Laminar and Turbulent Natural Convection in the Annulus Between Horizontal Concentric Cylinders

1982 ◽  
Vol 104 (4) ◽  
pp. 631-636 ◽  
Author(s):  
B. Farouk ◽  
S. I. Gu¨c¸eri
Keyword(s):  
Natural Convection ◽  
Rayleigh Number ◽  
Numerical Solutions ◽  
Outer Cylinder ◽  
Turbulence Structure ◽  
Number Range ◽  
Turbulent Natural Convection ◽  
Cylinder Diameter ◽  
Concentric Cylinders ◽  
Good Agreement

Numerical solutions are presented for the steady-state, two-dimensional natural convection in the annulus between two horizontal concentric cylinders which are held at different constant temperatures. Solutions for the laminar case are obtained up to Rayleigh number (based on gap width, L) of 105. Turbulent flow results are presented for the Rayleigh number range of 106–107. the k-ε turbulence model has been applied to obtain the results. Buoyancy effects on the turbulence structure are also accounted for. The results for both the laminar and turbulent cases are in good agreement with available experimental data and other solutions in the literature. All results presented are for the outer cylinder diameter to inner cylinder diameter ratio of 2.6.

Natural Convection From a Horizontal Cylinder—Turbulent Regime

1982 ◽  
Vol 104 (2) ◽  
pp. 228-235 ◽  
Author(s):  
B. Farouk ◽  
S. I. Gu¨c¸eri
Keyword(s):  
Natural Convection ◽  
Numerical Solutions ◽  
Horizontal Cylinder ◽  
Equation Model ◽  
Turbulence Structure ◽  
Turbulent Regime ◽  
Closed Set ◽  
Number Range ◽  
Turbulent Natural Convection ◽  
Nusselt Numbers

A two-equation model has been adopted in obtaining numerical solutions of turbulent natural convection from an isothermal horizontal circular cylinder. The k-ε model employed in this study characterizes turbulence through the kinetic energy and its volumetric rate of dissipation. The transport equations for these two variables, along with those for time-averaged stream function, vorticity, and temperature, form a closed set of five coupled partial differential equations. These equations are solved for the entire flow domain, without boundary layer approximations. Buoyancy effects on the turbulence structure are also accounted for. Results are presented for a Rayleigh number range of 5×107 to 1010 and the average Nusselt numbers are compared with existing correlations and limited available experimental data.

Natural Convection in a Stably Heated Corner Filled With Porous Medium

1985 ◽  
Vol 107 (2) ◽  
pp. 293-298 ◽  
Author(s):  
S. Kimura ◽  
A. Bejan
Keyword(s):  
Porous Medium ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Single Cell ◽  
Numerical Solutions ◽  
Vertical Wall ◽  
Temperature Fields ◽  
Number Range ◽  
Corner Flow ◽  
Horizontal Wall

This is a study of the single-cell natural convection pattern that occurs in a “stably heated” corner in a fluid-saturated porous medium, i.e., in the corner formed between a cold horizontal wall and a hot vertical wall situated above the horizontal wall, or in the corner between a hot horizontal wall and a cold vertical wall situated below the horizontal wall. Numerical simulations show that this type of corner flow is present in porous media heated from the side when a stabilizing vertical temperature gradient is imposed in order to suppress the side-driven convection. Based on numerical solutions and on scale analysis, it is shown that the single cell corner flow becomes increasingly more localized as the Rayleigh number increases. At the same time, the mass flow rate engaged in natural circulation and the conduction-referenced Nusselt number increase. Numerical results for the flow and temperature fields and for the net heat transfer rate are reported in the Darcy-Rayleigh number range 10–6000.

