Local Nusselt Number Distribution Research Articles

Heat Transfer and Thermal Characteristics Effects on Moving Plate Impinging from Cu-Water Nanofluid Jet

The present article is focused on modelling of flow and heat transfer behaviour of Cu-water nanofluid in a confined slot jet impingement on hot moving plate. Different parameters such as various moving plate velocities, nanoparticles at various concentrations, variation in turbulent Reynolds number and jet nozzle to plate distance have been considered to study the flow field and convective heat transfer performance of the system. Results of distribution of local and average Nusselt number and skin friction coefficients at the plate surface are shown to elucidate the heat transfer and fluid flow process. Qualitative analysis of both stream function and isotherm contours are carried out to perceive the flow pattern and heat transfer mechanism due to moving plate. The results revealed that average Nusselt number significantly rises with plate velocity in addition with jet inlet Reynolds number. Correlations of the average Nusselt numbers are presented.

A Study on Natural Convection in a Cold Square Enclosure With Two Vertical Eccentric Square Heat Sources Using the IB–LBM Scheme

In this article, the natural convection process in a two-dimensional cold square enclosure is numerically investigated in the presence of two inline square heat sources. Two different heat source boundary conditions are analyzed, namely, case 1 (when one heat source is hot) and case 2 (when two heat sources are hot), using the in-house developed flexible forcing immersed boundary–thermal lattice Boltzmann model. The isotherms, streamlines, local, and surface-averaged Nusselt number distributions are analyzed at ten different vertical eccentric locations of the heat sources for Rayleigh number between 103 and 106. Distinct flow regimes including primary, secondary, tertiary, quaternary, and Rayleigh–Benard cells are observed when the mode of heat transfer is changed from conduction to convection and heat sources eccentricity is varied. For Rayleigh number up to 104, the heat transfer from the enclosure is symmetric for the upward and downward eccentricity of the heat sources. At Rayleigh number greater than 104, the heat transfer from the enclosure is better for downward eccentricity cases that attain a maximum when the heat sources are near the bottom enclosure wall. Moreover, the heat transfer rate from the enclosure in case 2 is nearly twice that of case 1 at all Rayleigh numbers and eccentric locations. The correlations for heat transfer are developed by relating Nusselt number, Rayleigh number, and eccentricity of the heat sources.

Numerical investigation of the laminar natural convection heat transfer from the equilateral triangular cluster of three horizontal spheres

Natural convection heat transfer from the equilateral triangular cluster of three horizontal spheres in air has been investigated numerically over the range of 10≤Gr≤105. An extended model is used for the partially symmetric cluster in the three-dimensional condition, which is proposed initially by Bejan et al. (1995). The accuracy of the extended model has been validated by the single sphere. The comprehensive results consist of isothermal and streamline contours, the local drag coefficients as well as the local and average Nusselt number distributions with the different Grashof numbers. There is a thicker thermal boundary in the center clearance of the cluster due to the interaction of the three adjacent surface for all Grashof numbers, which weakens the heat transfer and deteriorates into the decreasing of local Nusselt number along the polar angle, while the negative velocity gradient has a similar effect. Then the correlation equation of the average Nusselt number in the range of 10≤Gr≤105 has been proposed. Compared with the single sphere, the average Nusselt number of the cluster changes from 64.69% to 92.45% of that of the single sphere due to the stronger buoyancy force and the larger temperature gradient with the increasing Grashof number.

Measurement of two-dimensional heat transfer and flow characteristics of an impinging sweeping jet

