Constructal Design of Rectangular Fin Intruded Into Mixed Convective Lid-Driven Cavity Flows

2016 ◽  
Vol 138 (10) ◽  
Author(s):  
G. Lorenzini ◽  
B. S. Machado ◽  
L. A. Isoldi ◽  
E. D. dos Santos ◽  
L. A. O. Rocha
Keyword(s):  
Nusselt Number ◽  
Aspect Ratio ◽  
Convective Flow ◽  
Numerical Study ◽  
Reynolds Numbers ◽  
Lower Surface ◽  
Driven Cavity ◽  
Constructal Design ◽  
Mixed Convective Flow ◽  
Forced Convective Flow

The present work shows a numerical study of laminar, steady, and mixed convective flow inside lid-driven square cavity with intruded rectangular fin in its lower surface. The main purpose here is to maximize the heat transfer between the rectangular fin and the surrounding mixed convective flow inside a lid-driven cavity by means of constructal design. The problem is subject to two constraints, the lid-driven cavity and intruded fin areas. The ratio between the fin and cavity areas is kept fixed (ϕ = 0.05). The investigated geometry has one degree-of-freedom (DOF), the fin aspect ratio (H1/L1), which is varied in the range 0.1 ≤ H1/L1 ≤ 10. The aspect ratio of the cavity is maintained fixed (H/L = 1.0). The effect of the fin geometry over the Nusselt number is investigated for several Rayleigh (RaH = 103, 104, 105 and 106) and Reynolds numbers (ReH = 10, 102, 3.0 × 102, 5.0 × 102, 7.0 × 102 and 103). For all simulations, the Prantdl number is fixed (Pr = 0.71). The conservation equations of mass, momentum, and energy are numerically solved with the finite volume method. Results showed that fin geometry (H1/L1) has strong influence over the Nusselt number in the fin. It was also observed that the effect of H1/L1 over Nusselt number changes considerably for different Rayleigh numbers and for the lowest magnitudes of Reynolds numbers, for example, differences of nearly 770% between RaH = 106 and forced convective flow were observed for the lowest Reynolds number studied (ReH = 10).

Free Convective Flow in a Two Enclosure Arrangement With a High Aspect Ratio Side Enclosure Joined to a Large Square Enclosure

2000 ◽  
Author(s):  
Patrick H. Oosthuizen
Keyword(s):  
Nusselt Number ◽  
Rayleigh Number ◽  
Aspect Ratio ◽  
High Aspect Ratio ◽  
Convective Flow ◽  
Numerical Study ◽  
Vertical Wall ◽  
Heated Wall ◽  
Free Convective Flow ◽  
Square Enclosure

Abstract A numerical study of free convective flow in a vertical joined two-enclosure arrangement has been undertaken. In this arrangement, a vertical heated wall kept at a uniform high temperature is contained in a high aspect ratio rectangular side enclosure. This enclosure is separated from a larger square enclosure by a vertical dividing wall which is impermeable but offers no resistance to heat transfer. The vertical wall of the main flow enclosure opposite to the dividing wall is maintained at a uniform lower temperature. All remaining walls in both enclosures are adiabatic. The situation considered is an approximate model of a window exposed to a hot outside environment and covered by a plane blind which in turn is exposed to cooled room. The flow has been assumed to be laminar and two-dimensional and results have been obtained for a Prandtl number of 0.7. The effects of Rayleigh number and the dimensionless width of the side enclosure on the Nusselt number have been investigated. The results show that there is a minimum in the Nusselt number variation with side enclosure width for a fixed Rayleigh number. The effect of Rayleigh number on the conditions under which this minimum occurs and on the value of the minimum Nusselt number has been investigated.

scholarly journals GEOMETRICAL EVALUATION OF RECTANGULAR FIN MOUNTED IN LATERAL SURFACE OF LID-DRIVEN CAVITY FORCED CONVECTIVE FLOWS

2019 ◽  
Vol 18 (2) ◽  
pp. 98
Author(s):  
E. D. dos Santos ◽  
P. M. Rodrigues ◽  
L. A. Isoldi ◽  
J. F. Prolo Filho ◽  
L. A. O. Rocha ◽  
...  
Keyword(s):  
Aspect Ratio ◽  
Thermal Performance ◽  
Degrees Of Freedom ◽  
Reynolds Numbers ◽  
Cavity Surface ◽  
Square Cavity ◽  
Driven Cavity ◽  
Convective Flows ◽  
Constructal Design ◽  
Volume Method

