Results For Average Nusselt Number Research Articles

PARAMETRIC STUDY AND DEVELOPMENT OF A CORRELATION FOR NUSSELT NUMBER IN NANOFLUID JET IMPINGEMENT

Numerical simulations for nanofluid ( water with Al<sub>2</sub>O<sub>3</sub> nanoparticles) jet impinging perpendicularly on a flat circular heated p late have been performed. A heated p late is subjected to constant heat flux boundary condition. A two-phase modified mixture mo del was used for the prediction of heat transfer coefficient, and comparisons are made with standard mixture model. Present results for average Nusselt number are validated with experimental data available in the literature. Though a standard mixture model predicted heat transfer with accepted accuracy, it was found that accuracy of modified mixture model is better (around 5% improvement) compared to standard mixture model. Thereafter, parametric study was performed considering nozzle exit Reynolds number (Re), spacing ratio (<i>H/D</i>), nanoparticle volume fraction (φ), and nanoparticle diameter (dp) on heat transfer prediction. The results reveal that particle diameter in the range 10-100 nm has no effect on the Nusselt number, Furthermore, heat transfer increased with increasing Reynolds number and volume fraction. However, spacing ratio shows first increasing and then, decreasing trend (similar to a log-normal distribution curve) in the prediction of heat transfer. Finally, a new correlation was developed for Nusselt number using nonlinear regression analysis. In the correlation, a two-phase multiplier was used, which is the ratio between two-phase Nusselt number (Nu<sub>nf</sub> ) and single-phase Nusselt number (Nu<sub>sp</sub>). The simplified correlation is found to predict data with maximum error of 8.9%, average error of 2.74% and <i>R</i><sup>2</sup> = 0.955.

Solar air heater performance enhancement with differently shaped miniature combined with dimple shaped roughness: CFD and experimental analysis

A numerical study was carried out in a solar air heater (SAH) using different shapes of miniature (V, arc and transverse broken-miniature) combined with dimples on an absorber panel to improve heat transfer. For an experimental and simulation study using ANSYS (Fluent), a dimple with a V-miniature rib was fabricated on a plate (absorber) as a roughness element. By providing the angle of attack (α), relative long way (RLL) length (l/d), relative height (roughness) and relative wire lengths (w/Dh) ranging from 45 to 75°, 15–25, 0.024–0.036 and 0.14–0.21 respectively. The thermohydraulic performance (THP) factor of the proposed roughness was also investigated at Reynolds numbers (Re) ranging from 5000 to 20000. Results of average Nusselt number, turbulent kinetic energy (TKE), fluid flow characteristics and temperature are included to analyse the comparative merits of each dimple with miniature arrangements. The results revealed that among dimples with different miniatures, 90° transverse broken-miniature with dimple shows best thermohydraulic performance at Re below 10,000 while a dimple with V-miniature at an angle of attack (α) 45° shows the highest thermohydraulic performance at Re above 8750. It was found that THP achieved a maximum value of 1.63 at α = 45°, l/d = 20 and w/Dh = 0.18 at Reynolds number 12,500 for the dimple with a V-miniature rib.

Mixed convection from semi-circular cylinder in Bingham plastic fluids: Adding buoyancy

Mixed convection heat transfer from a heated semi-circular cylinder in Bingham plastic fluids with adding buoyancy configuration has been studied numerically. Extensive results of fluid flow and heat transfer characteristics are presented in terms of the velocity and temperature profiles, shape and size of yield/unyielded zone. In the steady flow regime, Reynolds number, Prandtl number, and Richardson number are expected to be positively dependent on the average Nusselt number (which decreases the convection boundary layer). In contrast, the average Nusselt number decreases as the value of the Bingham number increases from its maximum value in Newtonian media to its conduction limit when most of the fluid is frozen.. Finally, using a simple expression, the numerical results of average Nusselt number have been predicted in terms of the j-factor for new applications.