Turbulent Natural Convection in Enclosures With Clear Fluid and Completely Filled With Porous Material

2002 ◽  
Author(s):  
Edimilson J. Braga ◽  
Marcelo J. S. de Lemos
Keyword(s):  
Porous Media ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Turbulent Flows ◽  
Energy Transport ◽  
Numerical Solutions ◽  
Clear Fluid ◽  
Turbulent Natural Convection ◽  
Onset Of Turbulence ◽  
Volume Method

Steady laminar and turbulent natural convection in a two-dimensional square cavity, isothermally heated from the left side and cooled from the opposing side, is numerically analyzed using the finite volume method. Benchmark results for laminar and turbulent flows are compared with similar numerical solutions in the literature. The cases of clear and porous media are considered. Governing equations are written in terms of primitive variables and are recast into a general form. The effects of Rayleigh number on flow pattern and energy transport are investigated for Ra ranging from 103 to 1010 for clear media and 101 to 106 for porous media. The turbulence model used was the standard k–ε along with the wall function approach. All results presented herein showed reasonable agreement with calculations presented in the literature. Critical values for the Rayleigh number for the onset of turbulence are suggested. The main objective of this work is to validate a numerical tool for simulating turbulent natural convection in both clear and porous media.

scholarly journals A RANS K-? SIMULATION OF 2D TURBULENT NATURAL CONVECTION IN AN ENCLOSURE WITH HEATING SOURCES

2019 ◽  
Vol 20 (1) ◽  
pp. 229-244
Author(s):  
Mehdi Ahmadi ◽  
Seyed Ali Agha Mirjalily ◽  
Seyed Amir Abbas Oloomi
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Kinetic Energy ◽  
Aspect Ratio ◽  
Heat Transfer Rate ◽  
Transfer Rate ◽  
Turbulent Natural Convection ◽  
Cold Source ◽  
Thermal Sources

ABSTRACT: This study is conducted to investigate turbulent natural convection flow in an enclosure with thermal sources using the low-Reynolds number (LRN) k-? model. This enclosure has a cold source with temperature Tc and a hot source with temperature Th as thermal sources, other walls of the enclosure are adiabatic. The aim of this study is to predict the effect of change in Rayleigh number, repositioning of cold and hot sources, and thermal sources aspect ratio on the flow field, temperature, and rate of heat transfer. To achieve this aim, the equations of continuity, momentum, energy, turbulent kinetic energy, and kinetic energy dissipation are employed in the case of 2D turbulence with constant thermo-physical properties except the density in the buoyancy term (Boussinesq approximation). To numerically solve these equations, the finite volume method and SIMPLE algorithm are used. According to the modeling results, the most optimal temperature distribution in the enclosure is seen when the hot source is below the cold source. With decreasing distance between hot and cold sources, heat transfer rate increases. The maximal heat transfer rate is derived via study of the heating sources aspect ratio. In constant positions of cold and hot sources on a wall, the heat transfer rate increases with increasing Rayleigh number (Ra=109-1011). ABSTAK: Kajian ini dijalankan bagi mengkaji perubahan semula jadi aliran perolakan dalam tempat tertutup dengan sumber haba menggunakan model k-? nombor Reynolds-rendah (LRN). Bekas tertutup ini mempunyai dua sumber haba iaitu sumber sejuk dengan suhu Tc dan sumber panas dengan suhu Th, manakala dinding lain bekas ini adalah adiabatik. Tujuan kajian ini adalah bagi mengesan perubahan nombor Rayleigh, mengubah sumber sejuk dan panas dan nisbah sumber haba kepada kawasan aliran, suhu dan halaju perubahan haba. Bagi mencapai tujuan tersebut, persamaan sambungan, momentum, tenaga, tenaga kinetik perolakan, dan pengurangan tenaga kinetik telah dilaksanakan dalam kes perolakan 2D dengan sifat fizikal-haba berterusan (malar) kecuali isipadu terma keapungan (anggaran Boussinesq). Bagi menyelesaikan persamaan ini secara berangka, kaedah isipadu terhad dan algorithma MUDAH telah digunakan. Berdasarkan keputusan model, suhu distribusi optimal dalam bekas tertutup dilihat apabila sumber panas adalah kurang daripada sumber sejuk. Dengan pengurangan jarak antara sumber panas dan sejuk, kadar pertukaran haba meningkat. Kadar pertukaran haba maksima telah diperoleh melalui kajian nisbah  aspek sumber pemanasan. Kadar pertukaran haba bertambah dengan bertambahnya nombor Rayleigh  (Ra=109-1011), pada posisi tetap sumber sejuk dan panas pada dinding bekas.

