Numerical study of nanofluid forced convection flow in channels using different shaped transverse ribs

A numerical investigation is performed to study the effects of different rib shapes and turbulent nanofluid flow on the thermal and flow fields through transversely roughened rectangular channels with Reynolds number ranging from 5000 to 20000 and uniform heat flux of 10 kW/m². Considering single-phase approach, the two-dimensional continuity, Navier–Stokes, and energy equations were solved by using the finite volume method (FVM). The optimization was carried out by using various rib shapes (rectangular shape, triangular shape, wedge pointing upstream, and wedge pointing downstream) in two arrangements (in-line and staggered) and three different aspect ratios (w/e = 0.5, 2, and 4) to reach the optimal geometry with maximum performance evaluation criterion (PEC). The main aim of this study is to analyze the effects of nanoparticle types (Al₂O₃, CuO, SiO₂, and ZnO), concentration (1–4%), and nanoparticle diameter (30–80 nm), on the heat transfer and fluid flow characteristics. Simulation results show that the ribbed channels' performance was greatly influenced by rib shapes and their geometrical parameters. The highest PEC was obtained for the in-line triangular ribs with w/e = 4 at Re = 5000. It is found that the water–SiO₂ shows the highest heat transfer enhancement compared with other tested nanofluids. The Nusselt number through the ribbed channels was enhanced with the increase of the particle volume fraction and Reynolds number, and with the decrease of nanoparticle diameter.     

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.     

Heat transfer enhancement of nanofluids in a double pipe heat exchanger with louvered strip inserts

The effect of using louvered strip inserts placed in a circular double pipe heat exchanger on the thermal and flow fields utilizing various types of nanofluids is studied numerically. The continuity, momentum and energy equations are solved by means of a finite volume method (FVM). The top and the bottom walls of the pipe are heated with a uniform heat flux boundary condition. Two different louvered strip insert arrangements (forward and backward) are used in this study with a Reynolds number range of 10,000 to 50,000. The effects of various louvered strip slant angles and pitches are also investigated. Four different types of nanoparticles, Al₂O₃, CuO, SiO₂, and ZnO with different volume fractions in the range of 1% to 4% and different nanoparticle diameters in the range of 20 nm to 50 nm, dispersed in a base fluid (water) are used. The numerical results indicate that the forward louvered strip arrangement can promote the heat transfer by approximately 367% to 411% at the highest slant angle of α = 30° and lowest pitch of S = 30 mm. The maximal skin friction coefficient of the enhanced tube is around 10 times than that of the smooth tube and the value of performance evaluation criterion (PEC) lies in the range of 1.28–1.56. It is found that SiO₂ nanofluid has the highest Nusselt number value, followed by Al₂O₃, ZnO, and CuO while pure water has the lowest Nusselt number. The results show that the Nusselt number increases with decreasing the nanoparticle diameter and it increases slightly with increasing the volume fraction of nanoparticles. The results reveal that there is a slight change in the skin friction coefficient when nanoparticle diameters of SiO₂ nanofluid are varied.     

Heat transfer of rectangular narrow channel with two opposite scale-roughened walls

An experimental study of heat transfer and pressure drop in a rectangular channel roughened by scaled surfaces on two opposite walls with flows directed in the forward and downward directions for Reynolds numbers (Re) in the range of 1500 ⩽ Re ⩽ 15,000 was performed. Nusselt number ratios between the scale-roughened and smooth-walled ducted flows (Nu/Nu_∞) were in the range of 7.4–9.2 and 6.2–7.4 for laminar forward and downward flows respectively. The Nu/Nu_∞ values for turbulent developed flows in the scale-roughened channel with forward and downward flows were about 4.5 and 3 respectively. A comparison of present data with reported results using different types of surface roughness demonstrated the better thermal performances of present scale-roughened channel with forward flow at conditions of Re > 10,000. Experimental correlations of heat transfer and friction coefficient were derived for the present scale-roughened rectangular channel.     

