Numerical research of nature convective heat transfer enhancement filled with nanofluids in rectangular enclosures

Heat transfer enhancement utilizing nanofluids in a two-dimensional enclosure is investigated for various pertinent parameters. The Khanafer's model is used to analyze heat transfer performance of nanofluids inside an enclosure taking into account the solid particle dispersion. Transport equations are model by a stream function-vorticity formulation and are solved numerically by finite-difference approach. Based upon the numerical predictions, the effects of Rayleigh number (Ra) and aspect ratio (AR) on the flow pattern and energy transport within the thermal boundary layer are presented. The diameter of the nanoparticle d_p is taken as 10 nm in nanofluids. The buoyancy parameter is 10³ ≤ Ra ≤ 10⁶ and aspect ratios (AR) of two-dimensional enclosure are 1/2, 1, 2. Results show that increasing the buoyancy parameter and volume fraction of nanofluids cause an increase in the average heat transfer coefficient. Finally, the empirical equation was built between average Nusselt number and volume fraction.     

Thermal and fluid dynamic behaviors of confined laminar impinging slot jets with nanofluids

Heat transfer enhancement technologies play an important role in research and industrial fields; thus, they have been widely applied to many applications as in refrigeration, automotive, aerospace, and process industry. For example, heat transfer can be passively enhanced by increasing the thermal conductivity of the working fluids, adopting nanofluids, or actively by employing impinging jets.In this paper a numerical analysis on confined impinging slot jets working with pure water or water/Al₂O₃ based nanofluids is presented. The flow is laminar and a constant uniform temperature is applied on the target surface. The single-phase model approach has been adopted in order to describe the nanofluid behavior and different particle volume concentrations have been considered. Moreover, simulations have been performed for different geometric ratios in order to take into account the confining effects and Reynolds numbers. The behavior of the system has been analyzed in terms of average and local convective heat transfer coefficient, Nusselt number, and required pumping power profiles. Correlations for stagnation point and average Nusselt number for 100 ≤ Re ≤ 400, 0% ≤ ϕ ≤ 5% and 4 ≤ H/W ≤ 10 are provided.     

Mixed convective transport in a lid-driven cavity containing a nanofluid and a rotating circular cylinder at the center

The mixed convective transport of Cu-H₂O nanofluid in a differentially heated and lid-driven square enclosure in the presence of a rotating circular cylinder is investigated numerically. The top wall of the enclosure is sliding from left to right at a uniform speed while all other walls are stationary. A thermally insulated circular cylinder is placed centrally within the enclosure. The cylinder can rotate about its centroidal axis. The top and bottom walls are kept isothermal at different temperatures while the side walls are assumed adiabatic. Simulations are performed for, Richardson number 1 ≤ Ri ≤ 10, dimensionless rotational speed 0 ≤ Ω ≤ 5 and nanoparticle concentration 0 ≤ ϕ ≤ 0.20 keeping the Grashof number fixed as Gr = 10⁴. The flow and thermal fields are analyzed through streamline and isotherm plots for various Ω and Ri. Furthermore, the drag coefficient of the moving lid and Nusselt number of the hot wall are also computed to understand the effects of Ω and Ri on them. It is observed that the heat transfer greatly depends on the rotational speed of the cylinder, mixed convective strength and the nanoparticle concentration.     

Mixed convection from an open cavity in a horizontal channel

Heat transfer results for mixed convection from a bottom heated open cavity subjected to an external flow are reported in this study for a wide range of the governing parameters (i.e., 1 ≤ Re ≤ 2000, 0 ≤ Gr ≤ 10⁶) over cavities with various aspect ratios (A = 0.5, 1, 2 and 4). It has been found that the Reynolds number and Garshof number control the flow pattern and the occurrence of recirculating cells while the aspect ratio has a significant influence on the orientation of these cells. Heat transfer from the cavity base approaches that of natural convection at a low Reynolds number (i.e., the asymptotic natural convection regime) and approaches that of forced convection at a high Reynolds number (i.e., the asymptotic forced convection regime). In the mixed convection regime, the heat transfer rate is reduced and the flow may become unstable. A unique heat transfer correlation which covers all three convection regimes is also presented.     

