The Effect of the Top Wall Temperature on the Laminar Natural Convection in Rectangular Cavities With Different Aspect Ratios

2009 ◽  
Vol 131 (5) ◽  
Author(s):  
Wenjiang Wu ◽  
Chan Y. Ching
Keyword(s):  
Natural Convection ◽  
Aspect Ratio ◽  
Wall Temperature ◽  
Vertical Wall ◽  
Flow Region ◽  
Temperature Profiles ◽  
Aspect Ratios ◽  
Vertical Walls ◽  
C And N ◽  
Laminar Natural Convection

The effect of the top wall temperature on the laminar natural convection in air-filled rectangular cavities driven by a temperature difference across the vertical walls was investigated for three different aspect ratios of 0.5, 1.0, and 2.0. The temperature distributions along the heated vertical wall were measured, and the flow patterns in the cavities were visualized. The experiments were performed for a global Grashof number of approximately 1.8×108 and nondimensional top wall temperatures from 0.52 (insulated) to 1.42. As the top wall was heated, the flow separated from the top wall with an undulating flow region in the corner of the cavity, which resulted in a nonuniformity in the temperature profiles in this region. The location and extent of the undulation in the flow are primarily determined by the top wall temperature and nearly independent of the aspect ratio of the cavity. The local Nusselt number was correlated with the local Rayleigh number for all three cavities in the form of Nu=C⋅Ran, but the values of the constants C and n changed with the aspect ratio.

The Effect of the Top Wall Temperature on the Laminar Natural Convection in Rectangular Cavities With Different Aspect Ratios

2007 ◽  
Author(s):  
Wenjiang Wu ◽  
Chan Y. Ching
Keyword(s):  
Natural Convection ◽  
Aspect Ratio ◽  
Wall Temperature ◽  
Vertical Wall ◽  
Flow Region ◽  
Temperature Profiles ◽  
Aspect Ratios ◽  
Vertical Walls ◽  
C And N ◽  
Laminar Natural Convection

The effect of the top wall temperature on the laminar natural convection in air-filled rectangular cavities driven by a temperature difference across the vertical walls was investigated for three different aspect ratios of 0.5, 1.0 and 2.0. The temperature distributions along the heated vertical wall were measured and the flow patterns in the cavities were visualized. The experiments were performed for a global Grashof number of approximately 1.8×108 and non-dimensional top wall temperatures from 0.52 (insulated) to 1.42. As the top wall was heated, the flow separated from the top wall with an undulated flow region in the corner of the cavity, which resulted in a non-uniformity in the temperature profiles in this region. The location and extent of the undulation in the flow is primarily determined by the top wall temperature, and nearly independent of the aspect ratio of the cavity. The local Nusselt number was correlated to the local Rayleigh number for all three cavities in the form of Nu = C · Ran, but the values of the constants C and n changed with the aspect ratio.

Laminar Natural Convection in a Discretely Heated Cavity: I—Assessment of Three-Dimensional Effects

1995 ◽  
Vol 117 (4) ◽  
pp. 902-909 ◽  
Author(s):  
T. J. Heindel ◽  
S. Ramadhyani ◽  
F. P. Incropera
Keyword(s):  
Natural Convection ◽  
Vertical Wall ◽  
Three Dimensional ◽  
Companion Paper ◽  
Two Dimensional ◽  
Dimensional Model ◽  
Three Dimensional Model ◽  
Nusselt Numbers ◽  
Aspect Ratios ◽  
Laminar Natural Convection

Two and three-dimensional calculations have been performed for laminar natural convection induced by a 3 × 3 array of discrete heat sources flush-mounted to one vertical wall of a rectangular cavity whose opposite wall was isothermally cooled. Edge effects predicted by the three-dimensional model yielded local and average Nusselt numbers that exceeded those obtained from the two-dimensional model, as well as average surface temperatures that were smaller than the two-dimensional predictions. For heater aspect ratios Ahtr ≲ 3, average Nusselt numbers increased with decreasing Ahtr. However, for Ahtr ≳ 3, the two and three-dimensional predictions were within 5 percent of each other and results were approximately independent of Ahtr. In a companion paper (Heindel et al., 1995a), predictions are compared with experimental results and heat transfer correlations are developed.