In this work, it is investigated the geometric effect of rectangular fin inserted in a lid-driven square cavity over thermal performance of laminar, incompressible, steady and forced convective flows. This study is performed by applying Constructal Design to maximize the heat transfer between the fin and the cavity flow. For that, the problem is subjected to two constraints: area of the cavity and area of rectangular fin, and two degrees of freedom: height/length ratio of rectangular fin (H1/L1) and its position in upstream surface of the cavity (S/A1/2). It is considered here some fixed parameters, as the ratio between the fin and cavity areas (ϕ = 0.05), the aspect ratio of the cavity dimensions (H/L = 1.0) and Prandtl number (Pr = 0.71). The fin aspect ratio (H1/L1) was varied for three different placements of the fin at the upstream cavity surface (S/A1/2 = 0.1, 0.5 and 0.9) which represents a lower, intermediate and upper positions of the fin. The effects of the fin geometry over the spatial-averaged Nusselt number ( ) is investigated for three different Reynolds numbers (ReH = 10, 102 and 103). The conservation equations of mass, momentum and energy were numerically solved with the Finite Volume Method. Results showed that both degrees of freedom (H1/L1 and S/A1/2) had a strong influence over , mainly for higher magnitudes of Reynolds number. Moreover, the best thermal performance is reached when the fin is placed near the upper surface of the cavity for an intermediate ratio between height and length of rectangular fin, more precisely when (S/A1/2)o = 0.9 and (H1/L1)oo = 2.0.

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.

Numerical Study of Winglet at Low Reynolds Numbers

2013 ◽  
Author(s):  
Sina Pooladsanj ◽  
Mehran Tadjfar
Keyword(s):  
Aspect Ratio ◽  
Flow Field ◽  
Vortex Flow ◽  
Numerical Study ◽  
Reynolds Numbers ◽  
Flow Zone ◽  
Low Reynolds Numbers ◽  
Structured Grid ◽  
Flow Field Characteristics ◽  
Wing Aspect Ratio

A numerical study has been performed to evaluate the aerodynamics coefficients of a winglet in the range of Reynolds numbers below 30,000. In this study some parameters on winglet design have been considered. The effect of winglet-tip airfoil thickness has been investigated on aerodynamics coefficients. In order to explore this effect, two different airfoils (NACA0002 and NACA0012) were employed at the winglet-tip. The influence of varying the winglet connection angle to the wing on aerodynamics coefficients and flow field characteristics in the vortex flow zone such as; circulation magnitude and vorticity magnitude in the vortex core have been studied. Six connection angles including 20°, 30°, 40°, 50°, 60° and 70° have been studied. Negative values of these angles have also been considered. In addition, the effect of changing wing aspect ratio on aerodynamics coefficients has been investigated. To solve the flow field around the studied geometry a fully structured grid was used which consists of 84 blocks.

Effect of Wall Conduction on Combined Free and Forced Laminar Convection in Horizontal Rectangular Channels

1987 ◽  
Vol 109 (4) ◽  
pp. 936-942 ◽  
Author(s):  
G. J. Hwang ◽  
F. C. Chou
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Temperature Distribution ◽  
Finite Difference ◽  
Aspect Ratio ◽  
Finite Difference Method ◽  
Numerical Study ◽  
Fully Developed Flow ◽  
Rectangular Channels ◽  
Laminar Convection

This paper presents a numerical study of the effect of peripheral wall conduction on combined free and forced laminar convection in hydrodynamically and thermally fully developed flow in horizontal rectangular channels with uniform heat input axially, In addition to the Prandtl number, the Grashof number Gr+, and the aspect ratio γ, a parameter Kp indicating the significance of wall conduction plays an important role in heat transfer. A finite-difference method utilizing a power-law scheme is employed to solve the system of governing partial differential equations coupled with the equation for wall conduction. The numerical solution covers the parameters: Pr = 7.2 and 0.73, γ = 0.5, 1, and 2, Kp = 10−4–104, and Gr+ = 0–1.37×105. The flow patterns and isotherms, the wall temperature distribution, the friction factor, and the Nusselt number are presented. The results show a significant effect of the conduction parameter Kp.

Natural Convection in a Cylindrical Porous Enclosure With Internal Heat Generation

1989 ◽  
Vol 111 (4) ◽  
pp. 916-925 ◽  
Author(s):  
V. Prasad ◽  
A. Chui
Keyword(s):  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Aspect Ratio ◽  
Numerical Study ◽  
Vertical Wall ◽  
Internal Heat ◽  
Heat Removal ◽  
Maximum Temperature ◽  
Wall Boundary Conditions

A numerical study is performed on natural convection inside a cylindrical enclosure filled with a volumetrically heated, saturated porous medium for the case when the vertical wall is isothermal and the horizontal walls are either adiabatic or isothermally cooled. When the horizontal walls are insulated, the flow in the cavity is unicellular and the temperature field in upper layers is highly stratified. However, if the top wall is cooled, there may exist a multicellular flow and an unstable thermal stratification in the upper region of the cylinder. Under the influence of weak convection, the maximum temperature in the cavity can be considerably higher than that predicted for pure conduction. The local heat flux on the bounding walls is generally a strong function of the Rayleigh number, the aspect ratio, and the wall boundary conditions. The heat removal on the cold upper surface decreases with the aspect ratio, thereby increasing the Nusselt number on the vertical wall. The effect of Rayleigh number is, however, not straightforward. Several correlations are presented for the maximum cavity temperature and the overall Nusselt number.

