Development of Nusselt number correlation in natural convection over the walls of a blast furnace: A CFD approach

2021 ◽  
pp. 095440892110637
Author(s):  
Shafiq Mohamad ◽  
Jnana Ranjan Senapati ◽  
Sachindra Kumar Rout ◽  
Sunil Kumar Sarangi
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Blast Furnace ◽  
Rayleigh Number ◽  
Surface Temperature ◽  
Cylindrical Surface ◽  
Vertical Cylinder ◽  
Maximum Diameter ◽  
Cylinder Surface ◽  
Thermal Plume

Blast furnaces are large and costly devices, and contribute enormous wealth to world economy. A tiny improvement of furnace performance can translate to huge saving not only in cost of operation but also in air pollution. It presents a numerical solution of the continuity, momentum, and energy equations for a fluid domain surrounding the outer cylindrical surface of a vertical cylinder with the specific longitudinal section using ANSYS FLUENT 18. The main parameters of this study are the dimensionless ratio of cylinder length to the maximum diameter varying between 3.24 and 5.4, the Rayleigh number ranging between 104 and 107, and the cylinder surface temperature ([Formula: see text]) varying between 375 K and 600 K, the ambient temperature being taken as 300 K. These parameters have been varied during the simulation to determine their influence on the free convection characteristics. The study clearly shows that the computed Nusselt number increases with increase of Rayleigh number and surface temperature, the increment being minimal for high values of length to the maximum diameter. It is also observed from the simulation that the rate of heat transfer goes down with increase of length to the maximum diameter. The results present local heat transfer and skin friction coefficients over the outer cylindrical surface of the blast furnace of chosen dimensions. The thermal plume and the velocity vector field around the furnace are displayed. An empirical Nusselt number to Rayleigh number relationship has been proposed for the blast furnace of any size within range of Rayleigh numbers covered in this study. This formula derived is correct within ±5%, and is expected to be very useful to field engineers.

Natural Convection Heat Transfer of Concentric/Eccentric Annulus Subjected to Inner Tube of Constant Heat Flux

2011 ◽  
Author(s):  
R. Hosseini ◽  
M. Alipour ◽  
A. Gholaminejad
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Surface Temperature ◽  
Convection Heat Transfer ◽  
Natural Convection Heat Transfer ◽  
Convection Heat ◽  
Eccentric Annulus

This paper describes the experimental results of natural convection heat transfer from vertical, electrically heated cylinder in a concentric/eccentric annulus and develops correlations for the dependence of the average annulus Nusselt number upon the Rayleigh number. Wall surface temperature have been recorded for diameter ratio of d/D = 0.4, with the apparatus immersed in stagnant air with uniform temperature. Measurements have been carried out for eccentric ratios of E = 0, 0.19, 0.34, 0.62 and 0.89 in the range of heat flux of 45 to 430 W/m2. The surface temperature of the heater was found to increase upwards and reach a maximum at some position, beyond which it decreases again. It is observed, that this maximum temperature occurs near h/l = 0.8 for 0 ≤ E ≤ 0.62 at almost all power levels, but shifts downwards for E = 0.89. Moreover, empirical correlations between the average Nusselt number and the Rayleigh number are derived for concentric and eccentric annuli.

Heat transfer characteristics of nanofluids from a sinusoidal corrugated cylinder placed in a square cavity

2021 ◽  
pp. 095440622110272
Author(s):  
Salaika Parvin ◽  
Nepal Chandra Roy ◽  
Litan Kumar Saha ◽  
Sadia Siddiqa
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Rayleigh Number ◽  
Aspect Ratio ◽  
Average Nusselt Number ◽  
Numerical Study ◽  
Heat Transfer Characteristics ◽  
Number Range ◽  
Transfer Characteristics ◽  
Wide Range