COMPUTATION OF GOLD-WATER NANOFLUID NATURAL CONVECTION IN A THREE-DIMENSIONAL TILTED PRISMATIC SOLAR ENCLOSURE WITH ASPECT RATIO AND VOLUME FRACTION EFFECTS

Nanofluids are increasingly being deployed in numerous energy applications owing to their impressive thermal enhancement properties. Motivated by these developments in the current study we present finite volume numerical simulations of natural convection in an inclined 3-dimensional prismatic direct absorber solar collector (DASC)containing gold-water nanofluid. Steady-state, incompressible laminar Newtonian viscous flow is assumed. The enclosure has two adiabatic walls, one hot (solar receiving) and one colder wall. ANSYS FLUENT software(version 19.1) is employed. The Tiwari-Das volume fraction nanofluid model is utilized to simulate nanoscale effects and allows a systematic exploration of volume fraction effects. The effects of thermal buoyancy (Rayleighnumber), geometrical aspect ratio and enclosure tilt angle on isotherm and temperature contour distributions are presented with extensive visualizationin three dimensions. Grid-independence tests are included. Validation with published studies from the literature is also conducted. A significant modification in vortex structure and temperature distribution is computed with volume fraction, Rayleigh number, aspect ratio and tilt angle. Heat flux and average Nusselt number results are also included. Gold nano-particles even at relatively low volume fractions are observed to achieve substantial improvement in heat transfer characteristics.

Numerical investigation of heat transfer enhancement and fluid flow characteristics in a microchannel heat sink with different wall/design configurations of protrusions/dimples

The convective cooling associated with Microchannel heat sink (MCHS) devices for electronic components with high power density is a recent topic of cutting-edge research. However, thermal improvement with minimum degradation in hydrodynamic characteristic by extending the effective heat transfer area of different walls of MCHS is still a major challenge. In this regard, the heat transfer enhancement and fluid flow behavior of MCHS with protrusions, dimples and their different wall, geometric and design combinations are numerically studied in the present study. The wall configurations considered for the present analysis includes: Base wall protrusions/dimples (BWP/D), Side wall protrusions/dimples (SWP/D) and all walls protrusions/dimples (AWP/D). While for design configurations, the (AWP/D-Aligned), (AWP/D-staggered) and all wall protrusions and dimples mix (AWPD-Mix) cases are considered. The governing equations are discretized and solved across the computational domain using commercial computational fluid dynamics code with three-dimensional conjugate laminar flow model. The numerical model is then validated with experiment and theory in the literature and reasonable agreement in the results of average Nusselt number (Nuavg) and apparent friction factor (fapp) are observed. The effect of geometric parameters i.e. protrusion/dimple’s diameter (Dfr = 200 - 230 μm) and Pitch (Sfr = 400 - 1200 μm), operating parameters i.e. Reynolds number (Re = 100–1000) and Heat flux (qw = 50–100 W/cm2) on the heat transfer and fluid flow characteristics are examined to provide a better physical understanding of the energy management. The results indicate that the addition of protrusions/dimples to different walls of MCHS significantly improves the heat transfer with reasonable increase in pressure drop. The fluid flow pattern with the addition of the protrusions/dimples to different walls is improved through better mixing and lower pumping power augmentation to transport the same heat load than Straight MCHS. The favorable configuration along with geometric and operating parameters in terms of better thermal and hydrodynamic performance is suggested based on thermal enhancement factors (ƞ) and entropy generation rates ($$ {\dot{\mathrm{S}}}_{\mathrm{gen}} $$). Among the proposed wall configurations, AWP demonstrates superior thermal performance by resulting in maximum improvement of 82% in ƞ compared to BWP configuration. When compared to the straight MCHS, AWP-aligned MCHS achieved maximum enhancement of 115% in Nuavg at the cost of 152% higher fapp at same operating conditions of Re = 1000 and qw = 100 W/cm2 for design configurations. Furthermore, the outcomes of this study is expected to provide some important guidelines for the future experiments on such MCHS devices for energy saving and management.