Closed-Form Analytical Solutions for Laminar Natural Convection on Horizontal Plates

2013 ◽  
Vol 135 (10) ◽  
Author(s):  
Abhijit Guha ◽  
Subho Samanta
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Heat Flux ◽  
Natural Convection ◽  
Prandtl Number ◽  
Boundary Layers ◽  
Wall Temperature ◽  
Temperature Profiles ◽  
Integral Analysis ◽  
Laminar Natural Convection

A boundary layer based integral analysis has been performed to investigate laminar natural convection heat transfer characteristics for fluids with arbitrary Prandtl number over a semi-infinite horizontal plate subjected either to a variable wall temperature or variable heat flux. The wall temperature is assumed to vary in the form T¯w(x¯)-T¯∞=ax¯n whereas the heat flux is assumed to vary according to qw(x¯)=bx¯m. Analytical closed-form solutions for local and average Nusselt number valid for arbitrary values of Prandtl number and nonuniform heating conditions are mathematically derived here. The effects of various values of Prandtl number and the index n or m on the heat transfer coefficients are presented. The results of the integral analysis compare well with that of previously published similarity theory, numerical computations and experiments. A study is presented on how the choice for velocity and temperature profiles affects the results of the integral theory. The theory has been generalized for arbitrary orders of the polynomials representing the velocity and temperature profiles. The subtle role of Prandtl number in determining the relative thicknesses of the velocity and temperature boundary layers for natural convection is elucidated and contrasted with that in forced convection. It is found that, in natural convection, the two boundary layers are of comparable thickness if Pr ≤ 1 or Pr ≈ 1. It is only when the Prandtl number is large (Pr > 1) that the velocity boundary layer is thicker than the thermal boundary layer.

Natural Convection Patterns in Right-Angled Triangular Cavities with Heated Vertical Sides and Cooled Hypotenuses

2005 ◽  
Vol 127 (10) ◽  
pp. 1181-1186 ◽  
Author(s):  
El Hassan Ridouane ◽  
Antonio Campo ◽  
Jane Y. Chang
Keyword(s):  
Natural Convection ◽  
Vertical Wall ◽  
Ambient Air ◽  
Correlation Equation ◽  
Apex Angle ◽  
Cross Sectional ◽  
Vertical Walls ◽  
Laminar Natural Convection ◽  
Convection Patterns ◽  
Volume Method

The present investigation deals with the numerical computation of laminar natural convection in a gamma of right-angled triangular cavities filled with air. The vertical walls are heated and the inclined walls are cooled while the upper connecting walls are insulated from the ambient air. The defining apex angle α is located at the lower vertex formed between the vertical and inclined walls. This unique kind of cavity may find application in the miniaturization of electronic packaging severely constrained by space and/or weight. The finite volume method is used to perform the computational analysis encompassing a collection of apex angles α compressed in the interval that extends from 5° to 63°. The height-based Rayleigh number, being unaffected by the apex angle α, ranges from a low 103 to a high 106. Numerical results are reported for the velocity field, the temperature field and the mean convective coefficient along the heated vertical wall. Overall, the matching between the numerically predicted temperatures and the experimental measurements of air at different elevations inside a slim cavity is of ordinary quality. For purposes of engineering design, a Nu¯H correlation equation was constructed and also a figure-of-merit ratio between the Nu¯H and the cross sectional area A of the cavity was proposed.

A Numerical Study of Natural Convection in Partially Open Enclosures With a Conducting Side-Wall

2004 ◽  
Vol 126 (1) ◽  
pp. 76-83 ◽  
Author(s):  
G. Desrayaud ◽  
G. Lauriat
Keyword(s):  
Natural Convection ◽  
Numerical Study ◽  
Finite Thickness ◽  
Vertical Wall ◽  
Side Wall ◽  
Practical Applications ◽  
Hot Air ◽  
Aspect Ratios ◽  
Vertical Walls ◽  
Rayleigh Numbers

A numerical study of natural convection generated by a cold vertical wall of an enclosure with two openings on the opposite wall of finite thickness is presented. The enclosure is connected to an infinite reservoir filled with hot air. A two-dimensional laminar flow is assumed both within the enclosure and along the side of the bounding wall immersed into the reservoir. The effects of the size of the openings, spacing between the vertical walls and thermal resistance of the bounding wall are investigated. Numerical results are discussed for aspect ratios of the enclosure and Rayleigh numbers relevant to practical applications.