The effect of nanofluids flow on mixed convection heat transfer over microscale backward-facing step

Laminar mixed convection flow over a 2D horizontal microscale backward-facing step (MBFS) placed in a duct is numerically investigated. The governing equations along with the boundary conditions are solved using the finite volume method (FVM). The upstream wall and the step wall are considered adiabatic, while the downstream wall is heated by uniform heat flux. The straight wall of the duct is maintained at a constant temperature that is higher than the inlet fluid temperature. Different types of nanoparticles such as Al₂O₃, CuO, SiO₂ and ZnO, with volume fractions in the range of 1–4% are used. The nanoparticles diameter was in the range of 25 nm ? d_p ? 70 nm. The expansion ratio was 2 and the step height was 0.96 μm. The Reynolds number was in the range of 0.05 ? Re ? 0.5. The results revealed that the Nusselt number increases with increasing the volume fraction and Reynolds number. The nanofluid of SiO₂ nanoparticles is observed to have the highest Nusselt number value. It is also found that the Nusselt number increases with the decrease of nanoparticle diameter. However, there is no recirculation region was observed at the step and along the duct.     

Bias effects on heat transfer measurements in microchannel flows

This work is devoted to both experimental and numerical investigations of the hydrodynamics and associated heat transfer in two-dimensional microchannels from 700 μm to 200 μm in height. The design of the test section enabled to vary the channel height and to set a quasi-constant heat flux at the microchannel surface. Laminar developing, transitional and turbulent regimes of water flows were explored (200 < Re < 8000). A significant decrease in the Nusselt number was observed in the laminar regime when the channel spacing was decreased while the Poiseuille number remained unchanged in regard to conventional channel flow. It is shown that a bias effect in the solid/fluid interface temperature measurements is most likely responsible for this scale effect. The temperature error was estimated and accounted for in the determination of the Nusselt number. The corrected values have been found to be consistent with the conventional laws both in the laminar and in the beginning of the turbulent regime.     

Experimental and numerical study of nanofluid flow and heat transfer over microscale forward-facing step

Experimental and numerical investigations are presented to illustrate the nanofluid flow and heat transfer characteristics over microscale forward-facing step (MFFS). The duct inlet and the step height were 400 μm and 600 μm respectively. All the walls are considered adiabatic except the downstream wall was exposed to a uniform heat flux boundary condition. The distilled water was utilized as a base fluid with two types of nanoparticles Al₂O₃ and SiO₂ suspended in the base fluid. The nanoparticle volume fraction range was from 0 to 0.01 with an average nanoparticle diameter of 30 nm. The experiments were conducted at a Reynolds number range from 280 to 480. The experimental and numerical results revealed that the water–SiO₂ nanofluid has the highest Nusselt number, and the Nusselt number increases with the increase of volume fraction. The average friction factor of water–Al₂O₃ was less than of water–SiO₂ mixture and pure water. The experimental results showed 30.6% enhancement in the average Nusselt number using water–SiO₂ nanofluid at 1% volume fraction. The numerical results were in a good agreement with the experimental results.     

Natural convection in a rectangular enclosure containing an oval-shaped heat source and filled with Fe3O4/water nanofluid

This work concerns with the study of natural convection heat transfer in rectangular cavities with an inside oval-shaped heat source filled with Fe₃O₄/water nanofluid. The finite element method is employed to solve the governing equations for this problem. Average Nusselt numbers are presented for a wide range of Rayleigh number (10³ ≤ Ra ≤ 10⁵), volume fraction of nanoparticles (0 ≤ ϕ ≤ 14%), and four different size and shapes of the heat source. Depending on concentration of the nanoparticle, geometry of the heat source, and the value of Rayleigh number different behaviors are monitored for average Nusselt numbers. Configuration of the heat source dictates a significant change on the behavior of the average Nusselt number, while addition of the nanoparticles has a negative effect on the magnitude of Nusselt number for this problem.     

