Natural Convection in High Aspect Ratio Three-Dimensional Enclosures with Uniform Heat Flux on the Heated Wall (original) (raw)
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Anbar Journal of Engineering Sciences, 2017
Laminar natural convection heat transfer and fluid flow due to the heating from below at variable heat source length inside two dimensional enclosure has been analyzed numerically in this study. The enclosure has filled with air as a working fluid. The vertical inclined walls of the enclosure are maintained at lower temperature while the remaining walls are insulated. The value of Rayleigh number from (1x10 3 ≤ Ra ≤ 4x10 4), the inclination angle at (γ = 0 o , 22.5 o , 45 o) and dimensionless heat source length at (S = 1 and 0.5). The continuity, momentum and energy equations have been applied to the enclosure and solved by using finite difference method. The results showing that the average Nusselt number increases with the increasing of the heating source length and decreases with the increasing in an inclination angle of the vertical walls.
Numerical Analysis of Natural Convection in a Right-Angle Triangular Enclosure
Frontiers in Heat and Mass Transfer, 2014
A numerical investigation has been performed for heat transfer analysis in a right-angled triangular enclosure filled with water. The side wall of the enclosure is maintained at high temperature compare to the base wall while hypotenuse is kept thermally insulated. Two-dimensional steady-state continuity, momentum and energy equations along with the boussinesq approximation are solved by finite volume method using commercial available software, FLUENT 6.3. The computational results are shown in terms of isotherms, streamlines and velocity contour for Rayleigh number (10 5 ≤ Ra ≤ 10 7). The heat transfer is presented in terms of local and average Nusselt number. The result encapsulates that both flow field and temperature distributions are affected with Rayleigh number. The simulated results are validated with the experimental and numerical results and it shows a good agreement with the published results. Finally, a correlation for Nusselt number (Nu) with Rayleigh number (Ra) has been developed for vertical hot wall.
NUMERICAL ANALYSIS OF NATURAL CONVECTION IN A RIGHT- ANGLED TRIANGULAR ENCLOSURE
A numerical investigation has been performed for heat transfer analysis in a right-angled triangular enclosure filled with water. The side wall of the enclosure is maintained at high temperature compare to the base wall while hypotenuse is kept thermally insulated. Two-dimensional steady-state continuity, momentum and energy equations along with the boussinesq approximation are solved by finite volume method using commercial available software, FLUENT 6.3. The computational results are shown in terms of isotherms, streamlines and velocity contour for Rayleigh number (10 5 ≤ Ra ≤ 10 7). The heat transfer is presented in terms of local and average Nusselt number. The result encapsulates that both flow field and temperature distributions are affected with Rayleigh number. The simulated results are validated with the experimental and numerical results and it shows a good agreement with the published results. Finally, a correlation for Nusselt number (Nu) with Rayleigh number (Ra) has been developed for vertical hot wall.
This work numerically investigates the natural convection in an arch enclosure filled with Al2O3-water based nanofluid. The left side wall of the enclosure is maintained at a higher temperature than that of right side wall while the remaining walls are kept adiabatic. Two-dimensional steady-state governing equations are solved using the finite volume method (FVM). The present work is conducted to state the effects of pertinent parameters such as nanoparticles volume faction () = 0 to 9%, curvature ratio (CR) = 1 to 1.5 and Rayleigh number (Ra) = 10 4 to 10 6 on fluid flow and temperature distribution. The numerical results are presented in the form of streamlines, isotherms, local and average Nusselt number. It is observed from the investigation that the variables are exhibiting a significant impact on the heat transfer. The heat transfer rate is enhanced with the increment in the volume fraction of the nanoparticles up to 5% and after that it is decreased gradually. The heat transfer rate is increased with the increase of curvature ratio and it is significantly higher at CR = 1.5. As per the expectation, the heat transfer is increased along with the increment in Rayleigh number. A good agreement is found between the present work and experimental & numerical results from the literature.