Laminar Natural Convection in an Air-Filled Square Cavity With Partitions on the Top Wall

2009 ◽  
Author(s):  
Wenjiang Wu ◽  
Chan Y. Ching
Keyword(s):  
Boundary Layer ◽  
Natural Convection ◽  
Thermal Effect ◽  
Rear Surface ◽  
Vertical Wall ◽  
Square Cavity ◽  
Recirculating Flow ◽  
Vertical Walls ◽  
Laminar Natural Convection ◽  
Temperature And Flow Fields

The laminar natural convection in an air-filled square cavity with a partition on the top wall was experimentally investigated. Temperature measurements and flow visualizations were performed for cases with heated and cooled vertical walls (corresponding to a global Grashof number GrH of approximately 1.3 × 108) and non-dimensional top wall temperatures θT of 0.56 (insulated) to 2.3. Experiments were performed with an aluminum partition with non-dimensional height HP/H of 0.0625 and 0.125 attached to the top wall at x/H = 0.1, 0.2, 0.4 and 0.6. The blockage effect and/or the thermal effect of the partition resulted in changes to the temperature and flow fields, but were mainly limited to the vicinity of the partition. The partition on the heated top wall resulted in a recirculating flow between the partition and the heated vertical wall. For a given partition height, the structure of this recirculating flow was dependent on the partition location and θT. A thermal boundary layer developed along the rear surface of the partition due to the thermal effect of the partition. The ambient temperature outside the boundary layer and Nu near the corner region were affected by the partition height due to the changes in the recirculating flow and due to the thermal effect on the rear surface of the partition.

The Effect of Partitions on the Laminar Natural Convection in a Square Cavity

2008 ◽  
Author(s):  
Wenjiang Wu ◽  
Chan Y. Ching
Keyword(s):  
Boundary Layer ◽  
Natural Convection ◽  
Secondary Flow ◽  
Rear Surface ◽  
Vertical Wall ◽  
Convection Flow ◽  
Square Cavity ◽  
Flow Circulation ◽  
Laminar Natural Convection ◽  
Layer Flow

The effect of a partition on the laminar natural convection flow in an air-filled square cavity driven by a temperature difference across the vertical walls was investigated experimentally. Two partitions with non-dimensional heights of 0.0625 and 0.125 was attached either to the upper half of the heated vertical wall or the top wall at different locations. The experiments were performed for a global Grashof number of approximately 1.24×108 and non-dimensional top wall temperatures of approximately 0.48 to 2.28. At the higher top wall temperatures, a secondary flow circulation region formed between the partition attached to the top wall and the heated vertical wall of the cavity. This secondary flow circulation region was sensitive to the location and height of the partition, in addition to the top wall temperature of the cavity. The secondary flow circulation region moved the location where the upward boundary layer flow along the heated vertical wall turned over to be further away from the top wall, than in the cavity without the partition. A thermal boundary layer was observed to move along the rear surface of the partition attached to the top wall. In the region close to the top wall, the partitions caused the non-dimensional temperature outside of the boundary layer and the local Nusselt number along the heated vertical wall to be different from that in the cavity without the partition. There were no significant effects of the partition on the flow and heat transfer characteristics in the lower half of the cavity.

Natural Convection of Cu-Gallium Nanofluid in Enclosures

2011 ◽  
Vol 133 (12) ◽  
Author(s):  
Cong Qi ◽  
Yurong He ◽  
Yanwei Hu ◽  
Juancheng Yang ◽  
Fengchen Li ◽  
...  
Keyword(s):  
Thermal Conductivity ◽  
Nusselt Number ◽  
Natural Convection ◽  
Aspect Ratio ◽  
Convection Heat Transfer ◽  
Low Velocity ◽  
Grashof Number ◽  
Aspect Ratios ◽  
Wide Range ◽  
Temperature Dependent Properties

In this work, the natural convection heat transfer of Cu-gallium nanofluid in a differentially heated enclosure is investigated. A single-phase model is employed with constant or temperature-dependent properties of the fluid. The results are shown over a wide range of Grashof numbers, volume fractions of nanoparticles, and aspect ratios. The Nusselt number is demonstrated to be sensitive to the aspect ratio. It is found that the Nusselt number is more sensitive to thermal conductivity than viscosity at a low velocity (especially for a low aspect ratio and a low Grashof number), however, it is more sensitive to the viscosity than the thermal conductivity at a high velocity (high aspect ratio and high Grashof number). In addition, the evolution of velocity vectors, isotherms, and Nusselt number for a small aspect ratio is investigated.

Sign in / Sign up

Export Citation Format

Share Document