Flow over and forced convection heat transfer in Newtonian fluids from a semi-circular cylinder

Momentum and heat transfer characteristics of a semi-circular cylinder immersed in unconfined flowing Newtonian fluids have been investigated numerically. The governing equations, namely, continuity, Navier–Stokes and energy, have been solved in the steady flow regime over wide ranges of the Reynolds number (0.01 ? Re ? 39.5) and Prandtl number (Pr ? 100). Prior to the investigation of drag and heat transfer phenomena, the critical values of the Reynolds number for wake formation (0.55 < Re^c < 0.6) and for the onset of vortex shedding (39.5 < Re_c < 40) have been identified. The corresponding values of the lift coefficient, drag coefficient, and Strouhal number are also presented. After establishing the limit of the steady flow regime, the influence of the Reynolds number (0.01 ? Re ? 39.5) and Prandtl number (Pr = 0.72, 1, 10, 50 and 100) on the global flow and heat transfer characteristics have been elucidated. Detailed kinematics of the flow is investigated in terms of the streamline and vorticity profiles and the variation of pressure coefficient in the vicinity of the cylinder. The functional dependence of the individual and total drag coefficients on the Reynolds number is explored. The Nusselt number shows an additional dependence on the Prandtl number. In addition, the isotherm profiles, local Nusselt number (Nu_L) and average Nusselt number (Nu) are also presented to analyze the heat transfer characteristic of a semi-circular cylinder in Newtonian media.     

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.     

Heat transfer augmentation through the use of wire-rod bundles under constant wall heat flux condition

This article reports an experimental investigation on heat transfer, friction factor and thermal performance characteristics of turbulent flow (6000 ≤ Re ≤ 20,000) in heat exchanger tubes with wire-rod bundles as flow turbulators. The experiments were carried out at three different pitch ratios (P/D) of 1.0, 1.5 and 2.0 and three wire-rod number per bundle (N) of 4, 6 and 8. The experimental results show that Nusselt number increases with increasing Reynolds number and wire-rod number per bundle, and decreasing pitch ratio (P/D) of the turbulators. As compared to the results of the tube without wire-rod (the plain tube), heat transfer rate and friction factor are respectively increased in ranges of 3.5 to 68.8% and 156 to 353%, depending on the operating conditions. At the same pumping power, the use of wire-rod turbulators results in thermal performance factor up to 1.02 times of those of the plain tube. In addition, the correlations that developed from the present experimental data for Nusselt number, friction factor and thermal performance factor are also presented.     

Numerical study of assisting and opposing mixed convective nanofluid flows in an inclined circular pipe

A numerical investigation of mixed convection is carried out to study the heat transfer and fluid flow characteristics in an inclined circular pipe using the finite volume method. The pipe has L/D of 500 and it was subjected to a uniform heat flux boundary condition. Four types of nanofluids (Al₂O₃, CuO, SiO₂, and TiO₂ with H₂O) with nanoparticles concentration in the range of 0 ≤ φ ≤ 5% and nanoparticles diameter in the range of 20 ≤ dp ≤ 60 nm were used. The pipe inclination angle was in the range of 30^∘ ≤ θ ≤ 75^∘ using assisting and opposing flow. The influences of Reynolds number in the range of 100 ≤ Re ≤ 2000, and Grashof numbers in the range of 6.3 × 10² ≤ Gr ≤ 8.37 × 10³ were examined. It is found that the velocity and wall shear stress are increased as Re number increases, while the surface temperature decreases. There is no significant effect of increasing Gr number on thermal and flow fields. The velocity and wall shear stress are increased and the surface temperature is decreased as φ and dp are decreased. It is concluded that the surface temperature is increased as the pipe inclination angle increases from the horizontal position (θ = 0^°) to the inclined position (θ = 75^°). In addition, it is inferred that the heat transfer is enhanced using SiO₂ nanofluid compared with other nanofluids types. Furtheremore, it is enhanced using assisting flow compared to opposing flow.     

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.     