Experimental investigation of opposing mixed convection hear transfer in the vertical flat channel in a laminar–turbulent transition region

In this paper we present the results on experimental investigation of the local opposing mixed convection heat transfer in the vertical flat channel with symmetrical heating in a laminar–turbulent transition region. The experiments were performed in airflow (p = 0.1–1.0 MPa) in the range of Re from 1.5 × 10³ to 6.6 × 10⁴ and Gr_q up to 1 × 10¹¹ at the limiting condition q_w1 = q_w2 = const. The analysis of the results revealed significant increase in the heat transfer with increasing of air pressure (Gr number). Also sharp increase in heat transfer was noticed in the region with vortex flow in comparison with the turbulent flow region.     

Laminar forced convection flow over a backward facing step using nanofluids

Laminar forced convection flow of nanofluids over a 2D horizontal backward facing step placed in a duct is numerically investigated using a finite volume method. A 5% volume fraction of nanoparticles is dispersed in a base fluid besides using various types of nanoparticles such as Au, Ag, Al₂O₃, Cu, CuO, diamond, SiO₂, and TiO₂. The duct has a step height of 4.8 mm, and an expansion ratio of 2. The Reynolds number was in the range of 50 ≤ Re ≤ 175. A primary recirculation region has been developed after the sudden expansion and it starts to change to become fully developed flow downstream of the reattachment point. The reattachment point is found to move downstream far from the step as Reynolds number increases. Nanofluid of SiO₂ nanoparticles is observed to have the highest velocity among other nanofluids types, while nanofluid of Au nanoparticles has the lowest velocity. The static pressure and wall shear stress increase with Reynolds number and vice versa for skin friction coefficient.     

Numerical thermal analysis and optimization of a water jet impingement cooling with VOF two-phase approach

The fluid flow and heat transfer characteristics of a free-surface liquid jet impingement cooling have been investigated numerically. The slot jet with water impinging normally on a flat plate is employed. To describe the turbulent structure, the turbulent governing equations are solved by a control-volume-based finite-difference method with a power-law scheme and the well-known turbulence model, which are associated with wall function. Numerical computations have been conducted with variations of jet exit Reynolds number (11,000 ≤ Re_d ≤ 17,000), dimensionless jet-to-surface distance (3 ≤ H/d₀ ≤ 12), dimensionless jet width (1 ≤ B/d₀ ≤ 2), and the heat flux (140 kW/m² ≤ q″ ≤ 280 kW/m²). The theoretical model developed is validated by comparing the numerical predictions with available experimental data in the literature. Under the studied ranges, the variations of local Nusselt numbers by hydraulic diameter Nu_d of the dimensionless jet-to-surface distance 3 ≤ H/d₀ ≤ 12 along the flat plate decrease monotonically from its maximum value at the stagnation point. In addition, the shape of the inlet area and jet-to-surface distance are optimized by using the response surface methodology (RSM) and the genetic algorithm (GA) method after solutions are carefully validated with available experimental results in the literature. Based on the optimal results, the optimum condition is in H/d₀ = 7.86 and B/d₀ = 2 for this physical model.     

Numerical investigation on heat transfer and friction factor characteristics of laminar and turbulent flow in an elliptic annulus utilizing nanofluid

In this paper, a numerical investigation on heat transfer performance and flow fields of different nanofluids flows through elliptic annulus in a laminar and turbulent flow regimes. The three-dimensional continuity, Navier–Stokes and energy equations are solved by using finite volume method (FVM) and the SIMPLE algorithm scheme is applied to examine the effects of laminar and turbulent flow on heat transfer characteristics. This study evaluates the effects of four different types of nanoparticles, Al₂O₃, CuO, SiO₂ and ZnO, with different volume fractions (0.5–4%) and diameters (25–80 nm) under constant heat flux boundary condition using water as a base fluid were used. The Reynolds number of laminar flow was in the range of 200 ≤ Re ≤ 1500, while for turbulent flow it was in the range of 4000 ≤ Re ≤ 10,000. The results have shown that SiO₂–water nanofluid has the highest Nusselt number, followed by ZnO–water, CuO–water, Al₂O₃–water, and lastly pure water. The Nusselt number for all cases increases with the volume fraction but it decreases with the rise in the diameter of nanoparticles. In all configurations, the Nusselt number increases with Reynolds number. It is found that the glycerine–SiO₂ shows the best heat transfer enhancement compared with other tested base fluids.     