A numerical study is performed to investigate nanofluids' flow field and heat transfer characteristics between the domain bounded by a square and a wavy cylinder. The left and right walls of the cavity are at constant low temperature while its other adjacent walls are insulated. The convective phenomena take place due to the higher temperature of the inner corrugated surface. Super elliptic functions are used to transform the governing equations of the classical rectangular enclosure into a system of equations valid for concentric cylinders. The resulting equations are solved iteratively with the implicit finite difference method. Parametric results are presented in terms of streamlines, isotherms, local and average Nusselt numbers for a wide range of scaled parameters such as nanoparticles concentration, Rayleigh number, and aspect ratio. Several correlations have been deduced at the inner and outer surface of the cylinders for the average Nusselt number, which gives a good agreement when compared against the numerical results. The strength of the streamlines increases significantly due to an increase in the aspect ratio of the inner cylinder and the Rayleigh number. As the concentration of nanoparticles increases, the average Nusselt number at the internal and external cylinders becomes stronger. In addition, the average Nusselt number for the entire Rayleigh number range gets enhanced when plotted against the volume fraction of the nanofluid.

Heat Transfer Characteristics of the Phase Change Material Microcapsule Slurry in Solid Phase State

2011 ◽  
Vol 71-78 ◽  
pp. 1187-1190
Author(s):  
Yan Lai Zhang ◽  
Zhong Hao Rao ◽  
Shuang Feng Wang ◽  
Hong Zhang ◽  
Li Jun Li ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Rayleigh Number ◽  
Aspect Ratio ◽  
Phase State ◽  
Solid Phase ◽  
Heat Transfer Characteristics ◽  
Rectangular Enclosure ◽  
Transfer Characteristics ◽  
Change Material

This experiment is performed to investigate heat transfer characteristics with the PCM microcapsule slurry in a solid phase state at a horizontal rectangular enclosure heating from below and cooling from top. Some important parameters are taken into account such as the mass concentration of the PCM, the temperature difference between heating plate and cooling plate, Nusselt number Nu, Rayleigh number Ra and the aspect ratio (width/height) of the horizontal rectangular enclosure. Experiment is done under the thermal steady condition in the PCM microcapsule slurry. Heat transfer coefficient is measured under various temperature differences in PCM mass concentrations of 10% and 20%. And relationship with Nusselt number Nu and Rayleigh number Ra is summarized to various heights H or the aspect ratio (width/height) Ar of enclosure.

3D optimization of baffle arrangement in a multi-phase nanofluid natural convection based on numerical simulation

2019 ◽  
Vol 30 (5) ◽  
pp. 2583-2605 ◽  
Author(s):  
Mohammad Mohsen Peiravi ◽  
Javad Alinejad ◽  
D.D. Ganji ◽  
Soroush Maddah
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Rayleigh Number ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Volume Fraction ◽  
Target Function ◽  
Optimal Arrangement ◽  
Content Type ◽  
Multi Phase

Purpose The purpose of this study is investigating the effect of using multi-phase nanofluids, Rayleigh number and baffle arrangement simultaneously on the heat transfer rate and Predict the optimal arrangement type of baffles in the differentiation of Rayleigh number in a 3D enclosure. Design/methodology/approach Simulations were performed on the base of the L25 Taguchi orthogonal array, and each test was conducted under different height and baffle arrangement. The multi-phase thermal lattice Boltzmann based on the D3Q19 method was used for modeling fluid flow and temperature fields. Findings Streamlines, isotherms, nanofluid volume fraction distribution and Nusselt number along the wall surface for 104 < Ra < 108 have been demonstrated. Signal-to-noise ratios have been analyzed to predict optimal conditions of maximize and minimize the heat transfer rate. The results show that by choosing the appropriate height and arrangement of the baffles, the average Nusselt number can be changed by more than 57 per cent. Originality/value The value of this paper is surveying three-dimensional and two-phase simulation for nanofluid. Also using the Taguchi method for Predicting the optimal arrangement type of baffles in a multi-part enclosure. Finally statistical analysis of the results by using of two maximum and minimum target Function heat transfer rates.

