An Analytical Study of Natural Convective Heat Transfer within a Trapezoidal Enclosure

1980 ◽  
Vol 102 (4) ◽  
pp. 640-647 ◽  
Author(s):  
L. Iyican ◽  
Y. Bayazitogˇlu ◽  
L. C. Witte
Keyword(s):  
Heat Transfer ◽  
Analytical Study ◽  
Temperature Fields ◽  
Nusselt Numbers ◽  
Method Of Solution ◽  
Different Temperatures ◽  
Nonlinear Form ◽  
Trapezoidal Enclosure ◽  
Energy Equations ◽  
Rayleigh Numbers

The natural convection motion and the heat transfer within a trapezoidal enclosure with parallel cylindrical top and bottom walls at different temperatures and plane adiabatic sidewalls are studied. Two-dimensional natural convective fields for a range of Rayleigh numbers, up to 2.7 × 106, and enclosure tilt angles, 0 to 180 deg measured from vertical, are investigated. The Galerkin’s method of solution is applied to nonlinear form of the momentum and energy equations to determine the velocity and temperature fields. The average and local Nusselt numbers are also presented.

Natural Convection in Cubic and Rhomb-Shaped Enclosures

2013 ◽  
Author(s):  
Milorad B. Dzodzo
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Temperature Fields ◽  
Nusselt Numbers ◽  
Different Temperatures ◽  
Vertical Walls ◽  
Laminar Natural Convection ◽  
Velocity And Temperature Fields ◽  
Prandtl Numbers ◽  
Volume Method

Laminar natural convection in cubic and rhomb–shaped enclosures (rhomb angles 59°, 44° and 28.2°) with two opposite vertical walls kept at different temperatures was investigated experimentally and numerically. The enclosures were filled with glycerol and the Rayleigh (Ra) and Prandtl (Pr) numbers ranged from 2,000<Ra<369,000 and 2,680<Pr<7,000. The visualization of the velocity and temperature fields was obtained by using Plexiglass and liquid crystal particles as tracers. The finite volume method based on the finite difference approach was applied for numerical analysis. The velocity and temperature fields and average Nusselt numbers were found as a function of the Reyleigh and Prandtl numbers. Comparison of the average Nusselt numbers for cubic and rhomb-shaped enclosures indicates decrease of heat transfer for the cases when the lower and upper vertical walls of the rhomb-shaped enclosures are at lower and higher temperatures, respectively. This is due to the tendency of fluid stratification in the lower and upper corners.

scholarly journals Natural Convection in Undivided and Partially Divided Rectangular Enclosures

1981 ◽  
Vol 103 (4) ◽  
pp. 623-629 ◽  
Author(s):  
M. W. Nansteel ◽  
R. Greif
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Temperature Fields ◽  
Transitional Flow ◽  
Two Dimensional ◽  
Injection Flow ◽  
Stabilizing Effect ◽  
Different Temperatures ◽  
Vertical Walls ◽  
Rayleigh Numbers

Heat transfer by natural convection in a two-dimensional rectangular enclosure fitted with partial vertical divisions is investigated experimentally. The horizontal walls of the enclosure are adiabatic while the vertical walls are maintained at different temperatures. The experiments are carried out with water, Pr ≃ 3.5, for Rayleigh numbers in the range, 2.3 × 1010 ⩽ RaL ⩽ 1.1 × 1011, and an aspect ratio, A = H/L = 1/2. The effect of the partial vertical divisions on the fluid flow and temperature fields is investigated by dye-injection flow visualization and by thermocouple probes, respectively. The effect of the partitions on the heat transfer across the enclosure is also studied and correlations for the Nusselt number as a function of RaL and partition length are generated for both conducting and non-conducting partition materials. Partial divisions are found to have a significant effect on the heat transfer; especially when the divisions are adiabatic. The results also indicate that the partial divisions may have a stabilizing effect on the laminar-transitional flow on the heated vertical walls of the enclosure.

