Thermal driven flows inside a square enclosure saturated with nanofluids: Convection heat functions and transfer rate revisions from a homogenous model

Abstract

In former theoretical researches of nanofluid flows, numerical investigations could not agree with experimental observations, particularly regarding whether the mixing nanoparticles will enhance or deteriorate the heat transfer. In the present work, thermal driven buoyancy flows of nanofluids in a square enclosure were modeled by the use of homogeneous assumptions and the effective kinematic viscosity and thermal conductivity formulas. Thoroughly developed heat transfer coefficient is subsequently proposed, aiming to critically evaluate the performance of nanofluid heat transport. Numerical results are presented over a wide range of thermal Rayleigh number (10³ ≤ Ra ≤ 10⁶) and nanoparticles volume fraction (0.001 ≤ φ?≤?0.04). Present modeling results accurately predict both the enhancement and deterioration of the natural convection heat transfer, fully validated by former experimental observations. Overall, mathematical models and Nusselt number definitions proposed in the present work effectively enhance the reliability of numerical modeling researches on the nanofluid heat transfer. Present clarification research on the Nusselt unifications could benefit future development of thermal carrier fluid enhanced by nano-particles.     

Toward the heat convection enhancement of nanofluids flowing in a 3D microchannel affected by a nonuniform magnetic field

In the present investigation, the behavior of laminar convective flow and heat transfer in a three-dimensional horizontal square duct using different water-based nanofluids (Fe₃O₄/water, and carbon nanotubes/water) is numerically investigated. The channel is subjected to a periodic partial or full magnetic field. The outer surface is subjected to a constant heat flux density. The problem is numerically solved via the finite volume method with a second-order precision. The numerical simulations covered a range of the Reynolds number 50 ≤ Re ≤ 400, Hartmann number 0 ≤ Ha ≤ 50, and concentration of nanoparticles 0 ≤ ϕ ≤ 0.02 for different modes of the magnetic field application and direction. Examination of the hydrodynamic and thermal behavior shows significant heat transfer performances obtained when applying transversal and partial periodic magnetic fields simultaneously. More precisely, it is found that the favorable protocol improved the heat transfer rate by 85% in the duct flowing by the Ferrofluid at Ha = 50. Furthermore, findings illustrate that the overall heat transfer rate presented in terms of the mean Nusselt number and the highest compromise (heat transfer augmentation-pressure losses diminution) are obtained in the case of Fe₃O₄ nanoparticles for all taken values of Reynolds and Hartmann numbers, whatever the manner and direction of the applied magnetic field.     

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     

Numerical Investigation of Double Diffusive Mixed Convection Laminar Flow in Two Sided Lid Driven Porous Cavity

This paper presents the numerical study of mixed convection in a two‐sided lid driven porous cavity due to temperature and concentration gradients. The top and bottom walls are stationary and insulated. The left and right walls are moving at an equal velocity (V_o) in the same direction. The temperature and concentration are kept high at the right wall and low at the left wall. The governing equations are discretized using finite volume method. The pressure–velocity coupling is performed by the SIMPLE algorithm. A third order differed QUICK scheme is applied at the inner nodes and a second order central difference scheme is used at the boundary nodes. The flow behavior and heat transfer are analyzed for different nondimensional numbers, such as, 1 × 10^?4 ≤ Ri ≤ 10, 1 × 10^?4 ≤ Da ≤ 0.1 and 0.7 < Pr < 10. The present numerical results are compared with the literature and are in good agreement. For the above selected nondimensional numbers, the heat and fluid flow behavior is investigated using local and average Nusselt (Nu) and Sherwood (Sh) numbers. Results show that the convection flow is significant up to Da = 0.1, beyond that the effect of porosity is negligible. The effect of Prandtl number (Pr) on average Nu is found to increase significantly.     

A numerical investigation of the effect of sinusoidal temperature on mixed convection flow in a cavity filled with a nanofluid with moving vertical walls

The aim of this study is to investigate numerically the effect of sinusoidal temperature on mixed convection flow in a cavity filled with nanofluid and moving vertical walls by using a new temperature function, where thermal heating takes the form of the sinusoidal temperature; and could be found in various natural processes and industries such as solar energy, and cooling of electronic components. The heating is concentrated in the center and then distributed to both ends at different values of Rayleigh numbers, Reynolds numbers, and volumetric fractions of nanoparticles ranging from 1.47 × 10³ to 1.47 × 10⁶, 1 to 100, and 0 to 0.1, respectively. The impact of nanoparticle size on thermal characteristics and hydrodynamics was considered and evaluated. From the results, the volume fraction concentration of nanoparticles affects the flow shape and thermal performance in the case of a constant Reynolds number. Moreover, the effect of nanoparticles decreases with the increase of the Reynolds number. Besides this, with increasing the volume percentage of nanoparticles, the rate of heat transmission increases. It is worth noting that the presence of nanoparticles results in height convective heat transfer coefficient. On the other hand, the thickness of thermal boundary layers decreases with increasing Rayleigh number. The current investigation found that the (sinusoidal) temperature change significantly affects heat transfer.     