Dynamic Nanoparticle Aggregation for a Flowing Colloidal Suspension with Nonuniform Temperature Field Studied by a Coupled LBM and PBE Method

Due to the high surface energy, aggregation of particles in colloidal dispersions is almost inevitable. In the present study, a comprehensive model was established by coupling a two-phase lattice Boltzmann method (LBM) and population balance equations (PBEs) to describe the dynamic particle aggregations in flowing and heated colloidal suspensions. Typically, the dynamic aggregations in suspensions under natural convection in a rectangular enclosure are investigated. The real-time particle size distribution (PSD) significantly depended on Ra (Rayleigh numbers), concentration, and enclosure geometry, where increasing particle concentrations can inevitably increase the particle size, but the effect of Ra on PSD is different when enclosure geometry changes. The results of average Nusselt number (Nuave) suggested a significant negative impact of particle aggregation on the heat transfer, especially for high concentration and low Ra cases. Our work should be of value when the properties of practical colloidal d...

ANALYSIS OF LAMINAR FORCED CONVECTION INSIDE A SQUARE VENTILATED CAVITY USING THE OPENFOAM®

Laminar forced convection inside a square cavity with inlet and outlet ports was numerically analyzed. The positions of the inlet and outlet ports were fixed and the ports sizes were equal 25% of the side wall. The influence of the Reynolds and Prandtl numbers on the flow and temperature fields inside the cavity was verified for nine cases, with Re = 50, 100 and 500 and Pr = 0.7, 3 and 5. The heat transfer process in the cavity was analyzed from obtained values for the average Nusselt number and the local Nusselt number on the walls. The open source computer package OpenFOAM® was used for simulations considering a two-dimensional flow. For all tested Prandtl numbers, there is a growth in the rotating vortex regions as Reynolds number is increases. The temperature fields are directly related to the presence of the rotating vortices and the temperature gradient is more noticeable at the interface sections of the throughflow stream with the neighboring vortices and the next to the walls for greater Reynolds and Prandtl numbers. It was verified that the local Nusselt number on the walls varies radically with minimum and maximum points and it is dependent on the flow and temperature fields adjacent to the respective wall. The results for average Nusselt number per wall indicated that the bottom wall is the most susceptible to variations in its average Nusselt number and that the top wall present higher values of this parameter for all tested cases. Finally, the average Nusselt number was increased with increasing the Reynolds and Prandtl numbers indicating the enhanced thermal exchange.

Unsteady convective heat transfer in cross flow past two tandem cylinders: an inverse heat conduction approach

Series of experiments were conducted in order to develop empirical correlations to predict average Nusselt number on different segments of each of the two tandem cylinders and the overall average Nusselt number for unsteady state heat transfer in cross flow of air past tandem cylinders under constant heat flux supply condition. The unsteady-state Nusselt number distributions over the cylinders surface were determined using inverse heat conduction approach. During experimentation, the center-to-center spacing between the cylinders was varied from 1.2 to 4.0 times the cylinder diameter and that the Reynolds number from 1.1 × 104 to 6.2 × 104. The air was allowed to flow past the tandem cylinders for few fraction of a second only. A curve of constant C was plotted as a function of spacing ratio, which was used in the empirical correlation to determine overall average Nusselt number. The mean deviation of overall average Nusselt number predicted from the developed correlation was found within ±2.9% from the experimental values. From the results of average Nusselt number, the maximum heat transfer condition was obtained at spacing ratio of 2.2.

