Dependence Of Nusselt Number Research Articles

Numerical modeling of natural convection heat transfer from radial branching heat sinks for LED cooling applications

Light Emitting Diodes (LEDs) have revolutionized the lighting industry due to their high energy efficiency. However, LEDs require effective thermal management to preserve their lifespan and luminous efficiency. In the current study, the design of a branching radial heat sink is numerically investigated and optimized for cooling LED panels of downlights under natural convection. Branching fins arranged radially on a horizontal circular plate were considered in the current study. The buoyant fluid flow over the heat sinks is observed and characterized using parameters such as fin length, height, inclination angle, and number. The dependency of Nusselt number, heat transfer coefficient and thermal resistance on the design parameters are explained by studying the buoyant fluid flow characteristics over the heat sink. Both heat transfer coefficient and thermal resistance decrease with geometric parameters such as fin length, height, and number. Due to branching, the Nusselt number decreases by 17% at lower fin lengths and by 20% at higher fin lengths, respectively. However, the thermal resistance of the heat sink arrays decreases by around 13% at lower fin lengths and remains constant at higher fin lengths due to branching. A comparative study is performed by plotting a contour map between the cooling performance of a radial branching heat sink and a radial flat plate heat sink using a heat transfer enhancement factor. Branching fins with angles above 25°and fin heights over 19 mm outperform plate-fin heat sinks of the same height and length for fin number n = 20. Finally, a correlation is proposed to predict the average Nusselt number of the fin arrays as a function of the design parameters.

Simulation for magnetic force impact on nanomaterial transportation through a porous closed curved container as a multi physics problem

It is a practical application to use porous zones for cooling systems of magnetic sensors. The importance of MHD (Magnetohydrodynamic) on the irreversibility of liquid within a chamber consisting of porous zone has been incorporated in current article. CVFEM (Control Volume based Finite Element Method) has been employed to model the simplified model obtained after employing the vorticity formula. Outputs indicated that the intensity of nanomaterial circulation increases as Ra increases, while it decreases with the inclusion of a magnetic field, which converts the heat transmission mode to conduction, and due to the appearance of a stretching eddy, the heat plume is removed. A reduction in permeability reflects an increase in the exergy drop, which means greater thermal irreversibility. A nonessential impact on the Bejan number (Be) distribution was reported with altering Darcy number (Da) if the buoyancy force was negligible. Regardless of the changing maximum magnitude of Be, augmenting Da results in lower Be. Due to the dependence of Nusselt number (Nu) on the inner surface temperature, Hartmann number (Ha) has a reverse relation with Nu, which means a lower cooling rate with the inclusion of Ha.

Heat transfer characteristics of mildly rarefied gaseous flows in the slip regime

The present numerical work aims to delineate the heat transfer characteristics present in mildly rarefied gaseous Nitrogen flows with comparable Knudsen number throughout the flow domain. The principal objective is to analyze the behavior of the resulting thermal flow field with an increasing degree of rarefaction and to establish the dependence of Nusselt number on Knudsen number and Reynolds number. The current analysis deals with the flow through an isothermally heated circular pipe with a temperature of 350K at the heating wall. The ranges of mean Knudsen numbers and Reynolds numbers considered in the analysis are (0.0009–0.09) and (20–0.004), respectively. These correspond to a pressure ratio less than 1.03 in all the test cases. The coupled set of governing equations are solved using the finite volume method algorithm SIMPLEC in FLUENT 2020-R2. The results are validated with the experimental results from Hemadri et al. [1] to authenticate the adopted solution methodology. Notably, with increasing Knudsen number, the fully developed Nusselt number is found to attain a maximum value of about 4.022 corresponding to Knudsen number ≈0.006 and Reynolds number ≈0.468. The fully developed Nusselt number starts dropping monotonically with a further rise in Knudsen number. The axial span of the thermally fully developed region is also observed to follow this pattern qualitatively with rising degree of rarefaction. Importantly, Brinkman number is seen to increase from about0 to 1 for each test case. All the same, the strength of viscous dissipation remains negligible in the complete flow domain. The rate of increase in the kinetic energy due to expansion work is observed to become marginally small with increasing rarefaction. These findings confirm that the rate of pressure work, viscous stress work at the wall, and viscous dissipation need not be considered for such practical situations. The defining factors that govern the overall heat transfer phenomena are advection, conduction, and the amount of non-equilibrium of the fluid parcels near the wall. These findings also defend the argument that the heat transfer correlations cannot be generalized in terms of Brinkman number or Peclet number only. Instead, they need to be formulated separately depending on the operating conditions of the problem.