Toward the thermohydrodynamic behavior of a nanofluid containing C-MWCNTs flowing through a 3D annulus channel under constant imposed heat flux

The heat transport and friction factor in a three-dimensional horizontal concentric annular duct filled with nanofluids comprising clove-treated multiwalled carbon nanotubes are investigated numerically in this paper. The cylinder's outer surface is thermally insulated, while uniform heat flux is imposed on the cylinder's inner surface. The problem is formulated in dimensionless cylindrical coordinates. The numerical solutions were obtained based on the finite volume technique with second-order precision, and cover a range of the Reynolds number 1000 ≤ Re ≤ 2000 and nanoparticle weight fractions 0.075, 0.125, and 0.175 wt%. To describe the results for both heat exchange and fluid flow performance, the temperature profile, Nusselt number, heat transfer coefficient, and friction factor are represented. The findings state that heat transport increases as Reynolds is increased and nanoparticles are introduced. The friction factor was also observed to improve as the concentration of nanoparticles increased. In addition, two new Nusselt number and friction factor correlations were established.     

Numerical analysis of Grashof number,Reynolds number and inclination effects on mixed convection heat transfer in rectangular channels

Mixed convection heat transfer in rectangular channels has been investigated computationally under various operating conditions. The lower surface of the channel is subjected to a uniform heat flux, sidewalls are insulated and adiabatic, and the upper surface is exposed to the surrounding fluid. Solutions were obtained for Pr=0.7, inclination angles 0° ≤ θ ≤ 90°, Reynolds numbers 50 ≤ Re ≤ 1000, and modified Grashof numbers Gr = 7.0×10⁵ to 4.0×10⁶. The three-dimensional elliptic governing equations were solved using a finite volume based computational fluid dynamics (CFD) code. From a parametric study, local Nusselt number distributions were obtained and effects of channel inclination, surface heat flux and Reynolds number on the onset of instability were investigated. Results obtained from the simulations are compared with the literature and a parallel conducted experimental study, from which a good agreement was observed. The onset of instability was found to move upstream for increasing Grashof number. On the other hand, onset of instability was delayed for increasing Reynolds number and increasing inclination angle.     

Thermal Performance Improvement of Tractor Radiator Using CuO/Water Nanofluid

This research work discusses the heat transfer improvement in a tractor radiator with nanosized particles of CuO with water as base fluid. The nano materials and its suspension in fluids as particles have been the subject of intensive study worldwide recently since pioneering researchers recently discovered the anomalous thermal behavior of these fluids. The engine cooling in heavy vehicles is an important factor for their performance in the intended application. Here, the tractor engine radiator cooling is enhanced by the nanofluid mechanism of heat transfer for its improved performance in agricultural work. Through the improvement of tractor engine cooling through the radiator a greater area can be ploughed and cultivated within a short time span. Heat transfer in automobiles is achieved through radiators. In this research work an experimental and numerical investigation for the improved heat transfer characteristics of a radiator using CuO/water nanofluid for 0.025 and 0.05% volume fraction is done with an inlet temp of 50 °C to 60 °C under the turbulent flow regime (8000 ≤ Re ≤ 25000). The overall heat transfer coefficient decreases with an increase in nanofluid inlet temperature of 50 °C to 60°C. The experimental results of the heat transfer using the CuO nanofluid is compared with the numerical values. The results in this work suggest that the best heat transfer enhancement can be obtained compared with the base fluid by using a system with CuO/ water nanofluid‐cooled radiators.     

Numerical Study of Nanofluid Condensation Heat Transfer in a Square Microchannel

This study presents a numerical study of nanofluid condensation heat transfer inside a single horizontal smooth square tube. The numerical results are compared to previous experimental predictions, and show that the heat transfer coefficient can be improved 20% by increasing the volume fraction of Cu nanoparticles by 5% or increasing the mass flux from 80 to 110 kg/m² s. Reducing the hydraulic diameter of the microchannel from 200 to 160 µm led to an increase in average condensation heat transfer coefficient of 10%. A new correlation estimating Nusselt number for condensation of nanofluids or pure vapor is proposed. It predicts average condensation heat transfer, with good agreement with the computed values.     