Local Heat Transfer Distribution in a Rotating Serpentine Rib-Roughened Flow Passage

1993 ◽  
Vol 115 (3) ◽  
pp. 560-567 ◽  
Author(s):  
N. Zhang ◽  
J. Chiou ◽  
S. Fann ◽  
W.-J. Yang
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Heat Transfer Performance ◽  
Local Heat Transfer ◽  
Local Heat ◽  
Transfer Performance ◽  
Height Ratio ◽  
Nusselt Numbers ◽  
Rayleigh Numbers ◽  
Rib Roughened

Experiments are performed to determine the local heat transfer performance in a rotating serpentine passage with rib-roughened surfaces. The ribs are placed on the trailing and leading walls in a corresponding posited arrangement with an angle of attack of 90 deg. The rib height-to-hydraulic diameter ratio, e/Dh, is 0.0787 and the rib pitch-to-height ratio, s/e, is 11. The throughflow Reynolds number is varied, typically at 23,000, 47,000, and 70,000 in the passage both at rest and in rotation. In the rotation cases, the rotation number is varied from 0.023 to 0.0594. Results for the rib-roughened serpentine passages are compared with those of smooth ones in the literature. Comparison is also made on results for the rib-roughened passages between the stationary and rotating cases. It is disclosed that a significant enhancement is achieved in the heat transfer in both the stationary and rotating cases resulting from an installation of the ribs. Both the rotation and Rayleigh numbers play important roles in the heat transfer performance on both the trailing and leading walls. Although the Reynolds number strongly influences the Nusselt numbers in the rib-roughened passage of both the stationary and rotating cases, Nuo and Nu, respectively, it has little effect on their ratio Nu/Nuo.

scholarly journals Effects of Anisotropy on Natural Convection in a Vertical Porous Cavity Filled with a Heat Generation

2020 ◽  
pp. 12-27
Author(s):  
Degan Gerard ◽  
Sokpoli Amavi Ernest ◽  
Akowanou Djidjoho Christian ◽  
Vodounnou Edmond Claude
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Temperature Fields ◽  
Poisson Equations ◽  
Gravitational Vector ◽  
Side Walls ◽  
Rayleigh Numbers ◽  
Vertical Cavity

This research was devoted to the analytical study of heat transfer by natural convection in a vertical cavity, confining a porous medium, and containing a heat source. The porous medium is hydrodynamically anisotropic in permeability whose axes of permeability tensor are obliquely oriented relative to the gravitational vector and saturated with a Newtonian fluid. The side walls are cooled to the temperature  and the horizontal walls are kept adiabatic. An analytical solution to this problem is found for low Rayleigh numbers by writing the solutions of mathematical model in polynomial form of degree n of the Rayleigh number. Poisson equations obtained are solved by the modified Galerkin method. The results are presented in term of streamlines and isotherms. The distribution of the streamlines and the temperature fields are greatly influenced by the permeability anisotropy parameters and the thermal conductivity. The heat transfer decreases considerably when the Rayleigh number increases.

scholarly journals Effect of Rayleigh Number on Internal Eccentricity in a Heated Horizontal Elliptical Cylinder to its Coaxial Square Enclosure

2020 ◽  
Vol 25 (3) ◽  
pp. 17-29
Author(s):  
Abdelkrim Bouras ◽  
Djedid Taloub ◽  
Zied Driss
Keyword(s):  
Heat Transfer ◽  
Rayleigh Number ◽  
Outer Cylinder ◽  
Boussinesq Approximation ◽  
Square Enclosure ◽  
Nusselt Numbers ◽  
Flow And Heat Transfer ◽  
Commercial Code ◽  
Volume Method ◽  
Rayleigh Numbers