Experimental and Numerical Investigation of Natural Convection Heat Transfer in Horizontal Elliptic Annuli

2008 ◽  
Vol 6 (1) ◽  
Author(s):  
Ramadan Y. Sakr ◽  
Nabil S. Berbish ◽  
Ali A. Abd-Aziz ◽  
Abdalla Said Hanafi
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Rayleigh Number ◽  
Average Nusselt Number ◽  
Orientation Angle ◽  
Elliptic Cylinder ◽  
Major Axis ◽  
Radius Ratio ◽  
Hydraulic Radius ◽  
Axis Ratio

Experimental and numerical studies for natural convection in two dimensional regions formed by a constant flux heat horizontal elliptic tube concentrically located in a larger, isothermally cooled horizontal cylinder were investigated. Both ends of the annulus are closed. Experiments were carried out for the Rayleigh number based on the equivalent annulus gap length ranges from 1.12x107 up to 4.92x107; the elliptic tube orientation angle varies from 0o to 90o and the hydraulic radius ratio, HRR, was 6.4. These experiments were carried out for the axis ratio of an elliptic tube (minor/major=b/c) of 1:3. The numerical simulation for the problem is carried out by using commercial CFD code. The effects of the orientation angle as well as other parameters such as elliptic cylinder axis ratio and hydraulic radius ratio on the flow and heat transfer characteristics are investigated numerically. The numerical simulations covered a range of elliptic tube axis ratios from 0.1 to 0.98 and for the hydraulic radius ratios from 1.5 to 6.4. The results showed that the average Nusselt number increases as the orientation angle of the elliptic cylinder increases from 0o (the major axis is horizontal) to 90o (the major axis is vertical) and with the Rayleigh number as well. Also, the average Nusselt number decreases with the increase of the hydraulic radius ratio. An increase up to 1.75 and further increases in the hydraulic radius ratio leads to an increase in the average Nusselt number. The axis ratio of the elliptic cylinder has an insignificant effect on the average Nusselt number. Both the average and local Nusselt number from the experimental results are compared with those obtained from the CFD code.Both the fluid flow and heat transfer characteristics for different operating and geometric conditions are illustrated velocity vectors and isotherm contours that were obtained from the CFD code. Also, two correlation equations that relate the average Nusslet number with the Rayleigh number, orientation angle, and hydraulic radius ratio and axis ratio are obtained.

Effects of Variable Viscosity and Thermal Conductivity of CuO-Water Nanofluid on Heat Transfer Enhancement in Natural Convection: Mathematical Model and Simulation

2010 ◽  
Vol 132 (5) ◽  
Author(s):  
Eiyad Abu-Nada
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Nusselt Number ◽  
Aspect Ratio ◽  
High Aspect Ratio ◽  
Average Nusselt Number ◽  
Volume Fraction ◽  
Variable Viscosity ◽  
Cylinder Surface ◽  
Transfer Enhancement

Heat transfer enhancement in horizontal annuli using variable thermal conductivity and variable viscosity of CuO-water nanofluid is investigated numerically. The base case of simulation used thermal conductivity and viscosity data that consider temperature property dependence and nanoparticle size. It was observed that for Ra≥104, the average Nusselt number was deteriorated by increasing the volume fraction of nanoparticles. However, for Ra=103, the average Nusselt number enhancement depends on aspect ratio of the annulus as well as volume fraction of nanoparticles. Also, for Ra=103, the average Nusselt number was less sensitive to volume fraction of nanoparticles at high aspect ratio and the average Nusselt number increased by increasing the volume fraction of nanoaprticles for aspect ratios ≤0.4. For Ra≥104, the Nusselt number was deteriorated everywhere around the cylinder surface especially at high aspect ratio. However, this reduction is only restricted to certain regions around the cylinder surface for Ra=103. For Ra≥104, the Maxwell–Garnett and the Chon et al. conductivity models demonstrated similar results. But, there was a deviation in the prediction at Ra=103 and this deviation becomes more significant at high volume fraction of nanoparticles. The Nguyen et al. data and the Brinkman model give completely different predictions for Ra≥104, where the difference in prediction of the Nusselt number reached 50%. However, this difference was less than 10% at Ra=103.