MHD natural convection flow in cavities filled with square solid blocks

Purpose – The purpose of this paper is to study the influence of magnetic field on natural convection inside the enclosures partially filled with conducting square solid obstacles. Also, the effect of thermal conductivity ratio between the solid and fluid materials is investigated for different number of solid blocks. Design/methodology/approach – The dimensionless governing equations are transformed into sets of algebraic equations using finite volume method and momentum equations are solved by the SIMPLE algorithm with the hybrid scheme. The validation of the numerical code was conducted by comparing the results of average Nusselt number with previously published works. Findings – The results indicate that both the magnetic field and solid blocks can significantly affect the flow and temperature fields. It is shown that for a given Rayleigh number, variation of Nusselt number might be increasing or decreasing with change in solid-to-fluid thermal conductivity ratio depending on magnetic field strength and number of solid blocks. Originality/value – No work has been reported previously on the effect of magnetic field on natural convection flow in a cavity partially filled with square solid blocks. The numerical analysis of conductivity ratio between the solid and fluid materials under the effect of magnetic field have been carried out for the first time.

Performance predictions of laminar heat transfer and pressure drop in an in-line flat tube bundle using an adaptive neuro-fuzzy inference system (ANFIS) model

This paper shows how to predict the heat transfer and pressure drop for in-line flat tube configuration in a crossflow, using an adaptive neuro-fuzzy inference system (ANFIS). A numerical study of a 2D steady state and incompressible laminar flow for in-line flat tube configuration in a crossflow is also considered in this study. A finite volume technique and body-fitted coordinate system is used to solve the Navier–Stokes and energy equations. The Reynolds number varies from 10 to 320. Heat transfer and pressure drop results are presented for a tube configuration at transverse pitch and longitudinal pitch. The variation in velocity profile, isotherm contours and streamlines were compared for various configurations. The predicted results for average Nusselt number and dimensionless pressure show a good agreement with available previous work. The accuracy between numerical values and ANFIS model results were obtained with a mean relative error for average Nusselt number, pressure drop less than 1.9% and 2.97% respectively. Therefore, the ANFIS model is capable of predicting the performance of thermal systems in engineering applications, including the model of the tube bundle for heat transfer analysis and pressure drop.

Comments on ‘Lattice Boltzmann simulation of alumina-water nanofluid in a square cavity’ by Yurong He, Cong Qi, Yanwei Hu, Bin Qin, Fengchen Li and Yulong Ding

This work presents some comments concerning the paper entitled ‘Lattice Boltzmann simulation of alumina-water nanofluid in a square cavity’ by Yurong He, Cong Qi, Yanwei Hu, Bin Qin, Fengchen Li and Yulong Ding which was published in Nanoscale Research Letters in 2011. The comments are related to the numerical parameters and the computed results of average Nusselt number.

Numerical investigation of fluid flow and heat transfer under high heat flux using rectangular micro-channels

A 3D-conjugate numerical investigation was conducted to predict heat transfer characteristics in a rectangular cross-sectional micro-channel employing simultaneously developing single-phase flows. The numerical code was validated by comparison with previous experimental and numerical results for the same micro-channel dimensions and classical correlations based on conventional sized channels. High heat fluxes up to 130W/cm2 were applied to investigate micro-channel thermal characteristics. The entire computational domain was discretized using a 120×160×100 grid for the micro-channel with an aspect ratio of (α=4.56) and examined for Reynolds numbers in the laminar range (Re 500–2000) using FLUENT. De-ionized water served as the cooling fluid while the micro-channel substrate used was made of copper. Validation results were found to be in good agreement with previous experimental and numerical data [1] with an average deviation of less than 4.2%. As the applied heat flux increased, an increase in heat transfer coefficient values was observed. Also, the Reynolds number required for transition from single-phase fluid to two-phase was found to increase. A correlation is proposed for the results of average Nusselt numbers for the heat transfer characteristics in micro-channels with simultaneously developing, single-phase flows.

Double-diffusive convection in a cubical lid-driven cavity with opposing temperature and concentration gradients

A numerical study of three-dimensional incompressible viscous flow inside a cubical lid-driven cavity is presented. The flow is governed by two mechanisms: (1) the sliding of the upper surface of the cavity at a constant velocity and (2) the creation of an external gradient for temperature and solutal fields. Extensive numerical results of the three-dimensional flow field governed by the Navier-Stokes equations are obtained over a wide range of physical parameters, namely Reynolds number, Grashof number and the ratio of buoyancy forces. The preceding numerical results obtained have a good agreement with the available numerical results and the experimental observations. The deviation of the flow characteristics from its two-dimensional form is emphasized. The changes in main characteristics of the flow due to variation of Reynolds number are elaborated. The effective difference between the two-dimensional and three-dimensional results for average Nusselt number and Sherwood number at high Reynolds numbers along the heated wall is analyzed. It has been observed that the substantial transverse velocity that occurs at a higher range of Reynolds number disturbs the two-dimensional nature of the flow.