On the thermofluidics of a steady laminar jet impacting on a rotating hot plate: An ab initio scaling perspective

We provide an ab initio scaling analysis for liquid film thickness and Nusselt number of a steady laminar jet impinging a rotating heated plate. We have probed the limiting scaling regimes by incorporating the evaporative effects at the liquid–vapor interface. The dependence of liquid film thickness and Nusselt number on Reynolds, Rossby, and Prandtl numbers has been unearthed using scaling analysis of the integral and differential form of the continuity, Navier–Stokes, and energy equation in a cylindrical coordinate system. Boundary layer analysis has been used to discover a critical length that plays a significant role in understanding the effect of evaporation on hydrodynamic, thermal boundary layer thicknesses, and subsequently Nusselt number. The evaporative effects on liquid film thickness become increasingly important after a certain critical radius. The scaling laws derived are compared with existing experimental data available in the literature, and the trends predicted were consistent.

Free convection and heat transfer characteristics in differentially heated finned cavities with inclination

Convection flow and heat transfer within differentially heated finned and non-finned cavities are numerically investigated at series of angle of inclination in this study. The present numerical results demonstrate that at the investigated Rayleigh number 1.84 × 109, for the non-finned cavity and at fully developed state, the flow is steady at Θ ≤ 25° and it bifurcates with multimodal evolution when Θ increases beyond 30°, where Θ denotes angle of inclination of the cavities. An examination of the spatial evolution of propagation of the travelling wave underneath the ceiling suggests that the corresponding flow is convectively unstable at large Θ, which, unlike the extensively studied Θ = 0° scenario, self-sustains a cavity-wide perturbation. The present finned-cavity calculations suggest that two flow regimes could be identified for the quasi-steady state. Regime I is featured with distinct plume-wraps-fin behaviour and it occurs at small Θ, while Regime II has no discernible plume-wraps-fin behaviour and it occurs at large Θ. It is further found that with tilting the cavity, the thermal stratification at the cavity centreline occurs over a narrower temperature range, whilst an increase in the velocity is clearly seen for both the non-finned and finned cavities. Flow rate across the cavity centreline is found to fluctuate in the quasi-steady state and its time averaged value dramatically improves with Θ. Heat transfer is estimated by integrating the local Nusselt number at the heated sidewall. The present work shows that immediately after the cavity is inclined, the Nusselt number is first increased. Further tilting the cavity will lead to a steady drop in the Nusselt number. It is demonstrated that the dependency of Nusselt number on Θ is similar for the non-finned and finned cavities with Nu of the finned cavity larger by approximately 5%.

Mass/Heat Transfer Analogy Method in the Research on Convective Fluid Flow through a System of Long Square Mini-Channels.

The paper presents the results of experimental investigations of mass transfer processes with the use of the limiting current technique. This experimental work analyzed the not fully developed entrance laminar region. The tested case refers to the convective fluid flow through a system of nine long, square mini-channels that are 2 mm wide and 100 mm long. The method used in the measurements allows one to determine mass transfer coefficients during the electrolyte flow by utilizing electrochemical processes. The received mass transfer coefficients were applied to the analogous heat transfer case. The Chilton–Colburn analogy between mass and heat transfer was applied. The obtained results, in the form of the dependence of Nusselt number within the function of Reynolds and Prandtl numbers, can be a useful formula in the design and analysis of heat transfer processes in mini heat exchangers.