Comparative Numerical Simulation of Natural Convection in a Porous Horizontal Cylindrical Annulus

2014 ◽  
Vol 670-671 ◽  
pp. 613-616 ◽  
Author(s):  
Jabrane Belabid ◽  
Abdelkhalek Cheddadi
Keyword(s):  
Natural Convection ◽  
Numerical Study ◽  
Saturated Porous Medium ◽  
Published Data ◽  
Governing Equations ◽  
Alternating Direction Implicit ◽  
Cylindrical Annulus ◽  
Alternating Direction ◽  
Concentric Cylinders ◽  
Good Agreement

This work presents a numerical study of the natural convection in a saturated porous medium bounded by two horizontal concentric cylinders. The governing equations (in the stream function and temperature formulation) were solved using the ADI (Alternating Direction Implicit) method and the Samarskii-Andreev scheme. A comparison between the two methods is conducted. In both cases, the results obtained for the heat transfer rate given by the Nusselt number are in a good agreement with the available published data.

Effect of Viscous Dissipation on Heat Transfer Between Two Concentric Cylinders for Carreau Fluids

2010 ◽  
Author(s):  
Meriem Amoura ◽  
Noureddine Zeraibi
Keyword(s):  
Heat Transfer ◽  
Viscous Dissipation ◽  
Numerical Solutions ◽  
Numerical Study ◽  
Mixed Finite Element ◽  
Outer Cylinder ◽  
Flow Characteristics ◽  
Weissenberg Number ◽  
Stress Strain Relation ◽  
Concentric Cylinders

In this paper, we present a numerical study of the flow characteristics and heat transfer mechanism of a non-Newtonian fluid in an annular space between two coaxial rotating cylinders taking into account the effect of viscous dissipation. The Carreau stress-strain relation was adopted to model the rheological fluid behavior. The problem is studied when the heated inner cylinder rotates around the common axis with constant angular velocity and the cooled outer cylinder is at the rest. The horizontal endplates are assumed adiabatic. In-house code which is based on a Galerkin mixed finite element is developed to obtain numerical solutions of the complete governing equations and associated boundary conditions and is validated with the results reported in the literature. It is found that five parameters can describe the problem under consideration, the Reynolds number (Re), the Grashof number (Gr), the index of structure (n), Weissenberg number (We) and the Eckert number (Ec). The velocity, temperature and stream function distributions and the local Nusselt number variations are drawn for different dimensionless groups.

Natural Convection Heat Transfer From a Plate in a Semicircular Enclosure

1992 ◽  
Vol 114 (1) ◽  
pp. 121-126 ◽  
Author(s):  
G. A. Moore ◽  
K. G. T. Hollands
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Plate Thickness ◽  
Fluid Motion ◽  
Convection Heat Transfer ◽  
Bulk Fluid ◽  
Number Range ◽  
Balance Technique ◽  
Conductive Component

In the subject geometry, a long thin plate at uniform temperature is contained coaxially and symmetrically in a long semicircular trough closed at the top and having a uniform but different temperature. Heat flows across the air-filled region between the two by both natural convection and gaseous conduction. The problem of characterizing the free convective component of this heat transfer—that is, the component caused by bulk fluid motion—is treated experimentally by using a heat balance technique, with the measurements being repeated at different pressures, in order to cover a wide Rayleigh number range, from Ra ≈ 10 to Ra ≈ 108. Nusselt number versus Rayleigh number plots are presented for each of several combinations of plate-to-trough spacing and tilt angle, and the plots are correlated by equations. The problem of characterizing the conductive component is treated by numerically solving the steady diffusion equation in the air-filled region, and the results are correlated as a function of the spacing and the plate thickness.