An experimental study on convection heat transfer from an array of discrete heat sources

Convection heat transfer from an array of discrete heat sources inside a rectangular channel has been investigated experimentally for air. The lower surface of the channel was equipped with 8×4 flush-mounted heat sources subjected to uniform heat flux; the sidewalls and the upper wall were insulated and adiabatic. The experimental parametric study was made for an aspect ratio of AR=2, Reynolds numbers 864≤Re_Dh≤7955, and modified Grashof numbers Gr*=1.72×10⁸ to 2.76×10⁹. From the experimental measurements, surface temperature distributions of the discrete heat sources were obtained and effects of Reynolds and Grashof numbers on these temperatures were investigated. Furthermore, Nusselt number distributions were calculated for different Reynolds and Grashof numbers. Results show that surface temperatures increase with increasing Grashof number and decrease with increasing Reynolds number. However, with the increase in the buoyancy affected secondary flow and the onset of instability, temperatures level off and even drop as a result of heat transfer enhancement. This outcome can also be observed from the variation of the row-averaged Nusselt number showing an increase towards the exit.     

Numerical simulation of heat transfer and fluid flow over two rotating circular cylinders at low Reynolds number

This paper presents a numerical investigation of the characteristics of two‐dimensional heat transfer in a steady laminar flow around two rotating circular cylinders in a side‐by‐side arrangement. The simulation is validated by comparing our computational results for the large gap‐spacing between cylinder surfaces with the available numerical and experimental data for a single cylinder. Numerical simulations were carried out for the Reynolds number range 10≤Re ≤40, for the Prandtl number range 0.7≤Pr ≤50, and for a variety of absolute rotational speeds (|α|≤2.5) at different gap spacings. The study revealed that for the range of parameters considered the rate of heat transfer decreases with the increasing speed of rotation. An increase of the Prandtl number resulted in an increase in the average Nusselt number. The streamlines and isotherms are plotted for a numbers of cases to show the details of the velocity and thermal fields. © 2010 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20293     

Numerical investigation on the single phase forced convection heat transfer characteristics of TiO2 nanofluids in a double-tube counter flow heat exchanger

In this study, forced convection flows of nanofluids consisting of water with TiO₂ and Al₂O₃ nanoparticles in a horizontal tube with constant wall temperature are investigated numerically. The horizontal test section is modeled and solved using a CFD program. Palm et al.'s correlations are used to determine the nanofluid properties. A single-phase model having two-dimensional equations is employed with either constant or temperature dependent properties to study the hydrodynamics and thermal behaviors of the nanofluid flow. The numerical investigation is performed for a constant particle size of Al₂O₃ as a case study after the validation of its model by means of the experimental data of Duangthongsuk and Wongwises with TiO₂ nanoparticles. The velocity and temperature vectors are presented in the entrance and fully developed region. The variations of the fluid temperature, local heat transfer coefficient and pressure drop along tube length are shown in the paper. Effects of nanoparticles concentration and Reynolds number on the wall shear stress, Nusselt number, heat transfer coefficient and pressure drop are presented. Numerical results show the heat transfer enhancement due to presence of the nanoparticles in the fluid in accordance with the results of the experimental study used for the validation process of the numerical model.     

Natural convection heat transfer of alumina-water nanofluid in vertical square enclosures: An experimental study

An experimental study has been undertaken concerning natural convection heat transfer of a nanofluid in vertical square enclosures of different sizes, whose dimensions, width × height × length (mm), are 25 × 25 × 60, 40 × 40 × 90, and 80 × 80 × 180, respectively. The nanofluid formulated in the present experiment is water dispersed with various volumetric fractions of the alumina (Al₂O₃) nanoparticles ranging from 0.1 vol.% to 4 vol.%. The Rayleigh number varies in the range of 6.21 × 10⁵–2.56 × 10⁸. A correlation analysis based on the thermophysical properties of the nanofluid formulated shows that efficacy of applying the nanofluid for natural convection heat transfer enhancement in enclosure is inferred to be generally infeasible. The experimental results for the average heat transfer rate across the three enclosures appear generally consistent with the assessment based on the changes in thermophysical properties of the nanofluid formulated, showing systematic heat transfer degradation for the nanofluids containing nanoparticles of c_v ≥ 2 vol.% over the entire range of the Rayleigh number considered. However, for the nanofluid containing much lower particle fraction of 0.1 vol.%, a heat transfer enhancement of around 18% compared with that of water was found to arise in the largest enclosure at sufficiently high Rayleigh number. Such enhancement cannot be explained simply based on the net influence due to relative changes in thermophysical properties of the nanofluid containing such low particle fraction, thus strongly suggesting other factors may come into play.     

