Influence of nanofluids on mixed convective heat transfer over a horizontal backward‐facing step

Predictions are reported for laminar mixed convection using various types of nanofluids over a horizontal backward‐facing step in a duct, in which the upstream wall and the step are considered adiabatic surfaces, while the downstream wall from the step is heated to a uniform temperature that is higher than the inlet fluid temperature. The straight wall that forms the other side of the duct is maintained at constant temperature equivalent to the inlet fluid temperature. Eight different types of nanoparticles, Au, Ag, Al₂O₃, Cu, CuO, diamond, SiO₂, and TiO₂, with 5% volume fraction are used. The conservation equations along with the boundary conditions are solved using the finite volume method. Results presented in this paper are for a step height of 4.9 mm and an expansion ratio of 1.942, while the total length in the downstream of the step is 0.5 m. The Reynolds number is in the range of 75 ≤ Re ≤ 225. The downstream wall was fixed at a uniform wall temperature in the range of 0 ≤ ΔT ≤ 30 °C which is higher than the inlet flow temperature. Results reveal that there is a primary recirculation region for all nanofluids behind the step. It is noticed that nanofluids without secondary recirculation region have a higher Nusselt number and it increases with Prandtl number decrement. On the other hand, nanofluids with secondary recirculation regions are found to have a lower Nusselt number. Diamond nanofluid has the highest Nusselt number in the primary recirculation region, while SiO₂ nanofluid has the highest Nusselt number downstream of the primary recirculation region. The skin friction coefficient increases as the temperature difference increases and the Reynolds number decreases. © 2011 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.20344     

Numerical Simulation of Natural Convection in a Triangle Cavity Filled with Nanofluids Using Tiwari and Das' Model: Effects of Heat Flux

In this article, we present a fully higher‐order compact (FHOC) finite difference method to investigate the effects of heat flux on natural convection of nanofluids in a right‐angle triangle cavity, where the left vertical side is heated with constant heat flux both partially and throughout the entire wall, the inclined wall is cooled, and the rest of walls are kept adiabatic. The Darcy flow and the Tiwari and Das’ nanofluid models are considered. Investigations with four types of nanofluids were made for different values of Rayleigh numbers with the range of 100 ≤ Ra ≤ 50,000, size of heat flux as 0.1 ≤ ε ≤ 1.0, enclosure aspect ratio as 0.5 ≤ AR ≤ 2.0, and solid volume fraction parameter of nanofluids with the range of 0% ≤ ? ≤ 20%. Results show that the average heat transfer rate increases significantly as particle volume fraction and Rayleigh numbers increase, and the maximum value of average Nusselt number is obtained by decreasing the enclosure aspect ratio. The results also show that the average heat transfer decreases with an increase in the length of the heater. Furthermore, multiple correlations in terms of the Rayleigh numbers and the solid volume fraction of four types of nanoparticles have been established in a general form.     

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.     

Brownian Motion Effects on Natural Convection of Alumina–Water Nanofluid in 2‐D Enclosure

This article reports a numerical study of natural convection heat transfer in a differentially heated enclosure filled with a Al₂O₃–water nanofluid. Fluent v6.3 is used to simulate nanofluid flow. Simulations have been carried out for the pertinent parameters in the following ranges: the Rayleigh number, Ra = 10⁶, 10⁷, and the volumetric fraction of alumina nanoparticles, ? = 0 ? 4%. The effect of Brownian motion on the heat transfer is considered and examined. The numerical results show a decrease in heat transfer with an increase in particle volume fraction. Similar to experimental results, the Nusselt number increases with the Rayleigh number in the numerical results. © 2013 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21121     

Forced convective heat transfer of nanofluids in microchannels

Convective heat transfer coefficient and friction factor of nanofluids in rectangular microchannels were measured. An integrated microsystem consisting of a single microchannel on one side, and two localized heaters and five polysilicon temperature sensors along the channel on the other side were fabricated. Aluminum dioxide (Al₂O₃) with diameter of 170 nm nanofluids with various particle volume fractions were used in experiments to investigate the effect of the volume fraction of the nanoparticles to the convective heat transfer and fluid flow in microchannels. The convective heat transfer coefficient of the Al₂O₃ nanofluid in laminar flow regime was measured to be increased up to 32% compared to the distilled water at a volume fraction of 1.8 volume percent without major friction loss. The Nusselt number measured increases with increasing the Reynolds number in laminar flow regime. The measured Nusselt number which turned out to be less than 0.5 was successfully correlated with Reynolds number and Prandtl number based on the thermal conductivity of nanofluids.     