Mixed convection flow and heat transfer across a square cylinder under the influence of aiding buoyancy at low Reynolds numbers

In this paper, mixed convection flow and heat transfer around a long cylinder of square cross-section under the influence of aiding buoyancy are investigated in the vertical unconfined configuration (Reynolds number, Re = 1–40 and Richardson number, Ri = 0–1). The semi-explicit finite volume method implemented on the collocated grid arrangement is used to solve the governing equations along with the appropriate boundary conditions. The onset of flow separation occurs between Re = 1–2, between Re = 2–3 and between Re = 3–4 for Ri = 0, 0.5 and 1, respectively. The flow is found to be steady for the range of conditions studied here. The friction, pressure and total drag coefficients are found to increase with Richardson number, i.e., as the influence of aiding buoyancy increases drag coefficients increase at the constant value of the Reynolds number. The temperature field around the obstacle is presented by isotherm contours at the Prandtl number of 0.7 (air). The local and average Nusselt numbers are calculated to give a detailed study of heat transfer over each surface of the square cylinder and an overall heat transfer rate and it is found that heat transfer increases with increase in Reynolds number and/or Richardson number. The simple expressions for the wake length and average cylinder Nusselt number are obtained for the range of conditions covered in this work.     

Measurement of local heat/mass transfer coefficients on a dimple using naphthalene sublimation

Local and average heat/mass transfer characteristics on a single dimple were investigated using a naphthalene sublimation technique. The dimple depth in this study ranged from 20% to 40% of the channel height. The experimental conditions covered the range from laminar to low-velocity turbulent flow regimes, 500 ? Re_H ? 5000. Secondary flows from the dimple were clearly observed in the transient flow regime of Re_H = 2000–3000. The velocity fluctuation in the mixing layer over the dimple increased with the dimple depth and the Reynolds number. The impingement of the mixing layer and the induced secondary flows augmented the Sherwood number around the rear rim of the dimple and in the rear plateau region, respectively. For a Reynolds number of 3000, the Sherwood number increased significantly due to the increased fluctuation in the mixing layer and the intensified secondary flows from the dimple. The heat/mass transfer augmentation factors increased as the Reynolds number increased, reaching 1.5 at a Reynolds number of 5000.     

Heat transfer enhancement by flow bifurcations in asymmetric wavy wall channels

The enhancement characteristics of heat transfer, through a transition scenario of flow bifurcations, in asymmetric wavy wall channels, are investigated by direct numerical simulations of the mass, momentum and energy equations, using the spectral element method. The heat transfer characteristics, flow bifurcation and transition scenarios are determined by increasing the Reynolds numbers for three geometrical aspect ratios r = 0.25, 0.375, and 0.5, and Prandtl numbers 1.0 and 9.4. The transition scenarios to transitional flow regimes depend on the aspect ratio. For the aspect ratios r = 0.25 and 0.5, the transition scenario is characterized by one Hopf flow bifurcation. For the aspect ratio r = 0.375, the transition scenario is characterized by a first Hopf flow bifurcation from a laminar to a periodic flow, and a second Hopf flow bifurcation from a periodic to quasi-periodic flow. The periodic and quasi-periodic flows are characterized by fundamental frequencies ω₁, and ω₁ and ω₂, respectively. For all the aspect ratios and Prandtl numbers, the time-average mean Nusselt number and heat transfer enhancement increases with the Reynolds number as the flow evolves from a laminar to a transitional regime. For both Prandtl numbers, the highest increase in the Nusselt number occurs for the aspect ratio r = 0.5; whereas, the lowest increases happen to r = 0.25. The increase of the Nusselt number occurs at the expense of a higher pumping power, which, for both Prandtl numbers, grows as the aspect ratio increases from r = 0.25 to r = 0.5 for reaching a specific Nusselt number. This enhancement is obtained without the necessity of high volumetric flow rates associated with turbulent flow regimes, which demand much higher pumping powers. Significant heat transfer enhancements are obtained when the asymmetric wavy channel is operated in the appropriate transitional Reynolds number range.     