Experimental investigation of mixed convection heat transfer in a rectangular channel with discrete heat sources at the top and at the bottom

Mixed convection heat transfer in a top and bottom heated rectangular channel with discrete heat sources has been investigated experimentally for air. The lower and upper surfaces of the channel were equipped with 8 × 4 flush-mounted heat sources subjected to uniform heat flux. Sidewalls, the lower and upper walls were insulated and adiabatic. The experimental study was made for an aspect ratio of AR = 6, Reynolds numbers 955 ≤ Re_Dh ≤ 2220 and modified Grashof numbers Gr* = 1.7 × 10⁷ to 6.7 × 10⁷. From experimental measurements, surface temperature and Nusselt number distributions of the discrete heat sources were obtained for different Grashof numbers. Furthermore, Nusselt number distributions were calculated for different Reynolds numbers. Results show that surface temperatures increase with increasing Grashof number. The row-averaged Nusselt numbers first decrease with the row number and then, due to the increase in the buoyancy affected secondary flow and the onset of instability, they show an increase towards the exit as a result of heat transfer enhancement.     

Transition of nanofluids flow in an inclined heated pipe

A numerical investigation is carried out to investigate the transitional flow behaviour of nanofluids flow in an inclined pipe using both single and multi-phase models. Two different nanofluids are considered, and these are Al₂O₃–water and TiO₂–water nanofluids. Moreover, SST κ − ω transitional model is implemented to study the nanofluids flow in inclined pipe. Gravitational force is also adopted by considering Boussinesq approximation in the momentum equation. Results reveal that Buoyancy force play a significant role on the degeneration of heat transfer rate with the increase of Reynolds number for different inclination angles. It indicates that mixed convection has opposite effect on the inclined pipe than the forced convection on the horizontal pipe. Moreover, some deformation of the flow and temperature fields near the upstream region is observed with the increase of inclination angle due to Buoyancy force.     

Analysis of entropy generation on mixed convection in square enclosures for various horizontal or vertical moving wall(s)

Entropy generation during the mixed convection process have been studied in a square enclosure for various moving horizontal (cases 1a–1d) or vertical wall(s) (cases 2a–2c) where the bottom wall of the cavity is isothermally hot, side walls are cold, and the top wall is adiabatic. Simulations have been performed for Prandtl number Pr = 0.026 and 7.2, Reynolds number Re = 10 − 100, and Grashof number Gr = 10³ − 10⁵. Results show that, in the case of the horizontally moving wall(s) (cases 1a–1d), the overall heat transfer rate $\left(\overline{N{u}_b}\right)$ and total entropy generation (S_total) are identical for cases 1a–1d and the cup-mixing temperature (θ_cup) is high for case 1b at Pr = 0.026, Re = 100, and Gr = 10⁵. Similarly, in the case of the vertically moving wall(s) (cases 2a–2c), $\overline{N{u}_b}$ and S_total are identical for cases 2a–2c with the maximum θ_cup occurring for the case 2a. At Pr = 7.2, Gr = 10⁵, and Re = 10, case 1a and case 1c are preferable for horizontally moving wall(s) and either of case 2a–2c is preferable for vertically moving wall(s). At Pr = 7.2, Gr = 10⁵, and Re = 100, case 1d may be preferable for the horizontally moving wall(s) and case 2a may be preferable for the vertically moving wall(s).     

Effect of titanium substitution in layered LiNiO2 cathode material prepared by molten-salt synthesis

LiNi_1−xTi_xO₂ (0 ≤ x ≤ 0.1) compounds have been synthesized by a direct molten-salt method that uses a eutectic mixture of LiNO₃ and LiOH salts. According to X-ray diffraction analysis, these materials have a well-developed layered structure (R3-m) and are an isostructure of LiNiO₂. The LiNi_1−xTi_xO₂ (0 ≤ x ≤ 0.1) compounds have average particle sizes of 1–5 μm depending on the amount of Ti salt. Charge–discharge tests show that a LiNi_1−xTi_xO₂ (0 ≤ x ≤ 0.1) cathode prepared at 700 °C has an initial discharge capacity as high as 171 mA h g⁻¹ and excellent capacity retention in the range 4.3–2.8 V at a current density of 0.2 mA cm⁻².     