Numerical studies on heat and fluid flow of nanofluid in a partially heated vertical annulus

A numerical investigation on natural convective heat transfer of nanofluid (Al₂O₃+water) inside a partially heated vertical annulus of high aspect ratio (352) has been carried out. The computational fluid dynamics solver Ansys Fluent is used for simulation and results are presented for various volume fraction of nanoparticles (0‐0.04) at different heat flux values (3‐12 kW/m²). Two well‐known correlations for evaluating thermal conductivity and viscosity have been used. Thus different combinations of the available correlations have been set to form four models (I, II, III, and IV). Therefore, a detailed analysis has been executed to identify effects of thermophysical properties on heat transfer and fluid flow of nanofluids using different models. The results show enhancement in heat transfer coefficient with volume fraction of nanoparticles. Highest enhancement achieved is found to be 14.17% based on model III, while the minimum is around 7.27% based on model II. Dispersion of nanoparticles in base fluid declines the Nusselt number and Reynolds number with different rates depending on various models. A generalized correlation is proposed for Nusselt number of nanofluids in the annulus in terms of volume fraction of nanoparticles, Rayleigh number, Reynolds number, and Prandtl number.     

Conjugate heat transfer enhancement of laminar slot jets with various nanofluids on an array of protruding hot sources using MPM approach

Conjugate heat transfer in laminar slot jets impinging on multiple protruding hot sources using various nanofluids has been investigated numerically by employing (i) a mass-based modeling and an (ii) Eulerian-based multi-phase modeling (MPM). Various parameters such as streamline contours, isotherm profiles, local Nusselt number (Nu), average Nusselt number (Nuavg) are evaluated for different nanofluids (Ag–water, Al₂O₃–water, CuO–water and TiO₂–water), various range of Reynolds number (Re), particle volume fraction (?), diameter of the nanoparticle (d) and thermal conductivity ratio (kr). The steady, laminar, incompressible and two-dimensional flows are considered for the analysis. Finite-volume method with SIMPLE algorithm is used to solve continuity, momentum and energy equations along with boundary conditions. The highest heat transfer rate is achieved at ??=?0.05 for any protruding blocks and Reynolds number. Conjugate heat transfer rate of nanofluids increases with decreasing the diameter of nanoparticles. Here, Al₂O₃–water nanofluid is found to exhibit highest average Nusselt number compared to other nanofluids. The mixture based MPM approach with considering slip velocity yields higher heat transfer rate compared to the results obtained by single phase modeling approach.     

Asymmetric Forced Convection of Nanofluids in a Channel with Symmetrically Mounted Rib Heaters on Opposite Walls

Laminar forced convection of nanofluids in a vertical channel with symmetrically mounted rib heaters on surfaces of opposite walls is numerically studied. The fluid flow and heat transfer characteristics are examined for various Reynolds numbers and nanoparticles volume fractions of water-Al₂O₃ nanofluid. The flow exhibits various structures with varying Reynolds number. Even though the geometry and heating is symmetric with respect to a channel vertical mid-plane, asymmetric flow and heat transfer are found for Reynolds number greater than a critical value. Introduction of nanofluids in the base fluid delays the flow solution bifurcation point, and the critical Reynolds number increases with increasing nanoparticle volume fraction. A skin friction coefficient along the solid-fluid interfaces increases and decreases sharply along the bottom and top faces of the heaters, respectively, due to sudden acceleration and deceleration of the fluid at the respective faces. The skin friction coefficient, as well as Nusselt numbers in the channel, increase with increasing volume fraction of nanoparticles.     