This study experimentally explores the two-dimensional heat transfer characteristics of an impinging sweeping jet generated from a feedback–channel-type fluidic oscillator. The results were compared to those of a steady square jet. A phosphor thermometry technique was used to measure the surface temperature field on an aluminum plate for different Reynolds numbers and jet-to-wall spacing. A two-dimensional planar Particle Image Velocimetry (PIV) measurement of the sweeping impinging jet was also conducted to couple the flow characteristics and heat transfer performance. The local Nusselt number distributions on the flat plate were evaluated by converting the temperature fields. The heat transfer performance of the sweeping jet is much higher than that of the steady jet because the sweeping motion of the jet induces significant turbulent flow and clearly improves the thermal transport near the impingement plate. However, when the jet-wall spacing becomes greater than 5, the heat transfer performance of the sweeping jet drastically decreases due to the reduced impinging velocity, and the heat transfer of the steady square jet surpasses that of the sweeping jet. In the ensemble averaged velocity fields, two main jet streams are ejected to the plate like oblique impinging jets near the sidewalls of the exit because the jet flow is attached to sidewall one or the other for more than 70% of an oscillation period. There was high similarity between the ensemble averaged velocity profiles and the Nusselt number profiles.

Natural convection heat transfer from a vertical single cylinder with helical wire spacer in liquid sodium

Abstract Natural convection heat transfer from a vertical single cylinder with helical wire spacer in liquid sodium was numerically analyzed on the following four effects, the influences of surface heat flux, gap between helical wire and heated cylinder surface, pitch of helical wire and helical wire diameter on heat transfer. The unsteady laminar three dimensional basic equations for natural convection heat transfer caused by a step heat flux were numerically solved until the numerical solution reaches a steady-state. The PHOENICS code was used for the calculation considering the temperature dependence of thermo-physical properties concerned. The heated cylinder for diameter (D = 7.6 mm), heated length (L = 200 mm) and L/d (= 26.32), and the helical wire spacers for gaps (0–1 mm), pitches (100–200 mm), helical wire diameters (d = 1–2 mm) and height (H = 470 mm) were used in this work. The surface heat fluxes for each cylinder with helical wire spacer were equally given for a modified Rayleigh number, (Raf,L)w-s, ranging from 3.059 × 104 to 3.147 × 107 (q = 1 × 104 to 7 × 106 W/m2) in liquid temperature (TL = 673.15 K). The values of gap were given from 0 to 1 mm at d = 1.2 mm and a pitch of 165 mm, those of pitch were given from 100 to 200 mm at d = 1.2 mm and a gap of 0.2 mm and those of wire diameter were given from 1 to 2 mm at a gap of 0.2 mm and a pitch of 165 mm on each cylinder with helical wire spacer. The spatial distributions of local and average Nusselt numbers, (Nuθ,z)w-s and (Nuav)w-s, on each cylinder with helical wire spacer were clarified. The values of average Nusselt number, (Nuav)w-s, for a vertical cylinder with helical wire spacer were calculated to examine the effects of (Raf,L)w-s, gap, pitch and helical wire diameter on heat transfer. The correlation for (Nuav)w-s for a vertical cylinder with helical wire spacer above mentioned including the effects of (Raf,L)w-s, gap, pitch and helical wire diameter was developed. The correlation can describe the theoretical values of (Nuav)w-s for a vertical cylinder with helical wire spacer within −2.74 to 1.63% differences.

Numerical investigation of heat transfer by an impinging jet using alumina–water nanofluid

This article reports numerical investigations of turbulent flow field and heat transfer performance of water-alumina nanofluid jet impingement. The jet impinges over a flat, circular heated surface from a circular pipe of diameter . The influence of jet Reynolds number (1,200 ≤ ≤ 40,000), jet-outlet-to-target wall distance (2 ≤ ≤ 12.8), and particle volumetric concentration (0 ≤ φ ≤ 10%) on the fluid flow and heat transfer are examined. The results of fluid flow and heat transfer are compared with the published experimental data. It is found that the heat transfer increases with increasing values of the particle volumetric concentration while the flow field and turbulent kinetic energy distribution remain unchanged with the inclusion of nanoparticles. About 28% enhancement in stagnation Nusselt number is observed at low values of nanoparticle volumetric concentration (φ = 0.1%) and in the Reynolds number range of 29,000–40,000. For jet-outlet-to-target wall spacing values used in the current study, the local Nusselt number distributions vary according to Nu ∝ . Numerical simulations are performed using Reynolds-averaged Navier–Stokes method with the shear stress transport k-ω model in commercial CFD code ANSYS-CFX.