Time evolution of double-diffusive convection in a vertical cylinder with radial temperature and axial solutal gradients

The characteristics of transient double-diffusive convection in a vertical cylinder are numerically simulated using a finite element method. Initially the fluid in the cavity is at uniform temperature and solute concentration, then constant temperature and solute concentration, which are lower than their initial values, are imposed along the sidewall and bottom wall, respectively. The time evolution of the double-diffusive convection is investigated for specific parameters, which are the Prandtl number, Pr = 7, the Lewis number, Le = 5, the thermal Grashof number, Gr_T = 10⁷, and the aspect ratio, A = 2, of the enclosure. The objective of the work is to identify the effect of the buoyancy ratio (the ratio of solutal Grashof to thermal Grashof numbers: N = Gr_S/Gr_T) on the evolution of the flow field, temperature and solute field in the cavity. It is found that initially the fluid near the bottom wall is squeezed by the cold flow from the sidewall, a crest of the solute field forms and then pushed to the symmetry line. In the case of N > 0, a domain with higher temperature and weak flow (dead region) forms on the bottom wall near the symmetry line, and the area of dead region increases when N varies from 0.5 to 1.5. More crests of the solute field are formed and the flow near the bottom wall fluctuates continuously for N < 0. The frequency of the fluctuation increases when N varies from −0.5 to −1.5. Corresponding to the variety of the thermal and solutal boundary layers, the average rates of heat transfer (Nu) at the sidewall remain almost unchanged while the average rates of mass transfer (Sh) at the bottom wall change much in the cases of N = 1, 0, −1.     

Heatlines based natural convection analysis in tilted isosceles triangular enclosures with linearly heated inclined walls: effect of various orientations

Natural convection in isosceles triangular enclosures with various configurations (case 1 — inverted, case 2 — straight and case 3 — tilted) is studied via heatline analysis for linear heating of inclined walls. Detailed analysis and comparison for various base angles (φ = 45°, 60°) of triangular enclosures have been carried out for a range of fluids (Pr = 0.015 − 1000) within Ra = 10³ − 10⁵ using Galerkin finite element method. The heat flow distributions indicate conduction dominant heat transfer at low Ra (Ra = 10³) for case 1 and case 2 whereas in case 3, convective heat flow is observed due to high buoyancy force. As Ra increases, enhanced thermal mixing is observed at the core of the cavity. Wall to wall heat transfer occurs at walls AB and AC due to linear heating boundary condition in all the cases. Although the distributions of fluid flow and heat flow are qualitatively similar for φ = 45° and 60°, the intensity of fluid flow and heat flow decreases as φ increases. Strength of fluid flow and heat flow circulation cells is found to be higher in case 3 for identical parameters. Results show that upper side wall (AC) for case 3 exhibits higher heat transfer rates whereas heat transfer rates for walls AB and AC are the same for case 1 and case 2. Also Nu_AB is higher for case 2 followed by case 1 and case 3 at the middle portion of wall AB. Thus to achieve high heat transfer from fluid to wall at the central region, case 2 and case 3 configurations may be recommended at high Ra (Ra = 10⁵) and Pr, irrespective of φ.     

Effect of a magnetic field on natural convection in an open cavity subjugated to water/alumina nanofluid using Lattice Boltzmann method

In this paper, the effect of a magnetic field on natural convection in an open enclosure which subjugated to water/alumina nanofluid using Lattice Boltzmann method has been investigated. The cavity is filled with water and nanoparticles of Al₂O₃ at the presence of a magnetic field. Calculations were performed for Rayleigh numbers (Ra = 10⁴–10⁶), volume fractions of nanoparticles (φ = 0,0.02,0.04 and .0.06) and Hartmann number (0 ≤ Ha ≤ 90) with interval 30 while the magnetic field is considered horizontally. Results show that the heat transfer decreases by the increment of Hartmann number for various Rayleigh numbers and volume fractions. The magnetic field augments the effect of nanoparticles at Rayleigh number of Ra = 10⁶ regularly. Just as the most effect of nanoparticles for Ra = 10⁴ is observed at Ha = 30, so the most influence of nanoparticles occurs at Ha = 60 for Ra = 10⁵.     

Heat transfer in a small gap between co-axial rotating cylinders

This paper investigates the local heat transfer of a co-axial rotating cylinder. In the inner flow field of the rotating cylinder, the dimensionless parameters include the rotational Reynolds number (Re_Ω) and buoyancy parameter (Gr). The test rig is designed to make the rotating in the inner cylinder and stationary in the outer cylinder. The local temperature distributions of the inner and outer cylinder on axial direction were measured. Under the experimental condition, whereas the ranges of the rotational Reynolds number are 2400 ≤ Re_Ω ≤ 45,000. Experimental results reveal that the rotational Reynolds number's increase is with the heat transfer coefficient distributions increase types. Finally, the local heat transfer rate on the wall are correlated and compared with that in the existing literature.     