Numerical investigation into the convective heat transfer of TiO2 nanofluids flowing through a straight tube under the laminar flow conditions

A numerical study has been performed by using both single phase method and combined Euler and Lagrange method on the convective heat transfer of TiO₂ nanofluids flowing through a straight tube under the laminar flow conditions. The effects of nanoparticles concentrations, Reynolds number, and various nanoparticle aggregates sizes are investigated on the flow and the convective heat transfer behaviour. The results show significant enhancement of heat transfer of nanofluids particularly in the entrance region. The numerical results are compared with the experimental data and reasonable good agreement is achieved.     

Numerical study of transient buoyancy-driven convective heat transfer of water-based nanofluids in a bottom-heated isosceles triangular enclosure

A numerical study of transient buoyancy-driven convective heat transfer of water-based nanofluids inside a bottom-heated horizontal isosceles triangular cylinder is presented. Nano-sized copper oxide (CuO) particles suspended in water with two different volume fractions are considered. The thermophysical properties of water in the presence of nanoparticles are predicted using existing models, in which the effects of the Brownian motion of nanoparticles are taken into account. It is shown that pitchfork bifurcation appears for relatively high Grashof numbers and the critical Grashof number is found to be 5.60 × 10⁴. The predicted development of convective flow of nanofluids is presented by means of the average Nusselt number over the bottom. Additionally, the flow development time towards a steady/quasi-steady state and the time-averaged Nusselt number are scaled with Grashof number. It is also shown that at constant Grashof numbers the time-averaged Nusselt number is lowered as more nanoparticles are added to the base liquid and will be overestimated if the Brownian motion effects are not considered.     

Confined Submerged Jet Impingement Boiling of Subcooled FC-72 over Micro-Pin-Finned Surfaces

Heat transfer characteristics of confined submerged jet impingement boiling of air-dissolved FC-72 on heated micro-pin-finned surfaces are presented. The dimension of the silicon chips is 10 × 10 × 0.5 mm³ (length × width × thickness) on micro-pin-fins with the four dimensions of 30 × 30 × 60 μm³, 50 × 50 × 60 μm³, 30 × 30 × 120 μm³, and 50 × 50 × 120 μm³ fabricated by using the dry etching technique. For comparison, experiments of jet impinging on a smooth surface were also conducted. The results have shown that submerged jet impingement boiling gives a large heat transfer enhancement compared with pool boiling, and all micro-pin-fins showed better heat transfer performance than a smooth surface. The effects of jet Reynolds number, jet inlet subcooling, micro-pin-fins, and nozzle-to-surface distance on jet impingement boiling heat transfer were explored. For micro-pin-fins, the maximum allowable heat flux increases with jet Reynolds number and subcooling. The largest value of the maximum allowable heat flux of micro-pin-fins by submerged jet impingement boiling is 157 W/cm², which is about 8.3 times as large as that for the smooth surface in pool boiling. Also, Nusselt number has a strong dependence on Reynolds number.     

Momentum and Heat Transfer Phenomena for Power–Law Liquids in Assemblages of Solid Spheres of Moderate to Large Void Fractions

This work extends our previously reported results for the flow of and heat transfer from expanded beds of solid spheres to power–law fluids by using a modified and more accurate numerical solution procedure. Extensive results have been obtained to elucidate the effects of the Reynolds number (Re), the Prandtl number (Pr), the power–law index (n), and the bed voidage (ε) on the flow and heat transfer behavior of assemblages of solid spheres in the range of parameters: 1 ≤ Re ≤ 200, 1 ≤ Pr ≤ 1000, 0.6 ≤n ≤ 1.6, and 0.7 ≤ε ≤ 0.999999. The large values of bed voidage are included here to examine the behavior in the limit of an isolated sphere. As compared to Newtonian fluids, for fixed values of the Reynolds number and the voidage, the total drag coefficient decreases and the average Nusselt number increases for shear thinning fluids (n < 1); whereas, for shear thickening fluids (n > 1), the opposite behavior is observed. The drag results corresponding to bed voidage, ε = 0.99999, are very close to that of a single sphere; whereas, the heat transfer results approach this limit at ε = 0.999. Based on the present numerical results, simple correlations for drag coefficient and average Nusselt number are proposed which can be used to calculate the pressure drop for the flow of a power–law fluid through a bed of particles, or rate of sedimentation in hindered settling and the rate of heat transfer in assemblages of solid spheres in a new application. Broadly speaking, all else being equal, shear-thinning behavior promotes heat transfer, whereas shear-thickening behavior impedes it.     