AbstractThis paper deals with numerical investigation of a natural convective flow in a horizontal annular space between a heated square inner cylinder and a cold elliptical outer cylinder with a Newtonian fluid. Uniform temperatures are imposed along walls of the enclosure. The governing equations of the problem were solved numerically by the commercial code Fluent, based on the finite volume method and the Boussinesq approximation. The effects of Geometry Ratio GR and Rayleigh numbers on fluid flow and heat transfer performance are investigated. The Rayleigh number is varied from 103 to 106. Throughout the study the relevant results are presented in terms of isotherms, and streamlines. From the results, we found that the increase in the Geometry Ratio B leads to an increase of the heat transfer coefficient. The heat transfer rate in the annulus is translated in terms of the average Nusselt numbers along the enclosure’s sides. Tecplot 7 program was used to plot the curves which cleared these relations and isotherms and streamlines which illustrate the behavior of air through the channel and its variation with other parameters. The results for the streamlines, isotherms, local and average Nusselt numbers average Nusselt numbers are compared with previous works and show good agreement.

scholarly journals Natural convection air flow in vertical upright-angled triangular cavities under realistic thermal boundary conditions

2016 ◽  
Vol 20 (5) ◽  
pp. 1407-1420 ◽  
Author(s):  
Jaime Sieres ◽  
Antonio Campo ◽  
José Martínez-Súarez
Keyword(s):  
Natural Convection ◽  
Vertical Wall ◽  
Aperture Angle ◽  
Temperature Fields ◽  
Uniform Heat Flux ◽  
Thermal Boundary Conditions ◽  
Nusselt Numbers ◽  
Horizontal Wall ◽  
Rayleigh Numbers

This paper presents an analytical and numerical computation of laminar natural convection in a collection of vertical upright-angled triangular cavities filled with air. The vertical wall is heated with a uniform heat flux; the inclined wall is cooled with a uniform temperature; while the upper horizontal wall is assumed thermally insulated. The defining aperture angle ? is located at the lower vertex between the vertical and inclined walls. The finite element method is implemented to perform the computational analysis of the conservation equations for three aperture angles ? (= 15?, 30? and 45?) and height-based modified Rayleigh numbers ranging from a low Ra = 0 (pure conduction) to a high 109. Numerical results are reported for the velocity and temperature fields as well as the Nusselt numbers at the heated vertical wall. The numerical computations are also focused on the determination of the value of the maximum or critical temperature along the hot vertical wall and its dependence with the modified Rayleigh number and the aperture angle.

scholarly journals CONSTRUCTAL DESIGN OF FINS IN COOLED CAVITIES BY NON-NEWTONIAN FLUIDS

2019 ◽  
Vol 18 (1) ◽  
pp. 85
Author(s):  
J. F. Bueno ◽  
A. R. S. Silva ◽  
T. A. Hirt ◽  
G. F. C. Bogo ◽  
F. S. F. Zinani ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Aspect Ratio ◽  
Newtonian Fluids ◽  
Rheological Parameters ◽  
Flow Index ◽  
Pseudoplastic Fluid ◽  
High Reynolds ◽  
Energy Equations ◽  
Rayleigh Numbers

The present work investigates the Construtal Design of fins inserted in cavities submitted to mixed convection by non-Newtonian fluids. The objective is to obtain the optimum aspect ratio for the fin considering different flow conditions and variations in the rheological parameters of the fluid. The phenomena of flow and heat transfer are modeled by mass balance, momentum and energy equations, and by the generalized Newtonian liquid constitutive equation. The viscosity is modeled as that of a pseudoplastic fluid, using the Carreau function. The optimization problem consists in maximizing heat transfer from the fin using the average Nusselt number. The investigated project variable is the aspect ratio between the edges of the rectangular plane fin profile. The restrictions are the volume of the cavity and the fin. The results are obtained numerically using a finite volume code and a two-dimensional geometry, through exhaustive searching. The results show that the fin geometry influences the maximum Nusselt number mainly for the cases with high Reynolds and Rayleigh numbers, such as was shown in previous studies. The results show that the fin geometry influences the maximum Nusselt number mainly for the cases with high Reynolds and Rayleigh numbers, as was shown in previous studies. It was also found that the Nusselt number increases as the increase in flow intensity, represented by the parameter p, and that the result of the maximum Nusselt number does not change monotonically with the non-Newtonian dimensionless viscosity and with the flow index, showing that the pseudoplasticity of the fluid implies optimal configurations very different from those predicted for Newtonian fluids.

scholarly journals Numerical Study of Mixed Convection in a Channel Filled with a Porous Medium