Particle Scale Investigation of Influencing Factors on Heat Transfer in Nonspherical Particle–Fluid System

Abstract Heat transfer characteristics of random suspensions of 0.25 aspect ratio (AR) cylinders are investigated for Reynolds numbers (Re) between 10 and 300 and solid fraction (φ) ranging from 0.1 to 0.3 using particle resolved simulations. The effect of particle inclination with respect to flow and particle clustering on heat transfer is investigated. The Nusselt number decreases with an increase in inclination angle and the dependence becomes stronger as φ and Re increase. On the other hand, while prolate ellipsoid suspensions of AR 2.5 follow the same trend, the Nusselt number increases with inclination angle as AR increases to 5 and 10 and as φ increases. Local particle clustering nominally decreases the Nusselt number because of the dominance of thermal wakes. At low φ, this effect is felt only at low Re, but as φ increases, the effect spreads to higher Re. Similar but weaker trends are also found in suspensions of prolate ellipsoids of AR 2.5, 5, and 10. High AR, low Re prolate ellipsoids exhibit the greatest dependence of Nusselt number on local solid fraction. Implementation of two independent definitions of reference length, i.e., volume equivalent sphere diameter deq for ellipsoids and diameter dp of the cylindrical particle in the correlation of Tavassoli et al. (2015, “Direct Numerical Simulation of Fluid-Particle Heat Transfer in Fixed Random Arrays of Non-Spherical Particles,” Chem. Eng. Sci., 129, pp. 42–48) provides good estimates of the respective suspension mean Nusselt numbers.

Entropy generation and natural convection on a cubic cavity with a pair of heat source at different configurations

Entropy generation and natural convection in a discretely heated cubic air-filled cavity has been numerically investigated in this study. A pair of discrete heat sources located at the bottom wall is at first considered for three different configurations. Both side walls are fixed at ambient condition, while the remaining walls are kept insulated. The three-dimensional, time-dependent continuity, momentum and thermal energy equations are selected as the governing equations of the present analysis. Galerkin finite element method is employed to solve those equations in non-dimensional forms. Parametric investigation is carried out by varying Rayleigh number within the range of 103–106 at fixed Prandtl number of 0.71. Results are presented in terms of qualitative plots of 3D velocity and thermal fields, and the quantitative evaluation of average Nusselt number and total entropy generation. A functional dependence of Nusselt number on the Rayleigh number and the distance between the symmetrically positioned heaters has also been presented in terms of empirical correlation. This comparative study shows that the configuration of the heaters has a great impact on the thermal characteristics, and thus provides one the opportunity to obtain an optimum arrangement for the system.

Impact of different arrangements of heated elliptical body, fins and differential heater in MHD convective transport phenomena of inclined cavity utilizing hybrid nanoliquid: Artificial neutral network prediction

In the current scenario, the impact of different arrangements of solid heated elliptical body, discrete heater (LH/H), array of fins with different sizes (1×2, 2×1, 2×2), conductivity ratio (r), magnetic field (Hartmann number, Ha), angle of inclination (β), nanoparticle volume fraction (χ) and Rayleigh number (Ra) is investigated for natural transport phenomena in the cavity containing hybrid nanoliquid. The cavity consists of three equally spaced fins on one wall and heated elliptical body inside the cavity. The homogeneous hybrid nanoliquid (Al2O3-Cu/water) model using experimental data is utilized and results are evaluated for different controlling parameters: Rayleigh numbers (Ra=103 to 106), Hartmann number (Ha=0 to 100), discrete heater (LH/H=0.1 to 0.9), angle of elliptical body (ω=0° to 180°) with three different positions (Center, POS I and II), angle of inclination (β=0 to π), thermal conductivity ratio (r=0.01–100), nanoparticle volume fraction (χ=0 to 0.02) using Galerkin Finite Element Method (GFEM). The mesh grid independency test is also performed for different combinations of meshes and a refined mesh with optimal degrees of freedom (DoFs=190275) has been considered for entire convection range (Ra=103−106).The impact of controlling parameters on average Nusselt number evaluated from the numerical heat transfer analysis has been compared and predicted using feed forward neural network model. The Levenberg-Marquardt back propagation algorithm is used for ANN training based on limited simulated data with optimal number of neurons and average R2 of 0.99988. The quadratic regression model, which is also determined using the MATLAB built-in subroutine ’fitlm’, demonstrates the greatest dependency of Nusselt number on nanoparticle concentration.