Measurement of Time-Averaged Turbulent Free Convection in a Tall Enclosure Using Interferometry

Laser interferometry is combined with high-speed digital cinematography to measure time-averaged transient and turbulent convective heat transfer rates. The method is applied to study free convection in a tall vertical air-filled enclosure. Measurements are made at three wall spacings in the turbulent flow regime (5.2×104≤RaW≤2.8×105). An automated image processing algorithm is used to calculate the instantaneous local heat flux from a sequence of interferograms that is captured by a high-speed camera. The local Nusselt number distributions on the hot and cold walls are obtained by time-averaging the fluctuations in local heat flux. The effects of key experimental parameters, such as the camera frame rate and the total image capture time, are investigated. For the current problem, it is shown that a total capture interval of about 10 s is required to accurately measure the time-average local Nusselt number. Within the measurement uncertainty, the average Nusselt number results are in agreement with a widely used empirical correlation from the literature.

Natural-Convection Heat Transfer in Channels with Isothermally Heated Convex Surfaces

This article reports on a numerical investigation conducted to study laminar natural-convection heat transfer in channels with convex surfaces that are isothermally heated. Six Grashof number (Gr) values (10 ≤ Gr ≤ 104) and 11 radii of curvature (1 ≤ κ ≤ ∞) are considered. The results are displayed in terms of streamline and isotherm plots, centerline pressure profiles, inlet mass flow rates, and local and average Nusselt number estimates. At the lowest radius of curvature (κ = 1), computations reveal the formation of recirculation zones in the exit section for all values of Grashof number considered. As the radius of curvature increases, the Gr value at which recirculation occurs also increases, until it disappears at κ values greater than 1.5. For all configurations studied, the average Nusselt number results indicate an increase in heat transfer with increasing Grashof number values. Moreover, the value of κ at which peaks increases with increasing Gr. Inlet volume flow rate and average Nusselt number correlations are presented.

Numerical study of local heat transfer coefficient and fin efficiency of wavy fin-and-tube heat exchangers

Three-dimensional numerical simulations were performed for laminar flow of wavy fin-and-tube heat exchangers by using body-fitted coordinates (BFC) method with fin efficiency effect accounted. The prediction results of average Nusselt number, friction factor and fin efficiency were compared with the related experimental correlations [R.C. Xin, H.Z. Li, H.J. Kang, W. Li, W.Q. Tao, An experimental investigation on heat transfer and pressure drop characteristics of triangular wavy fin-and-tube heat exchanger surfaces, J. Xi'an Jiaotong Univ. 28 (2) (1994) 77–83] and Schmidt approximation [T.E. Schmidt, Heat transfer calculations for extended surfaces, Refrigerating Engineering (April 1949) 351–357]. For Reynolds numbers based on the tube outside diameter ranging from 500 to 4000, the mean deviation is 3.3% for Nusselt number, 1.9% for friction factor and 3.6% for fin efficiency. The distributions of local Nusselt number and fin efficiency on fin surface were studied at wavy angle equal to 0° (plain plate fin), 10° and 20° respectively. The local Nusselt number decreases along the air flow direction, but fin efficiency increases in general. The wavy angle can greatly affect the distributions of local Nusselt number and fin efficiency, and make the distributions present fluctuation along the flow direction. The result also shows that the fin efficiency at the inlet region of wavy fin is larger than that of plain plate fin at the same region. With the increase of Reynolds number, the effects of wavy angle on the distributions of local Nusselt number and fin efficiency are more and more significant.