Effect of nanofluid variable properties on natural convection in enclosures filled with a CuO–EG–Water nanofluid

This work focuses on the study of natural convection heat transfer characteristics in a differentially-heated enclosure filled with a CuO–EG–Water nanofluid for different published variable thermal conductivity and variable viscosity models. The problem is given in terms of the vorticity–stream function formulation and the resulting governing equations are solved numerically using an efficient finite-volume method. Comparisons with previously published work are performed and the results are found to be in good agreement. Various results for the streamline and isotherm contours as well as the local and average Nusselt numbers are presented for a wide range of Rayleigh numbers (Ra = 10³–10⁵), volume fractions of nanoparticles (0 ≤ φ ≤ 6%), and enclosure aspect ratios (½ ≤ A ≤ 2). Different behaviors (enhancement or deterioration) are predicted in the average Nusselt number as the volume fraction of nanoparticles increases depending on the combination of CuO–EG–Water variable thermal conductivity and viscosity models employed. In general, the effects the viscosity models are predicted to be more predominant on the behavior of the average Nusselt number than the influence of the thermal conductivity models. The enclosure aspect ratio is predicted to have significant effects on the behavior of the average Nusselt number which decreases as the enclosure aspect ratio increases.     

Laminar natural convection in an air-filled square cavity with partitions on the top wall

The laminar natural convection in an air-filled square cavity with a partition on the top wall was experimentally investigated. Temperature measurements and flow visualizations were performed for cases with heated and cooled vertical walls (corresponding to a global Grashof number Gr_H of approximately 1.3 × 10⁸) and non-dimensional top wall temperatures θ_T of 0.56 (insulated) to 2.3. Experiments were performed with an aluminum partition with non-dimensional height H_P/H of 0.0625 and 0.125 attached to the top wall at x/H = 0.1, 0.2, 0.4 and 0.6. The blockage effect and/or the thermal effect of the partition resulted in changes to the temperature and flow fields, but were mainly limited to the vicinity of the partition. The partition on the heated top wall resulted in a recirculating flow between the partition and the heated vertical wall. For a given partition height, the structure of this recirculating flow was dependent on the partition location and θ_T. A thermal boundary layer developed along the rear surface of the partition due to the thermal effect of the partition. The ambient temperature outside the boundary layer and Nu near the corner region was affected by the partition height due to the change in the recirculating flow and due to the thermal effect on the rear surface of the partition.     

Numerical investigation for natural convection of a nanofluid in an inclined L-shaped cavity in the presence of an inclined magnetic field

The problem of natural convection in an inclined L-shaped enclosure filled with Cu/water nanofluid that operates under differentially heated walls in the presence of an inclined magnetic field is presented in this paper. The fully implicit finite difference method is used to solve the governing equations. A comparison with previously published results in special case of the present study is performed and a very good agreement is found. Heat transfer and fluid flow are examined for parameters of the Hartmann number (0 ≤ Ha ≤ 100), the nanoparticles volume fraction (0% ≤ ϕ ≤ 20%), the cavity inclination angle (0° ≤ ϑ ≤ 300°), the magnetic field inclination angle (0° ≤ γ ≤ 270°), the cavity aspect ratio (0.25 ≤ AR ≤ 0.6) and the Rayleigh number (10³ ≤ Ra ≤ 10⁶). It is found that, the presence of the magnetic field in the fluid region causes a significant reduction in the fluid flow and heat transfer characteristics. Also, a good enhancement in the heat transfer rate can be obtained by adding the copper nanoparticles to the base fluid.     

Oscillatory double-diffusive mixed convection in a two-dimensional ventilated enclosure

By starting from a steady flow configuration based on the work of Deng et al. [Qi-Hong Deng, Jiemin Zhou, Chi Mei, Yong-Ming Shen, Fluid, heat and contaminant transport structures of laminar double-diffusive mixed convection in a two-dimensional ventilated enclosure, Int. J. Heat Mass Transfer 47 (2004) 5257–5269], a numerical investigation was conducted to analyse the unsteady double-diffusive mixed convection in two-dimensional ventilated room due to heat and contaminant sources. Owing to the large number of parameters, the results are reported only for a constant buoyancy ratio N equal to 1. The flow is found to be oscillatory for a fixed Reynolds number (700 ⩽ Re ⩽ 1000) when the Grashof number is varied in a wide range (10³ ⩽ Gr ⩽ 10⁶). Results of the simulations show that the onset of the oscillatory indoor airflow occurs for couples (Re, Gr) values that can be correlated as Re = aGr^b.