Buoyancy Driven Flow, Heat Transfer, and Entropy Generation Characteristics for Different Heater Geometries Placed in Cryogenic Liquid: A Computational Fluid Dynamics Study

Abstract The present work reports a 3D computational study of buoyancy-driven flow and heat transfer characteristics for a localized heater (analogous to superconductor) submerged in cryogenic liquid nitrogen in an enclosure. Seven different heater geometries are considered and the effect of heater geometry on flow and heat transfer characteristics is illustrated. The heater is generating heat at a constant rate (W/m3). Continuity, momentum, and energy equations are solved using the finite volume method. Liquid flow and heat transfer features are demonstrated with the help of velocity vector and temperature contours. Rayleigh number, average Nusselt number, the maximum vertical velocity of fluid flow, and the average velocity of fluid flow are the parameters that are considered for comparing seven different geometries of the heater. Additionally, an analysis of the entropy generation owing to the transfer of heat and friction due to fluid flow is reported. Furthermore, the dependency of average Nusselt number, maximum velocity of the fluid, entropy generation owing to transfer of heat, and fluid friction as a function of heat generation rate is illustrated graphically. The results of this study indicate that heater geometry can considerably affect the transfer of heat, fluid flow features, and entropy generation under the same heat generation rate in the heater. The highest average Nusselt number on the heater surface is obtained when heater geometry is circular, whereas the lowest value of total entropy generation in the domain is obtained when heater geometry is an equilateral triangle.

Investigating heat transfer in an upward flow of liquid metal in the mercury facility with a loop of natural circulation

Research of heat transfer is performed in an upward flow of liquid metal in a vertical channel of rectangular cross-section under the condition of one-sided heating and in a vertical pipe in a mercury circuit with a natural circulation loop. Natural circulation loop enables measurements in mixed turbulent convection modes, which are inaccessible on a contour with a forced convection, that is, in the region of small Reynolds (Peclet) numbers of characteristics. Using a two-coordinate probe with a microthermocouple correlation sensor, profiles of averaged velocity and temperature and distribution of a wall temperature are obtained, and heat transfer coefficients are determined. Criterion dependences of Nusselt number on Peclet and Richardson are built. Experimental data on heat transfer are compared with similar data obtained earlier in a loop with a forced flow of mercury.

Convective heat transport in yield stress nanofluids in a differentially heated square enclosure

ABSTRACT In the present study, flow and heat transfer characteristics of some yield stress nanofluid filled in a differentially heated square enclosure are investigated. The rheology of the fluid is modeled by regularized Bingham model. The effects of Rayleigh number in the range of 5 × 103 to 5 × 106, Bingham number between 0 and 2, nanoparticle volume fraction varying between 0% and 5% and Prandtl number ranging 5 to 100 on the natural convection of yield stress nanofluid has been investigated. The phenomenon is explained through velocity, temperature distribution and contour plots of streamlines and isotherms. The rate of thermal transportation through test fluids rises with an increase in Rayleigh number and volume fraction, while it falls as yield stress and Prandtl number is increased. Dependency of mean Nusselt number is more pronounced on nanoparticle addition, rather than its yield stress. A correlation of mean Nu has been proposed. All predicted values of mean Nu are obtained to be within ±13% band.

The effects of thermal boundary conditions on the heat transfer characteristics of laminar flow in milli-scale confined impinging slot jets

This study experimentally investigated the effects of thermal boundary conditions on the laminar heat transfer characteristics of milli-scale, confined slot jets with flat, convex, and concave surfaces. We explored two thermal boundary conditions at the impinging surface: uniform heat flux and uniform wall temperature. The Reynolds number (Re) ranges from 120 to 600, the dimensionless nozzle-to-surface distance (H/B) from 2 to 10, and the dimensionless curved surface diameter-to-nozzle width (D/B) is 90. The results show that near the stagnation region, local Nusselt numbers for all three surfaces increase at each x/B location as H/B changes from 10 to 2 regardless of thermal boundary condition. In the wall jet region, However, in the wall jet region the uniform heat flux condition produces higher Nusselt numbers than the uniform wall temperature. As a result, local Nusselt numbers for both thermal boundary conditions show cross-over regions at x/B=1-5 where the dependence of local Nusselt number on H/B changes, depending upon the x/B location. These behaviors illustrate the sensitivity of Nusselt numbers for laminar boundary layer and laminar slot jet flows to thermal boundary condition. Empirical correlations for both stagnation and local Nusselt numbers with a concave surface are in an agreement with the experimental results to within ±15%.