Natural Convection Heat Transfer in a Partially Open Square Cavity With a Thin Fin Attached to the Hot Wall

2008 ◽  
Vol 130 (5) ◽  
Author(s):  
Abdullatif Ben-Nakhi ◽  
M. M. Eftekhari ◽  
D. I. Loveday
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Rayleigh Number ◽  
Inclination Angle ◽  
Computational Study ◽  
Vertical Wall ◽  
Temperature Fields ◽  
Arbitrary Length ◽  
Flow Modification ◽  
The Impact

A computational study of steady, laminar, natural convective fluid flow in a partially open square enclosure with a highly conductive thin fin of arbitrary length attached to the hot wall at various levels is considered. The horizontal walls and the partially open vertical wall are adiabatic while the vertical wall facing the partial opening is isothermally hot. The current work investigates the flow modification due to the (a) attachment of a highly conductive thin fin of length equal to 20%, 35%, or 50% of the enclosure width, attached to the hot wall at different heights, and (b) variation of the size and height of the aperture located on the vertical wall facing the hot wall. Furthermore, the study examines the impact of Rayleigh number (104⩽Ra⩽107) and inclination of the enclosure. The problem is put into dimensionless formulation and solved numerically by means of the finite-volume method. The results show that the presence of the fin has counteracting effects on flow and temperature fields. These effects are dependent, in a complex way, on the fin level and length, aperture altitude and size, cavity inclination angle, and Rayleigh number. In general, Nusselt number is directly related to aperture altitude and size. However, after reaching a peak Nusselt number, Nusselt number may decrease slightly if the aperture’s size increases further. The impact of aperture altitude diminishes for large aperture sizes because the geometrical differences decrease. Furthermore, a longer fin causes higher rate of heat transfer to the fluid, although the equivalent finless cavity may have higher heat transfer rate. In general, the volumetric flow rate and the rate of heat loss from the hot surfaces are interrelated and are increasing functions of Rayleigh number. The relationship between Nusselt number and the inclination angle is nonlinear.

Thermofluid Characteristics on Natural and Mixed Convection Heat Transfer From a Vertical Rotating Hollow Cylinder Immersed in Air: A Numerical Exercise

2020 ◽  
Vol 143 (2) ◽  
Author(s):  
Basanta Kumar Rana ◽  
Bhajneet Singh ◽  
Jnana Ranjan Senapati
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Fluid Flow ◽  
Rayleigh Number ◽  
Aspect Ratio ◽  
Mixed Convection ◽  
Hollow Cylinder ◽  
Vertical Cylinder ◽  
Cylinder Wall ◽  
Flow And Heat Transfer

Abstract Numerical investigations are performed on natural and mixed convection around stationary and rotating vertical heated hollow cylinder with negligible wall thickness suspended in the air. The fluid flow and heat transfer characterization around the hollow cylinder are obtained by varying the following parameters, namely, Rayleigh number (Ra), Reynolds number (ReD), and cylindrical aspect ratio (L/D). The heat transfer quantities are estimated by varying the Rayleigh number (Ra) from 104 to 108 and aspect ratio (L/D) ranging from 1 to 20. Steady mixed convection with active rotation of hollow vertical cylinder is further studied by varying the Reynolds number (ReD) from 0 to 2100. The velocity vectors and temperature contours are shown in order to understand the fluid flow and heat transfer around the vertical hollow cylinder for both rotating and nonrotating cases. The surface average Nusselt number trends are presented for various instances of Ra, ReD, and L/D and found out that the higher rate of heat loss from the cylinder wall occurs at high Ra, low L/D (short cylinder) and high ReD.