Thermal-Flow Characteristics of Ferrofluids in a Rotating Eccentric Cylinder under External Magnetic Force.

Heat dissipation has become an important issue due to the miniaturization of various electronic devices. Various methods such as spray and nozzle coolers, heat sinks and so on are used for heat dissipation. However, the emergence of ferrofluids drastically improves the operating characteristics of electromagnetic systems and devices. A ferrofluid is a suspension containing 10-nm magnetic particles in a colloidal solution. This material exhibits paramagnetic behavior and is sensitive to magnetic field and temperature. In this study, heat transfer characteristics of ferrofluids in a rotating eccentric cylinder were investigated using the commercial code, COMSOL Multiphysics. Numerical results of the local Nusselt number, magnetophoretic force and velocity distributions were obtained from various eccentricities of the cylinder, and the results were graphically depicted with various flow conditions.

Simultaneous measurement of velocity and temperature fields during natural convection in a water-filled cubical cavity

Many advanced schlieren systems have been reported in the literatures and a great number of it are associated in gas flow study, commonly air. Present research proposes an efficient use of Z-type schlieren technique for simultaneous measurement of ray-averaged velocity as well as temperature fields beside qualitative flow visualization. Experiments are conducted to study natural convective flow in de-ionized water in a differentially heated cubical enclosure. The same set of transient schlieren images has been used for simultaneous measurement of velocity and temperature field. The velocity field is also determined by using laser based particle image velocimetry (PIV) to compare with schlieren based technique. The developed schlieren system has been used to obtain ray-averaged quantities, such as, thermal and hydrodynamic boundary layer thicknesses, temperature gradient and temperature fields, distribution of local Nusselt number along the thermally active walls, average Nusselt number and velocity field. In this work, the above quantities have been simultaneously determined for the first time using halogen projector lamp based Z-type calibration schlieren system. The results inspire the use of calibration schlieren system for the study of natural convective flow in water-filled cubical enclosures. The above results also provide experimental data as new benchmark for researchers to compare results for high Rayleigh number free convective flow with water as the working medium.

Investigation of Heat Transfer and Flow Field Development Around a Low-Pressure Turbine Blade with the Use of Open Source CFD Tools

The present paper is focused on numerical investigations of the heat transfer and flow field development around a low pressure turbine blade (T106) with the use of computational fluid dynamics (CFD) tools and methods. The CFD computations were performed with OpenFoam open source CFD software with the use of the Shear Stress Transport (SST) low-Reynolds number turbulence model. At the first part of the present work, the CFD computations were validated in relation to available detailed isothermal experimental measurements and useful conclusions about the accuracy of the modelling approach and the flow field development were derived. At the next stage, additional CFD computations were performed for flow and thermal conditions adapted in order to reflect more closely the low-pressure turbine blade operation. In these CFD computations the interaction between the velocity and thermal boundary layers and their effect on the heat transfer was quantified through the derivation of the distribution of the local Nusselt number on the T106 surface, which was compared in relation to available correlations from open literature. Through the analysis of the CFD results it was possible to identify the regions on the low-pressure turbine surface in which decreased heat transfer performance was presented as a result of the non-optimum flow and thermal field development. Furthermore, through the CFD computations secondary flow effects resulting in operational efficiency decrease were identified. The elimination of these sources of operational decrease is planned to be the main target of future research efforts targeting the development of methodologies for the design of highly efficient turbomachinery components.

Lattice Boltzmann simulation of mixed convection of nanofluid with different heat sources in a double lid-driven cavity

In this study, mixed convection heat transfer of Al2O3/water nanofluid in a double lid-driven cubic cavity with different heat sources was numerically investigated. The lattice Boltzmann method (LBM) was developed to solve the governing equations. The effects of nanoparticle volume fraction, Reynolds number and Richardson number on heat transfer characteristics were examined. The results show that they have great effects on both velocity profiles and heat transfer performance. Additionally, the effects of different lid directions and heat sources on heat transfer were explored. It is found that the case of cold wall moving down and hot wall moving up double lid-driven cavity has the best heat transfer performance. Numerical results also indicate that different heat sources have significant impacts on both the local Nusselt number distribution on the hot wall and temperature field in the cavity. In order to improve the computation efficiency, the Open Multi-Processing (OpenMP) was employed for the parallelization of the proposed 3D LBM model. The phenomenon of super linear speedup was noted and discussed.