Low-Speed DSMC Simulations of Hotwire Anemometers at High-Altitude Conditions

Numerical simulations of hotwire anemometers in low-speed, high-altitude conditions have been carried out using the direct simulation Monte Carlo (DSMC) method. Hotwire instruments are commonly used for in-situ turbulence measurements because of their ability to obtain high spatial and temporal resolution data. Fast time responses are achieved by the wires having small diameters (1–5 μm). Hotwire instruments are currently being used to make in-situ measurements of high-altitude turbulence (20–40 km). At these altitudes, hotwires experience Knudsen number values that lie in the transition-regime between slip-flow and free-molecular flow. This article expands the current knowledge of hotwire anemometers by investigating their behavior in the transition-regime. Challenges involved with simulating hotwires at high Knudsen number and low Reynolds number conditions are discussed. The ability of the DSMC method to simulate hotwires from the free-molecular to slip-flow regimes is demonstrated. Dependence of heat transfer on surface accommodation coefficient is explored and discussed. Simulation results of Nusselt number dependence on Reynolds number show good agreement with experimental data. Magnitude discrepancies are attributed to differences between simulation and experimental conditions, while discrepancies in trend are attributed to finite simulation domain size.

Mixed convection in the heated semi-circular lid-driven cavity for non-Newtonian power-law fluids: Effect of presence and shape of the block

The present work delineates the hydrodynamics and thermal characteristics due to mixed convection in the lid-driven semi-circular cavity affected by the presence of the adiabatic block at its geometric center for two-dimensional, steady-state, laminar and for non-Newtonian power-law fluids. The semi-circular cavity has a diameter of D . The horizontal wall/lid is sliding with a uniform horizontal velocity ( u = U ) and is subjugated to the ambient thermal condition; while the curved surface is subjugated to a higher isothermal temperature. The convective characteristics inside the system is explored for the broad range of Richardson number (0.1 ≤ Ri ≤ 10), Prandtl number (1 ≤ Pr ≤ 100) and non-Newtonian power-law index (0.5 ≤ n ≤ 1.5) at a constant Grashof number of 10 4 . Apart from this, the effect of shape (cross-section) of the inserted block, i.e. , circular, square and triangular on heat transfer characteristics has also been explored. It is observed that the shear thickening fluids display better cooling characteristics. Besides, the cavity with immersed triangular block shows better heat transfer results than the circular and square blocks. The deviations observed in the flow and heat transfer characteristics in the cavity by inserting an adiabatic block as compared with cavity without block have been ascertained by calculating normalized Nusselt number ( Nu N ). The presence of the block was found to have a diminishing effect on the heat transfer due to convection in the cavity. In the end, the results of the study are summarized in the form of a predictive correlation exhibiting the functional dependence of average Nusselt number with Prandtl number, power-law index, and Richardson number.

Heat transfer of a spherical element with air-water aerosol in a cylindrical channel

The heat transfer from a single sphere suspended in a cylindrical channel with finely dispersed air-water (aerosol) flow is experimentally studied. Under stationary heating conditions, the values of the heat-transfer coefficients are obtained as dependent on the Reynolds number and the water mist rate. A physical model of heat transfer from the sphere surface with water mist-air flow is proposed, which allows evaluating the processes proceeding at the various stages of droplet evaporation in the flow near a heated surface and formation of a water film on the surface itself. The relative mass of the droplet moisture deposited on the sphere surface is estimated depending on the water mist rate and Reynolds number of the flow. A criterial equation is obtained that generalizes the experimental data in the form of the dependence of Nusselt number on the regime parameters of Reynolds, Weber, and the water-to-steam phase transition parameter is obtained.

The water heat pump operation under frost conditions on the evaporator surface

The conditions and characteristics of ice formation on the pipe surface of a heat pump evaporator which depends on water ( at a temperature lower than 280 K) as a low-grade energy source are investigated experimentally. Under the operating conditions of this heat pump, the ice thicknesses and temperatures values at freon pipe wall and for water in the evaporator are registered. The results allowed us to make a conclusion of the possibility to use a water source heat pump in practical applications under the conditions of partial ice coverage for the evaporator surface to heat up water in a condenser to 313 K. It is established from experiments that with the decrease in water initial temperature in the evaporator by 6 degrees, the maximum value of formed ice thickness on the evaporator surface is increased by 30 %. The dependence of Nusselt number on the natural convection characteristics undergoing phase change is established.