The Influence of the Angle of Inclination on Laminar Natural Convection in a Square Enclosure
Advances in Physics Theories and Applications, 2012
This paper discusses the results obtained by the numerical modeling of natural convection in a water-i¬lled two-dimensional square enclosure inclined to the horizontal. Here, the top and bottom walls of the cavity are considered adiabatic, left vertical wall is maintained at a constant low temperature and the right vertical wall is maintained at a constant high temperature. The aim is to investigate the effects of angle of inclination on the i¬‚ow patterns. We use the Krylov subspace method, GMRES, to solve the discretized formulation of the governing equations. At the validation stage, our results are in good agreement with those reported in the literature. Results are presented in the form of velocity vector and isotherm plots as well as the variation of the average Nusselt number for different angles of inclination. Keywords: natural convection, GMRES, Nusselt number
On natural convection in a single and two zone rectangular enclosure
International Journal of Heat and Mass Transfer, 1992
Convective heat transfer was investigated numerically for rectangular enclosures both undivided and divided in two zones by a vertical partition, and having opposite isothermal walls at different temperatures. The aspect ratio was varied from 0. I to 16 and the Rayleigh number from 3.5 * lo3 to 3.5 * I O7 (non-partitioned enclosures) and from I .O * 10' to 1.6 * 10' (partitioned enclosures). The thickness and conductivity of the partition were varied. The end wall thermal boundary conditions were adiabatic or LTP (Linear Temperature Profile). The continuity, momentum and energy equations for a 2-D laminar steady flow were solved under the Boussinesq approximation by using a finite-difference method and the SIMPLEC pressure-velocity coupling algorithm. Grid-independent results indicate that the reduction in the Nusselt number caused by a thin central partition can be predicted within a few per cent (in the range investigated) by assuming the partition to be isothermal, i.e. infinitely conducting. The finite conductivity of the partition causes a temperature distribution along its length, resulting in an increase in Nu which depends on Rayleigh number, aspect ratio and end wall thermal boundary conditions.
Energies
This paper proposes an analytical model for natural convection in a closed rectangular enclosure filled by a fluid, with imposed heat fluxes at the vertical walls and adiabatic horizontal walls. The analytical model offers a simplified, but easy to handle, description of the temperature and velocity fields. The predicted temperature, velocity, and pressure fields are shown to be in agreement with those obtained from a reliable numerical model. The Nusselt numbers for both the analytical and numerical solutions are then calculated and compared, varying both the aspect ratio of the enclosure and the Rayleigh number. Based on the comparisons, it is possible to assess the dependence of the reliability of the analytical model on the aspect ratio of the enclosure, showing that the prediction error rapidly decreases with the increase of the enclosure slenderness.
Natural Convection Heat Transfer within Octagonal Enclosure
The problem of steady, laminar and incompressible natural convection flow in an octagonal enclosure was studied. In this investigation, two horizontal walls were maintained at a constant high temperature, two vertical walls were kept at a constant low temperature and all inclined walls were considered adiabatic. The enclosure was assumed to be filled with a Bousinessq fluid. The study includes computations for different Prandtl numbers Pr such as 0.71, 7, 20 and 50 whereas the Rayleigh number Ra was varied from 103 to 106. The pressure-velocity form of Navier-Stokes equations and energy equation were used to represent the mass, momentum and energy conservations of the fluid medium in the enclosure. The governing equations and boundary conditions were converted to dimentionless form and solved numerically by penalty finite element method with discretization by triangular mesh elements. Flow and heat transfer characteristics were presented in terms of streamlines, isotherms and average Nusselt number Nu. Results showed that the effect of Ra on the convection heat transfer phenomenon inside the enclosure was significant for all values of Pr studied (0.71-50). It was also found that, Pr influence natural convection inside the enclosure at high Ra (Ra > 104 ).
International Journal of Heat and Mass Transfer, 1995
Abstraet--Steady natural convection in an enclosure heated from below and symmetrically cooled from the sides is studied numerically, using a streamfunction-vorticity formulation. The Allen discretization scheme is adopted and the discretized equations were solved in a line by line basis. The Rayleigh number based on the cavity height is varied from 103 to 10 7. Values of 0.7 and 7.0 for the Prandtl number are considered. The aspect ratio L/H (length to height of the enclosure) is varied from 1 to 9. Boundary conditions are uniform wall temperature and uniform heat flux. For the range of the parameters studied, a single cell is observed to represent the flow pattern. Numerical values of the Nusselt number as a function of the Rayleigh number are reported, and the Prandtl number is found to have little influence on the Nusselt number. A scale analysis is presented in order to better understand the phenomenon.