Effect of viscosity variation on natural convection flow of water–alumina nanofluid in an annulus with internal heat generation

Heat transfer enhancement in a horizontal annulus using the variable viscosity property of an Al₂O₃–water nanofluid is investigated. Two different viscosity models are used to evaluate heat transfer enhancement in the annulus. The base case uses the Pak and Cho model and the Brinkman model for viscosity which take into account the dependence of this property on temperature and nanoparticle volume fraction. The inner surface of the annulus is heated uniformly by a constant heat flux q_w and the outer boundary is kept at a constant temperature T_c. The nanofluid generates heat internally. The governing equations are solved numerically subject to appropriate boundary conditions by a penalty finite‐element method. It is observed that for a fixed Prandtl number Pr = 6.2, Rayleigh number Ra = 10⁴ and solid volume fraction ? = 10%, the average Nusselt number is enhanced by diminishing the heat generation parameter, mean diameter of nanoparticles, and diameter of the inner circle. The mean temperature for the fluids (nanofluid and base fluid) corresponding to the above mentioned parameters is plotted as well. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21016     

Impact of volume fraction and fluid layer thickness on heat transfer effectiveness of water-based nanofluids

The heat transfer effectiveness of nanofluids is adversely affected by the delay in convection onset. The lesser effectiveness, when compared to that of base fluid, is observed in a range of nanofluid layer thickness. The heat transfer coefficient of water–Al₂O₃ nanofluid can be enhanced by sustaining the equilibrium between Rayleigh number, temperature, particle volume fraction, and enclosure aspect ratio. In this paper, the specific correlation of fluid layer thickness and the onset of convection, which can significantly dominate the heat transfer characteristics of nanofluids are investigated using the concept of critical Rayleigh number. The water layer thickness for convection onset is first experimentally assessed for different real-life heat flux densities. It is then performed for Al₂O₃–water nanofluid for varying volume fractions. With the increase in volume fraction even though thermal conductivity increases, the overall heat transfer enhancement of the nanofluid is reduced. Temperature involved (heat flux density), the volume fraction of the nanofluid used, nanofluid layer thickness (space availability for the cooling system), and mass of the nanoparticle influence heat transfer enhancement. A higher volume fraction may not always result in enhancement of heat transfer as far as nanofluids are concerned.     

Numerical Analysis of Turbulent Forced Convection of Nanofluid Flow over a Heated Shallow Cavity

This work presents a numerical investigation of turbulent forced convection of a nanofluid over a heated cavity in a horizontal duct. Heat transfers in separated flows are frequently encountered in engineering applications, such as: heat exchangers, axial and centrifugal compressor blades, gas turbines blades, and microelectronic circuit boards. Thus, it is very essential to understand the mechanisms of heat transfer in such regions in order to enhance heat transfer. Different volume fractions of nanoparticles are presented in the base fluid and different types of nanoparticles are used. The objective of this study is to check the effect of nanofluid on heat transfer in such a configuration. Numerical simulations are performed for pure water and four nanofluids (Cu, CuO, Ag, and Al₂O₃). The results are analyzed through the thermal and dynamical fields with a particular interest to the skin friction coefficient and Nusselt number evolutions. The average Nusselt number increases with the volume fraction of nanoparticles for the whole tested range of Reynolds number. A correlation of average Nusselt number versus Reynolds number and volume fraction of each type of nanoparticles over the cavity wall is proposed in this paper.     

Effect of Volume Fraction of γ‐Al2O3 Nanofluid on Heat Transfer Enhancement in a Concentric Tube Heat Exchanger

In this work, γ-Al₂O₃ nanoparticles with mean diameter of 10 nm are dispersed in deionized water with four nanoparticle volume concentrations of 0.25, 0.5, 0.75, and 1%. The effect of γ-Al₂O₃/water nanofluids on the heat transfer enhancement of heat exchangers is investigated under turbulent regime for four different volumetric flow rates of 150, 200, 250, and 300 L/h. The experimental results showed that the convective heat transfer is increased by increasing particles volume fraction as well as flow rate. The maximum enhancement obtained in Nusselt number and heat transfer coefficient was 20 and 22.8%, respectively, at Reynolds number of 6026 and particle volume fraction of 1%. The experimental Nusselt numbers of nanofluids showed good agreement with the available empirical correlation at particle volume fractions of 0.25 and 0.5%. An empirical correlation is obtained to estimate the Nusselt number of nanofluid under the conditions of this work.     