Heat Transfer Augmenation Using Nanofluid of a Confined Slot Impingement Jet on Concave Surface

Numerical investigation of heat transfer process using A12O3-water nanofluid in a confined slot jet impingement on concave surface is performed. The simulation is conducted on a two-dimensional turbulent flow with k –ω SST model for the turbulence computation. A constant heat flux is considered on concave surface. Different parameters such as various Reynolds numbers, and nozzle-to-surface spacing have been considered to study the flow field and convective heat transfer performance of the system. Results in form of distribution of local and average Nusselt number and Convective heat transfer coefficients at the curved surface are shown to elucidate the heat transfer and fluid flow process. In addition, qualitative analysis of both stream function and isotherm contours is carried out to perceive the flow pattern and heat transfer mechanism due to addition of nanofluids. The results reveal that average Nusselt number as well as heat transfer coefficient significantly rises with jet inlet Reynolds number. It is also proved that heat transfer is augmented when nanoparticles are added to a base fluid.

Experimental Investigation of Heat Transfer Enhancement in Rectangular Duct with Pentagonal Ribs

ABSTRACTRib turbulators are extensively used in augmentation of convective heat transfer in several applications related to heat exchange and cooling in thermal energy systems. Present experimental investigation examines the local heat transfer and friction factor characteristics of pentagonal ribs mounted on bottom heated wall of a rectangular channel. The emphasis is towards assessing and analysing the potential impact of varying chamfering angle (0 to 20°) and rib pitch to height ratio (6 to 12) on the overall heat transfer enhancement and its distribution on the surface. Experiments are performed at different Reynolds numbers ranging from 9400 to 58850. Liquid crystal thermography is applied to measure surface temperature distribution and finally to demonstrate the local heat transfer coefficient over the ribbed surface. The results depict that the local augmentation Nusselt number distribution is axisymmetric and shows 2-dimensionalty in heat transfer distribution. Pentagonal ribs show a significant improvement for the low heat transfer zones in leeward vicinity of the square rib, specially prominent at higher Reynolds number, and therefore seen as the potential benefit in terms of obviating the hotspots. It is observed that the pentagonal ribs lead to superior heat transfer enhancement in conjunction with significant reduction in pressure penalty as compared to square ribs and thus ensures an enhanced thermo-hydraulic performance.

Performance assessment of turbular heat exchanger tubes containing rectangular-cut twisted tapes with alternate axes

This paper describes the numerical results of the heat transfer enhancement mechanism of tubes containing rectangular-cut twisted tapes with alternate axes (ARC-TTs). Influence of the length of cut ratio (LR = L/w = 2.0, 2.4 and 2.8) and width of cut ratio (WR = W/w = 0.7, 0.8 and 0.9) on the heat transfer rate, friction factor and thermal performance characteristics are presented. The contour plots of predicted streamlines, velocity field, temperature field, and local Nusselt number distribution are also given for a better understanding of heat transfer mechanism. The results of the tube containing a classical twisted tape are also reported, for comparison. It can be observed that the use of ARC-TTs results in more disordered streamlines and higher turbulent intensity than that of the classical twisted tape. The numerical results also show that heat transfer and friction loss decrease as Length of cut ratio (LR) and Width of cut ratio (WR) increase while thermal performance factor shows reverse trend. In the studied range, utilizing ARC-TTs offers thermal performance factor up to 1.5.