МАТЕМАТИЧЕСКОЕ МОДЕЛИРОВАНИЕ ПРОЦЕССОВ ТЕПЛОПЕРЕНОСА ПРИ РАБОТЕ ТЕПЛОНАСОСНЫХ СИСТЕМ ИСПОЛЬЗОВАНИЯ ГЕОТЕРМАЛЬНОЙ ЭНЕРГИИ

Актуальность. Использование теплонасосных установок для отопления вместо традиционных систем, которые получают энергию в процессе сжигания различных видов топлива, имеет ряд экологических и экономических преимуществ. Тепловые насосы могут получать энергию из воздуха, грунта и воды. Их сферы применения разнообразны: горячее водоснабжение и кондиционирование помещений, нагрев и охлаждение воды для различных нужд, сушки/осушения воздуха, производства пара, испарения, дистилляции. При применении природных водоёмов (озёра, пруды, водохранилища) в качестве низкопотенциального источника энергии теплонасосных установок на поверхности трубки испарителя образуется лёд. Важно рассматривать закономерности и характеристики процессов теплообмена между водой и трубкой испарителя при образовании льда на её поверхности. Цель: математическое моделирование нестационарного конвективного теплообмена между водой и трубками испарителя теплонасосных установок в условиях формирования льда на их поверхности. Объект: теплообменник испарителя теплового насоса, погружённый в воду. Методы: численное решение задач конвективного теплообмена в условиях фазового перехода воды методом конечных элементов в среде COMSOL. Результаты. Установлены закономерности нестационарного конвективного теплопереноса вблизи трубок испарителя водяного теплового насоса с температурой, при которой образуется лёд на их поверхности. Показана необходимость учета влияния термогравитационной конвекции в воде на тепловой поток и процесс образования льда на поверхности трубки испарителя теплонасосной установки. Получены зависимости числа Нуссельта от характеристики конвективного теплообмена в воде (чисел Рэлея, Фурье и Стефана). Выявлено, что перепад температур в воде вблизи трубки увеличивался при уменьшении глубины её расположения относительно поверхности водного источника при показателях температур воды выше 277 К. При температурах воды ниже 277 К тепловой поток достигал максимального значения у поверхности трубки, которая находилась глубже.

Specifics of heat flux from localized heater in a cylindrical layer

Thermal convection from a localized heat source in a cylindrical layer was studied experimentally. Experiments were done for Rayleigh numbers from 3.4·105 to 4.5·107 and different Prandtl numbers (38, 67, 209). The main problem of the study was the impact of boundary layer flows on the heat transfer. We demonstrated that for the chosen interval of Rayleigh number secondary flows are characterized by remarkable variation of their structure and intensity. It was found that the power law that describes dependence of Nusselt number on Rayleigh number for the considered experimental configuration does not respond to the transformation of the boundary layer convective structures. Physical interpretation of this result is proposed.

Numerical simulation of turbulence arising in the free convection boundary layer after a cross row of rectangular obstacles

The contribution covers results of direct numerical simulation of transitional processes and turbulence developing in the vertical-plate free convection boundary layer downstream of a periodic row of 3D obstacles. The Prandtl number is set at 0.7. Periodicity conditions are prescribed in the spanwise direction. Steamwise position of the obstacles being spanwise-elongated rectangular parallelepipeds corresponds either to the local Rayleigh number, Rax equal to 109 or to Rax = 2.5·108 . In the first (basic) case, 3D vortex structures of a wide spectrum start to develop at a relatively short distance from the obstacles. The largest-in-size vortices, occupying the outer part of the layer, have a hairpin-like shape, and their heads are oriented opposite to the main flow direction. Steamwise evolution of the transitional and turbulent flow structure is analysed based on iso-surfaces of the Q-criterion covering the flow region up to Rax = 2.6·1010. The predicted mean Nusselt number dependence on Rax is in a good agreement with the known measurement data, both for the transitional and the turbulent flow regions. For the second case, nonlinear spatial development of a nearly 2D instability wave occupying a large portion of the computational domain is predicted. Rapid destruction of this wave and occurrence of chaotic 3D eddies are observed in this case at Rax = 3 • 109.