A numerical comparison among different water-based hybrid nanofluids on their influences on natural convection heat transfer in a triangular solar collector for different tilt angles

Natural convection inside a triangular solar collector is investigated numerically for different nanofluids and hybrid nanofluids in this study. The individual effects of Al₂O₃–water, carbon nanotubes (CNT)–water, and Cu–water nanofluids are observed for different solid volume fractions of nanoparticles (0%–10%). Three types of hybrid nanofluids are prepared using different ratios of Al₂O₃, CNT, and Cu nanoparticles in water. A comparison is made varying the Rayleigh numbers within laminar range (10³–10⁶) for different tilt angles (0°, 30°, 60°, and 90°) of the solar collector. The inclined surface of the triangular solar collector is isothermally cold and the bottom wall (absorber plate) is isothermally hot, whereas the vertical wall with respect to the absorber plate is considered adiabatic. Average Nusselt numbers along the hot wall for different parameters are observed. Streamlines and isotherm contours are also plotted for different cases. Dimensionless governing Navier–Stokes and thermal energy conservation equations are solved by Galerkin weighted residual finite element method. Better convective heat transfer is found for higher Rayleigh number, solid volume fraction, and tilt angle. In the case of hybrid nanofluid, increasing the percentage of the nanoparticle that gives better heat transfer performance individually results in enhancing natural convection heat transfer inside the enclosure.     

Comparative study on heat transfer enhancement of nanofluids flow in ribs tube using CFD simulation

This study presents, a numerical investigation of two‐dimensional turbulent nanofluids flow in different ribs tube configurations on heat transfer, friction, and thermal performance coefficients using ANSYS‐FLUENT software version‐16. Governing equations of mass, momentum, and energy have been solved by means of a finite volume method (FVM). Four types of nanoparticles namely; Al₂O₃, CuO, SiO₂, and ZnO with volume fraction range (1%‐4%) and different size of nanoparticles (dp = 30 nm, 40 nm, 50 nm, and 60 nm) with various Reynolds number (10 000‐30 000) in a constant heat flux tube with rectangular, triangular, and trapezoidal ribs were conducted for simulation. The results exhibit that Nusselt number for all cases enhanced with Reynolds number and nanofluid volume fraction increases. Likewise, the results also reveal that SiO₂ with volume fractions of 4% and diameters of nanoparticles of 30 nm in triangular ribs offered the highest Nusselt number at Reynolds number of Re = 30 000. In addition, the higher value of thermal performance factor was obtained at Reynolds number of Re = 10 000.     

Numerical Simulation of Nanoparticles Concentration Effect on Forced Convection in a Tube With Nanofluids

The present study aims to identify effects due to convection heat transfer in a tube. Turbulent and laminar forced convection flow of a water–Al₂O₃ nanofluid in a tube subjected to a constant and uniform temperature at the wall was numerically analyzed. The single-phase model was employed to simulate the nanofluid convection, taking into account appropriate thermophysical properties. Particles are assumed spherical with a diameter equal to 24 nm. Simulations have been carried out for the pertinent parameters in the following ranges: Reynolds number from 10³ to 10⁵ and volumetric fraction of alumina nanoparticles between 0 to 4%. It is found that convective heat transfer coefficient for nanofluids is greater than that of the base liquid. Heat transfer enhancement is increasing with the particle volume concentration and Reynolds number. As for the friction factor, it shows a good agreement with the classical correlation used for normal fluid, such as the Blasius formula. Moreover, a study on wall shear stress was attempted.     

Modeling of conjugated heat transfer in a thick walled enclosure filled with nanofluid

The objective of this paper is to investigate the conjugated heat transfer in a thick walled cavity filled with copper-water nanofluid. The analysis uses a two-dimensional rectangular enclosure under conjugated convective-conductive heat transfer conditions and considers a range of Rayleigh numbers. The enclosure was subjected to a constant and uniform heat flux at the left thick wall generating a natural convection flow. The thicknesses of the other boundaries are assumed to be zero. The right wall is kept at a low constant temperature while the horizontal walls are assumed to be adiabatic. A moveable divider is located at the bottom wall of the cavity. The governing equations are derived based on the conceptual model in the Cartesian coordinate system. The study has been carried out for the Rayleigh number in the range of 10⁵ ≤ Ra ≤ 10⁸, and for the solid volume fraction at 0 ≤ ? ≤ 0.05. Results are presented in the form of streamlines, isotherms, average Nusselt number and input heat absorption by the nanofluid. The effects of solid volume fraction of nanofluids, the location of the divider and also the value of the ambient convective heat transfer coefficient on the hydrodynamic and thermal characteristics of flow have been analyzed. An increase in the average Nusselt number was found with the solid concentration for the whole range of Rayleigh number. In addition, results show that the position of the divider and the ambient convective heat transfer coefficient have a considerable effect on the heat transfer enhancement.     