Natural convective heat transfer in a hemispherical cavity filled with ZnO–H2O nanofluid saturated porous medium

2018 ◽  
Vol 29 (10) ◽  
pp. 1850097 ◽  
Author(s):  
Abderrahmane Baïri ◽  
Najib Laraqi
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Nusselt Number ◽  
Rayleigh Number ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Volume Fraction ◽  
Saturated Porous Medium ◽  
Physical Parameters ◽  
Numerical Work

This three-dimensional (3D) numerical work based on the volume control method quantifies the convective heat transfer occurring in a hemispherical cavity filled with a ZnO–H2O nanofluid saturated porous medium. Its main objective is to improve the cooling of an electronic component contained in this enclosure. The volume fraction of the considered monophasic nanofluid varies between 0% (pure water) and 10%, while the cupola is maintained isothermal at cold temperature. During operation, the active device generates a heat flux leading to high Rayleigh number reaching [Formula: see text] and may be inclined with respect to the horizontal plane at an angle ranging from 0[Formula: see text] to 180[Formula: see text] (horizontal position with cupola facing upwards and downwards, respectively) by steps of 15[Formula: see text]. The natural convective heat transfer represented by the average Nusselt number has been quantified for many configurations obtained by combining the tilt angle, the Rayleigh number, the nanofluid volume fraction and the ratio between the thermal conductivity of the porous medium’s solid matrix and that of the base fluid. This ratio has a significant influence on the free convective heat transfer and ranges from 0 (without porous media) to 70 in this work. The influence of the four physical parameters is analyzed and commented. An empirical correlation between the Nusselt number and these parameters is proposed, allowing determination of the average natural convective heat transfer occurring in the hemispherical cavity.

Optimizing Laminar Natural Convection for a Heat Generating Cylinder in a Channel

2014 ◽  
Vol 136 (11) ◽  
Author(s):  
Corey E. Clifford ◽  
Mark L. Kimber
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Spent Nuclear Fuel ◽  
Reactor Core ◽  
Horizontal Cylinder ◽  
Cylinder Surface ◽  
Transfer Program ◽  
Wet Storage

Natural convection heat transfer from a horizontal cylinder is of importance in a large number of applications. Although the topic has a rich history for unconfined cylinders, maximizing the free convective cooling through the introduction of sidewalls and creation of a chimney effect is considerably less studied. In this investigation, a numerical model of a heated horizontal cylinder confined between two vertical adiabatic walls is employed to evaluate the natural convective heat transfer. Two different treatments of the cylinder surface are investigated: constant temperature (isothermal) and constant surface heat flux (isoflux). To quantify the effect of wall distance on the effective heat transfer from the cylinder surface, 18 different confinement ratios are selected in varying increments from 1.125 to 18.0. All of these geometrical configurations are evaluated at seven distinct Rayleigh numbers ranging from 102 to 105. Maximum values of the surface-averaged Nusselt number are observed at an optimum confinement ratio for each analyzed Rayleigh number. Relative to the “pseudo-unconfined” cylinder at the largest confinement ratio, a 74.2% improvement in the heat transfer from an isothermal cylinder surface is observed at the optimum wall spacing for the highest analyzed Rayleigh number. An analogous improvement of 60.9% is determined for the same conditions with a constant heat flux surface. Several correlations are proposed to evaluate the optimal confinement ratio and the effective rate of heat transfer at that optimal confinement level for both thermal boundary conditions. One of the main application targets for this work is spent nuclear fuel, which after removal from the reactor core is placed in wet storage and then later transferred to cylindrical dry storage canisters. In light of enhanced safety, many are proposing to decrease the amount of time the fuel spends in wet storage conditions. The current study helps to establish a fundamental understanding of the buoyancy-induced flows around these dry cask storage canisters to address the anticipated needs from an accelerated fuel transfer program.

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