Turbulent Natural Convection Flow on a Heated Vertical Wall Immersed in a Stratified Atmosphere

1989 ◽  
Vol 111 (2) ◽  
pp. 378-384 ◽  
Author(s):  
A. K. Kulkarni ◽  
S. L. Chou
Keyword(s):  
Natural Convection ◽  
Numerical Solutions ◽  
Vertical Wall ◽  
Leading Edge ◽  
Transitional Flow ◽  
Convection Flow ◽  
Ambient Atmosphere ◽  
Ambient Conditions ◽  
Natural Convection Flow ◽  
Turbulent Natural Convection

This paper presents a comprehensive mathematical model and numerical solutions for a natural convection flow over an isothermal, heated, vertical wall immersed in an ambient atmosphere that is thermally stratified. The model assumes a laminar flow near the leading edge, which then becomes a transitional flow, and finally becomes fully turbulent away from the leading edge. Effects of several typical cases of ambient stratification on heat transfer to the wall, peak velocity, and temperature are examined. It is found that the velocity field is affected more significantly by the “memory” of upstream ambient conditions than the temperature field.

Scaling of the Turbulent Natural Convection Flow in a Heated Square Cavity

1994 ◽  
Vol 116 (2) ◽  
pp. 400-408 ◽  
Author(s):  
R. A. W. M. Henkes ◽  
C. J. Hoogendoorn
Keyword(s):  
Natural Convection ◽  
Rayleigh Number ◽  
Convection Flow ◽  
Convection Boundary Layer ◽  
Square Cavity ◽  
Natural Convection Flow ◽  
Turbulent Natural Convection ◽  
Convection Boundary ◽  
Vertical Walls ◽  
Rayleigh Numbers

By numerically solving the Reynolds equations for air and water in a square cavity, with differentially heated vertical walls, at Rayleigh numbers up to 1020 the scalings of the turbulent natural convection flow are derived. Turbulence is modeled by the standard k–ε model and by the low-Reynolds-number k–ε models of Chien and of Jones and Launder. Both the scalings with respect to the Rayleigh number (based on the cavity size H) and with respect to the local height (y/H) are considered. The scalings are derived for the inner layer, outer layer, and core region. The Rayleigh number scalings are almost the same as the scalings for the natural convection boundary layer along a hot vertical plate. The scalings found are almost independent of the k–ε model used.

An Experimental Study of Natural Convection in Trapezoidal Enclosures

1980 ◽  
Vol 102 (4) ◽  
pp. 648-653 ◽  
Author(s):  
L. Iyican ◽  
L. C. Witte ◽  
Y. Bayazitogˇlu
Keyword(s):  
Experimental Data ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Tilt Angle ◽  
Circulation Pattern ◽  
Two Dimensional ◽  
Number Range ◽  
Rectangular Channels ◽  
Trapezoidal Enclosure ◽  
Hot Surface

Experimental data for natural convection of air in an inclined trapezoidal enclosure are reported for a Rayleigh number range of ∼ 2 × 103 to ∼ 5 × 107. The small side of the trapezoid was electrically heated while the opposing large side was cooled to a uniform temperature. The effect of tilt angle from 0 to 90 deg (from horizontal) was investigated at 15 deg increments. Data were also obtained for 180 deg (hot surface facing down). A comparison of the data to an analysis using a two-dimensional circulation pattern showed reasonable agreement in the Rayleigh number-tilt angle range where two-dimensional circulation could be expected. The experimental data are correlated by an equation of the form, Nu = C Ran, over a wide Rayleigh number range. The data exhibit a local minimum in the Nusselt number-tilt angle curve between 90 and 0 deg in a manner similar to that observed in inclined rectangular channels.

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