Experimental investigation of nanofluids in confined laminar radial flows

This paper presents an experimental investigation of heat transfer enhancement capabilities of coolants with suspended nanoparticles (Al₂O₃ dispersed in water) inside a radial flow cooling device. Steady, laminar radial flow of a nanofluid between a heated disk and a flat plate with axial coolant injection has been considered. An experimental test rig was built. Results show that heat transfer enhancements are possible in radial flow cooling systems with the use of nanofluids. In general, it was noticed that the Nusselt number increases with particle volume fraction and Reynolds number and decreases with an increase in disk spacing.     

Effect of nanofluid variable properties on natural convection in enclosures

In this work, the heat transfer enhancement in a differentially heated enclosure using variable thermal conductivity and variable viscosity of Al₂O₃–water and CuO–water nanofluids is investigated. The results are presented over a wide range of Rayleigh numbers (Ra = 10³–10⁵), volume fractions of nanoparticles (0 ≤ φ ≤ 9%), and aspect ratios (½ ≤ A ≤ 2). For an enclosure with unity aspect ratio, the average Nusselt number of a Al₂O₃–water nanofluid at high Rayleigh numbers was reduced by increasing the volume fraction of nanoparticles above 5%. However, at low Rayleigh numbers, the average Nusselt number was slightly enhanced by increasing the volume fraction of nanoparticles. At high Rayleigh numbers, CuO–water nanofluids manifest a continuous decrease in Nusselt number as the volume fraction of nanoparticles is increased. However, the Nusselt number was not sensitive to the volume fraction at low Rayleigh numbers. The Nusselt number demonstrates to be sensitive to the aspect ratio. It was observed that enclosures, having high aspect ratios, experience more deterioration in the average Nusselt number when compared to enclosures having low aspect ratios. The variable thermal conductivity and variable viscosity models were compared to both the Maxwell-Garnett model and the Brinkman model. It was found that at high Rayleigh numbers the average Nusselt number was more sensitive to the viscosity models than to the thermal conductivity models.     

Lattice Boltzmann simulation of natural convection in tall enclosures using water/SiO2 nanofluid

Natural convection in enclosures using water/SiO₂ nanofluid is simulated with Lattice Boltzmann method (LBM). This investigation compared with other numerical methods and found to be in excellent agreement. This study has been carried out for the pertinent parameters in the following ranges: the Rayleigh number of base fluid, Ra = 10³-10⁵, the volumetric fraction of nanoparticles between 0 and 4% and aspect ratio (A) of the enclosure between 0.5 and 2. The thermal conductivity of nanofluids is obtained on basis of experimental data. The comparisons show that the average Nusselt number increases with volume fraction for the whole range of Rayleigh numbers and aspect ratios. Also the effect of nanoparticles on heat transfer augments as the enclosure aspect ratio increases.     

Heat transfer enhancement in a cubical cavity filled with a hybrid nanofluid

Mixed convection heat transfer in a cubical cavity with an isothermally heated blockage inside filled with a hybrid nanofluid (HBNF) is numerically studied. The natural convection is created by the temperature difference between the hot block and the cold lateral walls, while the forced convection is generated by moving the upper wall. The influence of some variables, like the aspect ratio (0.1 ≤ r ≤ 0.5), Richardson number (0 ≤ Ri≤ 20), Reynolds number (50 ≤ Re ≤ 200), volume concentration of nanoparticles (0 ≤ ϕ ≤ 0.06), and the concentration ratio (2:8, 5:5, and 8:2) on the flow field and heat transfer is analyzed. A comparison between hybrid and mono nanofluids (NFs) is realized to investigate the energy transport enhancement. Results show that the increase of each parameter causes an increase of average Nusselt number Nu_avg and improves the heat transfer; besides the use of HBNF gives better Nu_avg values. Three correlations of the effect of r, ϕ, Ri, and Re on Nu_avg are determined for both hybrid and mono NFs.