Combined Effect of Magnetic Field and Nanofluid Variable Properties on Heat Transfer Enhancement in Natural Convection

The current work investigated, numerically, enhancement of heat transfer in natural convection using CuO-water nanofluid in the presence of a magnetic field. The governing equations were discretized using the control volume method and solved numerically via the SIMPLE algorithm. For the case of absence of a magnetic field and for low Rayleigh number, the heat transfer was almost insensitive to the presence of nanoparticles. For moderate and high Rayleigh numbers, the presence of nanoparticles had an adverse effect on heat transfer at high volume fraction of nanoparticles. The highest reduction in heat transfer was registered for the case of Ra = 10⁵. Contour maps are generated for the normalized Nusselt number (Nu*) to determine the optimum selection of volume fraction of nanoparticles and magnetic field that gives maximum heat transfer enhancement. The results demonstrated the effectiveness and practicality of using high values of magnetic field in enhancing heat transfer using nanofluids.     

Natural convection heat transfer of high temperature gas in an annulus between two vertical concentric cylinders

Water cooling panels have been adopted as the vessel cooling system of the High Temperature Engineering Test Reactor (HTTR) to cool the reactor core indirectly by natural convection and thermal radiation. In order to investigate the heat transfer characteristics of high temperature gas in a vertical annular space between the reactor pressure vessel and cooling panels of the HTTR, we carried out experiments and numerical analyses on natural convection heat transfer coupled with thermal radiation heat transfer in an annulus between two vertical concentric cylinders with the inner cylinder heated and the outer cylinder cooled. In the present experiments, Rayleigh number based on the height of the annulus ranged from 2.0 × 10⁷ to 5.4 × 10⁷ for helium gas and from 1.2 × 10⁹ to 3.5 × 10⁹ for nitrogen gas. The numerical results were in good agreement with the experimental ones regarding the surface temperatures of the heating and cooling walls. As a result of the experiments and the numerical analyses, the heat transfer coefficient of natural convection coupled with thermal radiation was obtained as functions of Rayleigh number, radius ratio, and the temperatures and emissivities of the heating and cooling wall surfaces. © 2005 Wiley Periodicals, Inc. Heat Trans Asian Res, 34(5): 293–308, 2005; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20070     

MHD conjugate heat transfer and entropy generation analysis of MWCNT/water nanofluid in a partially heated divided medium

The aim of this article is to conduct the lattice Boltzmann simulation of the magnetohydrodynamic (MHD) natural conjugate heat transfer in an apportioned cavity loaded with a multiwalled carbon nanotube/water nanofluid. The divided cavity is, to some extent, heated and cooled at the upright walls, whereas the horizontal walls are adiabatic. The nanofluid properties are evaluated on the basis of experimental correlations. The parameters ranges in the study are as follows: nanoparticles' volume fraction (%): 0 ≤ ? ≤ 0.5, temperature (°C): T = 27, Rayleigh number (Ra): 10³ ≤ Ra ≤ 10⁵, Hartmann number (Ha): 0 ≤ Ha ≤ 90, and the magnetic field inclination angle (γ): 0 ≤ γ ≤ π/2. The current outcomes are observed to be in great concurrence with the numerical results introduced in the literature. The impacts of the aforesaid parameters on local and average heat transfer, entropy generation, and Bejan number (Be) are explored and discussed. Indeed, the transfer of heat increases linearly with ? for a low Ra. As Ra increases, the average Nusselt number decreases for a high value of ?. The increase of nanoparticles' volume fraction leads to a reduction in the entropy generation and an increase in the Bejan number for a high Ra, but at low Ra, these functions remain constant. As the Ha increases, the transfer of heat and the entropy generation decreases, whereas there is an increase in Be. The transfer of heat, total entropy generation, and the Be depends strongly on the direction of the magnetic field. The increase of heater and cooler size has a great influence on the transfer of heat, entropy generation, and Be.