive heat transfer conditions are provided for further interpretation and demonstration of the effects of the solid walls.