Local effectiveness and Nusselt number distributions for a rectangular jet impinging on a cylindrical convex surface at different angles

Local effectiveness and Nusselt number distribution measurements for heated rectangular jets impinging perpendicularly and obliquely on a cylindrical convex surface are reported here. The jets exit from a rectangular nozzle of height ‘H’ and width ‘W’ with aspect ratios, H/W, equal to 10 and 5 and the corresponding the curvature ratios (ratio of hydraulic diameter of nozzle to diameter of the impinging convex surface), b/D, were equal to 0.083 and 0.076. Studies were conducted for non dimensional jet-to-target distances, L/b, equal to 2, 3, 4 and 5, and for inclination of jet axis with the convex target surface, θ, equal to 0°, 30° and 45°. The Reynolds numbers, Re (based on average exit velocity of jet and hydraulic diameter of nozzle) was kept constant at 17000.The entrainment of the fluid from the surroundings into the walljet from the top surface and edge regions, which is symmetric on the either side of the impingement zone for perpendicular impingement, gives a ‘rhombus like’ shape for the effectiveness contours. However, the entrainment is asymmetric for oblique impingement, with the drop in effectiveness rapid in the uphill side and gradual in the downhill side, giving the effectiveness contours a ‘kite like’ shape. The fluid entrainment from the top surface and edge regions influence the Nusselt number distribution also. The relatively higher mixing of the jet fluid with the ambient at the edge regions increases the turbulence and thereby increases the Nusselt number at these locations, resulting in contour shapes different from those observed for the effectiveness.

Investigation of impingement surface geometry effects on heat transfer in a laminar confined impinging slot jet

We investigated the laminar heat transfer characteristics of a milli-scale confined slot jet impinging on concave and convex surfaces at a uniform wall temperature. The flow at the nozzle exit had a fully developed velocity profile. The effects of Reynolds number, dimensionless nozzle-to-surface distance, and target surface geometry on heat transfer were investigated. The results revealed that the axial distributions of local Nusselt numbers exhibited a peak at the stagnation point and decreased monotonically in the wall jet region for all values of Re and H/B tested. The local Nusselt numbers for the concave surface were, at maximum, 47% larger than those for the convex surface in the region corresponding to x/B≤2.0. This is due to the larger unsteady lateral distortions and earlier flapping motion of the jet column for the convex surface than for the concave surface, resulting in a larger heat transfer reduction for the convex surface.

Modeling Coupled Conduction–Convection Ice Formation on Horizontal Axially Finned and Unfinned Tubes

The freezing of water around immersed unfinned and finned horizontal tubes is simulated numerically. The impact of natural convection as well as the water density inversion with temperature is considered. The equations governing both fluid flow and heat transfer around the tubes and through the solid–liquid interface are solved using finite difference schemes. To follow the moving solid–liquid boundary, dynamic grid generation is performed using the elliptic partial differential equation method with iterative interpolating smoothing to avoid divergence. For validation, the present results for unfinned tubes are compared with experimental studies reported in the literature. The present numerical simulations are aimed at improving our understanding of the parameters affecting the freezing process around both finned and unfinned tubes. The results showed that the flow patterns are similar in both tube configurations with one main vortex in the liquid region when there is no inversion in the water density. The presence of fins complicates the distribution of local Nusselt number along the solid–liquid interface in comparison with the unfinned tube. The impact of natural convection on the rate of ice formation is limited to the initial period of the freezing process. The results also show the freezing enhancement when utilizing fins. An accumulated ice mass correlation is developed for each tube configuration. This model can be used to optimize the design of both finned and unfinned tubes in energy storage systems, which are viable tools for air conditioning load shifting and leveling.