PREDICTION OF THREE DIMENSIONAL NATURAL CONVECTION FROM A HORIZONTAL ISOTHERMAL SQUARE PLATE

A theoretical study of a three-dimensional natural convection heat transfer from an isothermal horizontal square plate, with upper and lower heated surfaces is present. The transient Navier–Stokes and energy equations were solved by using finite deference method (F.D.M). The complete Navier–Stokes equations are transformed and expressed in terms of vorticity–vector potential and solved using an Alternating Direction Implicit (ADI) method for the parabolic portion of the problem, and Successive Over–Relaxation (SOR) method for the elliptic portion .A computer program in (FORTRAN 77) was built to carry out the solution. The numerical results were obtained for laminar flow range of Grashof number up to (105) in up ward–facing and downward–facing with Prandtl number of (0.72). The results of local Nusselt number have maximum values at the outer edge of plate for two cases upward and downward facing heating.The comparison of the results of average Nusselt number with numerical data for downward facing and experimental data for upward facing shows acceptable agreement. It may be noted that the present data are generally different with experimental data, since the available data are extrapolated to high Grashof number. Thus the deviation may be large with present data.

NUMERICAL STUDIES OF NATURAL CONVECTION IN A SQUARE CAVITY

In the present work a numeric study of thermal and fluid dynamics behavior of natural air convection in a bi-dimensional square cavity is presented, in a laminar flow. The square cavity has two walls heated with different temperatures and two isolated walls, the Boussinesq approximation is used and a constant Prandtl number. The Finite Volume Method is used for the discretization of flow equations. The staggered load of variables is adopted and Power-Law and SIMPLE models are used. The numeric simulation is made up of several Rayleigh numbers, 104 Ra 106, and the results of average Nusselt numbers are compared to values obtained in the literature. Flow and isotherm lines are presented and analyzed. The numerical results presented here in this work agree with the ones available in the literature and can be used by researchers who work in the convection problem numeric simulation area.

Transient natural convection between concentric and vertically eccentric spheres with mixed boundary conditions

Transient analysis has been investigated numerically to determine heat transfer by natural convection between concentric and vertically eccentric spheres with constant heat flux on the inner wall and a specified isothermal temperature on the outer wall. The governing equations, in terms of vorticity, stream function and temperature are expressed in a spherical polar coordinate system. The alternating direction implicit method and the successive over-relaxation techniques are applied to solve the finite difference form of governing equations. A physical model is introduced which accounts for the effects of fluid buoyancy as well as eccentricity of the outer sphere. Transient solutions of the entire flow field are obtained for a range of modified Rayleigh number (103<Ra⋆<5×105), for a Prandtl number of 0.7 and a radius ratio of 2.0, with the outer sphere near the top and bottom of the inner sphere (e=±0.625). Results of the parametric study conducted further reveal that the heat and flow fields are primarily dependent on the modified Rayleigh number and the eccentricity of the spherical annulus. The results of average Nusselt numbers are also compared with the results obtained for flow between two isothermal spheres.

NATURAL CONVECTION IN VERTICAL PARALLEL PLATES WITH AN UNHEATED ENTRY OR UN HEATED EXIT

This study aims to investigate the effects of the unhealed entry or unheated exit section on the free convection heat transfer in airflow in vertical parallel plate channels resulting from the thermal boundary conditions of uniform heat flux (VHF) and uniform wall temperature (UWT). Results of average Nusselt number and dimensionless volume flow rate are presented in terms of the ratio of the length of heated section to the full channel length and a Rayleigh number, ranging from the limit for the fully developed flow to that for single-plate behavior. Analytical equations for dimensionless volume flow rate and average Nusselt number for both unheated restrictions and both thermal boundary conditions have been developed for the fully developed flow limit. The numerical solutions are shown to approach asymptotically the approximate solution for fully developed flow as the Rayleigh number approaches 1 or less. An important finding of the study is that an unheated exit characterizes greater total heat transfe...