2019 ◽  
Vol 9 (2) ◽  
pp. 211 ◽  
Author(s):  
Filiz Ozgen ◽  
Yasin Varol
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Mixed Convection ◽  
Nuclear Waste ◽  
Numerical Study ◽  
Temperature Fields ◽  
Dimensionless Form ◽  
Geothermal Resources ◽  
Nusselt Numbers ◽  
The Finite Difference Method

The heat transfer of mixed convection in a horizontal channel filled with a porous medium has been studied in this article, given that it plays an extensive role in various technical applications, such as flow of fluid in geothermal resources, formations in chemical industries, the storage of radioactive nuclear waste material, and cooling. Those equations written in a dimensionless form have been solved using the finite difference method for different values of the parameters. The results obtained from the study have been presented through streamlines, isotherms, and both local and average Nusselt numbers. It has been observed that parameters such as the Rayleigh and Peclet numbers have an effect on flow and temperature fields.

Effect of 3D Diffusion Over Vertical Thin Rectangular Geometries in Natural Convection Heat Transfer

2006 ◽  
Author(s):  
Mustafa Gursoy ◽  
Mehmet Arik ◽  
Tunc Icoz ◽  
Michael Yovanovich ◽  
Theodorian Borca-Tasciuc
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Fluid Motion ◽  
Heat Removal ◽  
Air Entrainment ◽  
Published Data ◽  
Diffusion Term ◽  
Nusselt Numbers ◽  
Wide Range ◽  
Rayleigh Numbers

Natural convection over vertical plates is a very well known problem in heat transfer. There are many available correlations to predict Nusselt numbers for a wide range of Rayleigh numbers. These benchmark studies on natural convection for vertical plates were conducted on rather large surfaces leading to Rayleigh numbers in the range of 0.1 to 109. In natural convection the sole driving force of fluid motion is the change in fluid density, when the diffusive limit is small compared to convective heat transfer. However, conduction to air, as well as air entrainment from sides also contributes to the heat removal from heater surfaces. An experimental study has been carried out with small and large heaters compared to published data for 2×103&lt;Ra&lt;4×107. Square surfaces of 12.5 and 25.4 mm, and rectangular heaters of sizes 25.4×101.6 and 25.4×203.2 mm were tested for a range of heat inputs such that the surface temperatures are controlled between 30 °C and 80 °C. It is found that published correlations underpredict the Nusselt numbers as much as 20%. It is observed that widely known correlations underpredict the experimental values since the 3D conduction and side air drifts on heat transfer are not accounted for in these correlations. However, the cuboid model which includes the 3D diffusion term showed much better agreement with the experimental results.

Effects of Dented Roughness on Laminar Flow and Heat Transfer in Microchannels

2010 ◽  
Author(s):  
Hui Miao ◽  
Yong Huang ◽  
Fa Xie ◽  
Haigang Chen ◽  
Fang Wang
Keyword(s):  
Heat Transfer ◽  
Laminar Flow ◽  
Working Fluid ◽  
Heat Transfer Characteristics ◽  
Nusselt Numbers ◽  
Flow And Heat Transfer ◽  
Micro Channels ◽  
Planar Area ◽  
Poiseuille Number ◽  
Energy Equations

Liquid laminar flow and heat transfer characteristics for parallel plate micro-channels consisting of many triangle shape hollows to fit with the etching surfaces are investigated numerically in the present paper. The height of the channel is 50μm, with three different relative depths, three relative spacing, and three oblique angles of the triangle surface, respectively. The 2D N-S and energy equations are solved using a commercial CFD code FLUENT6.3. Water is used as the working fluid, and the Reynolds number ranges from 100 to 1500. The global Poiseuille number and average Nusselt number are obtained. It is shown that the dented shapes cause a modest influence in Poiseuille number, but a greater impact on the Nusselt numbers. In addition, both of Po and Nu increase modestly with Re. The local Nusselt numbers are always lower in dented area and larger in planar area of dented roughness microchannels, than that of conventional smooth value. Finally, geometry parameters have modest impact on heat transfer for dented roughness.

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