Three Dimensional Numerical Modelling of Staggered Tube Bundle Turbulent Crossflow in Duct

2005 ◽  
Author(s):  
Ahad Ramezanpour ◽  
Hassan Shirvani ◽  
Ramin Rahmani ◽  
Iraj Mirzaee
Keyword(s):  
Nusselt Number ◽  
Numerical Study ◽  
Tube Bundle ◽  
Three Dimensional ◽  
Cross Flow ◽  
Reynolds Numbers ◽  
Wall Function ◽  
Flat Plates ◽  
Geometrical Characteristics ◽  
Commercial Code

A numerical study has been conducted to investigate the three dimensional (3D) staggered tube bundle turbulent cross flow confined between two parallel flat plates using RNG k-ε model and standard wall function utilizing commercial code FLUENT. The maximum Reynolds numbers of 1000, 5000, and 50000 and the distance between plates of H = 3, 5, 10, 15, and 20 mm have been considered. The arrangement of the staggered tube bundle is fix with geometrical characteristics of Sn/D = 1.5 and Sp/D = 1.2 which has been found optimum in previous two-dimensional studies. The constant temperature of 360K on tubes, constant inlet flow and plates’ temperature of 300K have been set as the boundary conditions. The global Nusselt number, friction factor for the dissimilar Reynolds numbers, distance between plates, local Nusselt number and different angles on first and third tubes have been evaluated.

scholarly journals Numerical study of magnetohydrodynamic mixed convective flow in a lid-driven enclosure filled with nanofluid saturated porous medium with center heater

2019 ◽  
Vol 23 (3 Part B) ◽  
pp. 1861-1873
Author(s):  
Thangavelu Mahalakshmi ◽  
Nagarajan Nithyadevi ◽  
Hakan Oztop
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Fluid Flow ◽  
Convective Flow ◽  
Numerical Study ◽  
Bottom Wall ◽  
Height Velocity ◽  
Flow And Heat Transfer ◽  
Mixed Convective Flow ◽  
Heater Length

This present numerical study explores the MHD mixed convective flow and heat transfer analysis in a square porous enclosure filled with nanofluid having center thin heater. The left and right walls of the enclosure are maintained at temperature T . The bottom wall is c considered with a constant heat source whereas the remaining part of bottom wall and top wall are kept adiabatic. The finite volume method based on SIMPLE algorithm is used to solve the governing equations in order to investigate the effect of heater length, Hartmann, Richardson, and Darcy numbers on the fluid-flow and heat transfer characteristics inside the enclosure. A set of graphical results are presented in terms of streamlines, isotherms, mid height velocity profiles and average Nusselt numbers. The results reveal that heat transfer rate increases as heater length increases for increasing Darcy and Richardson numbers. Among the two positions of heaters, larger enhancement of heat transfer is obtained for horizontal heater of maximum length. It is observed that, Hartmann number is a good control parameter for heat transfer in fluid-flow through porous medium in enclosure. Moreover, Ag-water nanofluid has greater merit to be used for heat transfer enhancement. This problem may be occurred in designing cooling system for electronic equipment to maximize the efficiency with active and secured operational conditions.

Natural Convective Flow in a Three Enclosure System Involving Two High Aspect Ratio Side Enclosures Joined to a Large Square Enclosure With Interfacial Heat Generation

2003 ◽  
Author(s):  
Patrick H. Oosthuizen
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Rayleigh Number ◽  
Aspect Ratio ◽  
Heat Generation ◽  
High Aspect Ratio ◽  
Convective Flow ◽  
Square Enclosure ◽  
Number Variation ◽  
Resistance To Heat

A numerical study of free convective flow in a vertical joined three enclosure arrangement has been undertaken. In this arrangement, a vertical heated wall kept at a uniform high temperature is contained in a high aspect ratio rectangular side enclosure. This enclosure is joined to a second high aspect ratio rectangular side enclosure which has the same height as the first side enclosure, the two enclosures being separated by a vertical impermeable dividing wall which offers no resistance to heat transfer. The second side enclosure is joined to a larger square enclosure, the vertical dividing wall between these two enclosures also being impermeable and offering no resistance to heat transfer. The vertical wall of the square main flow enclosure opposite to the dividing wall is maintained at a uniform lower temperature. There is a uniform rate of heat generation in the dividing wall between the inner side enclosure and the main enclosure. The situation considered is an approximate model of a double-paned window exposed to a hot outside environment and covered by a plane blind which in turn is exposed to cooled room. In some such cases there can be significant heat generation in the blind due to the absorbtion of solar energy, this being modeled by the heat generation in the one dividing wall. The flow has been assumed to be laminar and two-dimensional and results have been obtained for a Prandtl number of 0.7. The effects of Rayleigh number, dimensionless width of the side enclosures and dimensionless heat generation rate in the blind on the Nusselt number have been investigated. The results show that for a fixed Rayleigh number and for a given dimensionless first (i.e., outer) side enclosure width, there is a minimum in the Nusselt number variation with the dimensionless width of the second side enclosure. An approximate solution for the Nusselt number variation with the dimensionless width of the second side enclosure for small values of this dimensionless width has also been derived.

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