Heat and fluid flow across a rotating cylinder dissipating uniform heat flux in 2D laminar flow regime

Free-stream flow and forced convection heat transfer across a rotating cylinder, dissipating uniform heat flux, are investigated numerically for Reynolds numbers of 20–160 and a Prandtl number of 0.7. The non-dimensional rotational velocity (α) is varied from 0 to 6. Finite volume based transient heatline formulation is proposed. For Re = 100, the reasons for the onset/suppression of vortex shedding at a critical rotational velocity is investigated using vorticity dynamics. At higher rotational velocity, the Nusselt number is almost independent of Reynolds number and thermal boundary conditions. Finally, a heat transfer correlation is proposed in the 2D laminar flow regime. Cylinder rotation is an efficient Nusselt number reduction or cylinder-surface temperature enhancement technique.     

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.     

Heat transfer in all pipe flow regimes: laminar,transitional/intermittent,and turbulent

A predictive theory is presented which is capable of providing quantitative results for the heat transfer coefficients in round pipes for the three possible flow regimes: laminar, transitional, and turbulent. The theory is based on a model of laminar-to-turbulent transition which is also viable for purely laminar and purely turbulent flow. Fully developed heat transfer coefficients were predicted for the three regimes. The present predictions were brought together with the most accurate experimental data known to the authors as well as with several algebraic formulas which are purported to be able to provide fully developed heat transfer coefficients in the so-called transition regime between Re = 2300 and 10,000. It was found that over the range Re > 4800, both the present predictions and those of the Gnielinski formula [V. Gnielinski, New equations for heat and mass transfer in turbulent pipe and channel flow, Int. Chem. Eng. 16 (1976) 359–367] are very well supported by the experimental data. However, the Gnielinski model is less successful in the range from 2300 to 3100. In that range, the present predictions and those of Churchill [S. Churchill, Comprehensive correlating equations for heat, mass, and momentum transfer in fully developed flow in smooth tubes, Ind. Eng. Chem. Fundam. 16 (1977) 109–116] are mutually reinforcing. Heat transfer results in the development region have also been obtained. Typically, regardless of the Reynolds number, the region immediately downstream of the inlet is characterized by laminar heat transfer. After the breakdown of laminar flow, a region characterized by intermittent heat transfer occurs. Subsequently, the flow may become turbulent and fully developed or the intermittent state may persist as a fully developed regime. The investigation covered both of the basic thermal boundary conditions of uniform heat flux (UHF) and uniform wall temperature (UWT). In the development region, the difference between the respective heat transfer coefficients for the two cases was approximately 25% (UHF > UWT). For the fully developed case, the respective heat transfer coefficients are essentially equal in the turbulent regime but differ by about 25% in the intermittent regime. The reported results are for a turbulence intensity of 5% and flat velocity and temperature profiles at the inlet.     

Numerical modeling of natural convection in an open cavity with two vertical thin heat sources subjected to a nanofluid

This paper presents a numerical study of natural convection cooling of two heat sources vertically attached to horizontal walls of a cavity. The right opening boundary is subjected to the copper–water nanofluid at constant low temperature and pressure, while the other boundaries are assumed to be adiabatic. The governing equations have been solved using the finite volume approach, using SIMPLE algorithm on the collocated arrangement. The study has been carried out for the Rayleigh number in the range 10⁴ ≤ Ra ≤ 10⁷, and for solid volume fraction 0 ≤ φ ≤ 0.05. In order to investigate the effect of heat source location, three different placement configurations of heat sources are considered. The effects of both Rayleigh numbers and heat source locations on the streamlines, isotherms, Nusselt number are investigated. The results indicate that the flow field and temperature distributions inside the cavity are strongly dependent on the Rayleigh numbers and the position of the heat sources. The results also indicate that the Nusselt number is an increasing function of the Rayleigh number, the distance between two heat sources, and distance from the wall. In addition it is observed that the average Nusselt number increases linearly with the increase in the solid volume fraction of nanoparticles.