Boundary layer flow of nanofluid over a moving surface in a flowing fluid using revised model with stability analysis

This article reveals the boundary layer flow analysis of nanofluid past a moving surface in a uniform free stream with the physically more realistic approach by imposing both temperature and concentration fraction on the surface in such a way that nanoparticle concentration adjusts and flux becomes zero on the surface. In other word, nanoparticle fraction adjusts accordingly on the boundaries. The system of nonlinear ODEs is solved numerically using bvp4c function and shooting technique. With the help of various initial guesses, dual solutions are found up to a certain limit when the free stream and the plate are in the opposite directions. Then examined the stability of the solutions obtained using the method of stability analysis. The impact of various flow parameters on the skin friction coefficient and the local Nusselt number, the velocity, temperature and concentration distributions are conferred in detail. The reduced Nusselt number is estimated with the help of linear and quadratic regressions. For the validity, the comparison is made. Results indicate that the first (upper branch) solution is stable and thus, physically realizable. There is no effect on the reduced Nusselt number for any value of the Brownian motion parameter due to zero nanoparticle flux on the surface. On the other hand, the heat transfer rate decreases for higher values of the Schmidt number and thermophoresis parameter. The flow pattern behaved same as the stagnation point flow for the first (upper branch) solution but separated into two regions for the second (lower branch) solution.

Air-side thermal hydraulic performance of microchannel heat exchangers with different fin configurations

This paper presents three-dimensional steady state analysis of compact multi-louvered fin and flat tube heat exchangers applicable in domestic and mobile air conditioning systems. Conjugate heat transfer analysis has been conducted for five geometric configurations of the heat exchanger based on the louver pitch values (0.8, 1.0, 1.4, 1.7 and 2.0mm) in the laminar range of Reynolds number 50–450. For all geometric configurations, local air-side heat transfer coefficient and pressure drop are presented in terms of Colburn j factor and Fanning friction f factor, respectively. In addition, the effect of fin height on thermal hydraulic performance has also been addressed based on local Nusselt number distribution along the fin height. The results reveal that geometric configuration with the louver pitch of l.0mm showed the highest average Nusselt number of 123% at the penalty of 116% pressure drop compared to louver pitch of 2.0mm at the Reynolds number of 50.

Fluid flow and mixed convective heat transfer around a semi-circular cylinder at incidence with a tandem downstream square cylinder in cross flow

The present paper presents fluid flow and mixed convective heat transfer characteristics past a semi-circular cylinder at incidence with a tandem square cylinder in cross flow. Using air (Pr=0.71) as an operating medium, numerical simulations are performed for the range of Reynolds numbers, 10≤Re≤45 and incidence angles, 00≤α≤1800. The effect of thermal buoyancy is brought about by varying the Richardson number in the range 0≤Ri≤2. The mathematical model is firstly validated with the experimental and numerical results from the literature and found to be in good agreement. The steady separated flow is observed to become unsteady periodic under the superimposed thermal buoyancy. Furthermore, apart from thermal buoyancy effect, angle of incidence is found to play a pivotal role in bringing hydrodynamic instabilities and thereby vortex shedding for such steady mixed convective flows. Functional dependence of drag (CD), lift (CL), and moment (CM) coefficients on the combined influence of α and Ri, is explored and analysed in detail. Additionally, other global quantities, such as local and average Nusselt number distribution, Strouhal number (St) are determined with respect to the various ranges of parameters considered in the present investigation.

An analysis of turbulence models for prediction of forced convection of air stream impingement on rotating disks at different angles

In this study, the performance of seven turbulence models for the prediction of the flow and heat transfer in forced convection of jets and air streams impinging on a disk in different stationary, rotating and inclined rotating conditions are compared using a large number of experimental case studies. These models include four RANS models, i.e. k-ε RNG, k-ω SST, transition k-ω SST and RSM and three hybrid models, i.e. SAS, detached eddy simulation with transition k-ω SST and detached eddy simulation with realizable k-ε (DDES-RKE). Based on a detailed comparison and error analysis, it is shown that while no RANS model is found to perform well in all regions of the flow, DDES-RKE model can capture all flow, i.e. velocity and kinetic energy fields, and heat transfer, i.e. mean Nusselt number, features of the problem in excellent agreement with experiments in all regions of the flow and for all stationary, rotating and inclined rotating conditions. In addition, the local Nusselt number distribution predicted by these models are compared and analyzed carefully. It is observed that the presence and interaction of the swirling vortex and leading-edge flow bubble result in a complex local Nusselt number distribution with several extrema.