scholarly journals NATURAL CONVECTION IN HIGH ASPECT RATIO THREE-DIMENSIONAL ENCLOSURES WITH UNIFORM HEAT FLUX ON THE HEATED WALL

2004 ◽  
Vol 3 (2) ◽  
Author(s):  
T. Dias Jr. ◽  
L. F. Milanez
Keyword(s):  
Heat Flux ◽  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Aspect Ratio ◽  
Prandtl Number ◽  
High Aspect Ratio ◽  
Three Dimensional ◽  
Uniform Heat Flux ◽  
Uniform Heat

In this work, the laminar natural convection in high aspect ratio three-dimensional enclosures has been numerically studied. The enclosures studied here were heated with uniform heat flux on a vertical wall and cooled at constant temperature on the opposite wall. The remaining walls were considered adiabatic. Fluid properties were assumed constant except for the density change with temperature on the buoyancy term. The governing equations were solved using the finite volumes method and the dimensionless form of these equations has the Prandtl number and the modified Rayleigh number as parameters. The influences of the Rayleigh number and of the cavity aspect ratio on the Nusselt number, for a Prandtl number of 0.7, were analyzed. Results were obtained for values of the modified Rayleigh number up to 106 and for aspect ratios ranging from 1 to 20. The results were compared with two-dimensional results available in the literature and the variation of the average Nusselt number with the parameters studied were discussed.

scholarly journals NATURAL CONVECTION IN HIGH ASPECT RATIO THREE-DIMENSIONAL ENCLOSURES WITH UNIFORM HEAT FLUX ON THE HEATED WALL

2004 ◽  
Vol 3 (2) ◽  
pp. 100
Author(s):  
T. Dias Jr. ◽  
L. F. Milanez
Keyword(s):  
Heat Flux ◽  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Aspect Ratio ◽  
Prandtl Number ◽  
High Aspect Ratio ◽  
Three Dimensional ◽  
Uniform Heat Flux ◽  
Uniform Heat

In this work, the laminar natural convection in high aspect ratio three-dimensional enclosures has been numerically studied. The enclosures studied here were heated with uniform heat flux on a vertical wall and cooled at constant temperature on the opposite wall. The remaining walls were considered adiabatic. Fluid properties were assumed constant except for the density change with temperature on the buoyancy term. The governing equations were solved using the finite volumes method and the dimensionless form of these equations has the Prandtl number and the modified Rayleigh number as parameters. The influences of the Rayleigh number and of the cavity aspect ratio on the Nusselt number, for a Prandtl number of 0.7, were analyzed. Results were obtained for values of the modified Rayleigh number up to 106 and for aspect ratios ranging from 1 to 20. The results were compared with two-dimensional results available in the literature and the variation of the average Nusselt number with the parameters studied were discussed.

Natural Convection in a Partitioned Vertical Enclosure Heated With a Uniform Heat Flux

2006 ◽  
Vol 129 (6) ◽  
pp. 717-726 ◽  
Author(s):  
Kamil Kahveci
Keyword(s):  
Heat Flux ◽  
Nusselt Number ◽  
Natural Convection ◽  
Thermal Resistance ◽  
Average Nusselt Number ◽  
Numerical Study ◽  
Finite Thickness ◽  
Vertical Wall ◽  
Uniform Heat Flux ◽  
Uniform Heat

This numerical study looks at laminar natural convection in an enclosure divided by a partition with a finite thickness and conductivity. The enclosure is assumed to be heated using a uniform heat flux on a vertical wall, and cooled to a constant temperature on the opposite wall. The governing equations in the vorticity-stream function formulation are solved by employing a polynomial-based differential quadrature method. The results show that the presence of a vertical partition has a considerable effect on the circulation intensity, and therefore, the heat transfer characteristics across the enclosure. The average Nusselt number decreases with an increase of the distance between the hot wall and the partition. With a decrease in the thermal resistance of the partition, the average Nusselt number shows an increasing trend and a peak point is detected. If the thermal resistance of the partition further declines, the average Nusselt number begins to decrease asymptotically to a constant value. The partition thickness has little effect on the average Nusselt number.

Thermal Convection in a Rectangular Cavity Filled With a Heat-Generating, Darcy Porous Medium

1987 ◽  
Vol 109 (3) ◽  
pp. 697-703 ◽  
Author(s):  
V. Prasad
Keyword(s):  
Heat Flux ◽  
Porous Medium ◽  
Nusselt Number ◽  
Rayleigh Number ◽  
Aspect Ratio ◽  
Rectangular Cavity ◽  
Stratified Medium ◽  
Maximum Temperature ◽  
Wall Boundary ◽  
Uniform Heat

Two-dimensional, steady natural convection in a rectangular cavity filled with a heat-generating, saturated porous medium has been studied numerically for the case when the vertical walls of the cavity are isothermal and the horizontal walls are either adiabatic or cold. Results are presented in terms of the streamlines and isotherms, the maximum temperature in the cavity, and the local and overall Nusselt numbers. The buoyant flow together with the uniform heat generation produces a highly stratified medium at high Rayleigh numbers. Although the maximum temperature in the cavity θmax invariably increases with the Rayleigh number Ra and aspect ratio A, the rate of increase diminishes with this enhancement in Ra and A. However, the change in the horizontal wall boundary condition from adiabatic to cold reduces θmax. The local heat flux on the bounding walls is a strong function of the Rayleigh number, the aspect ratio, and the wall boundary conditions. The variation in overall Nusselt number is qualitatively similar to that observed in the case of a differentially heated cavity, and the present heat transfer rates are close to that for the cavity heated by applying a uniform heat flux. Several correlations are presented for maximum temperature and overall Nusselt number.

Natural Convective Heat Transfer From a Narrow Isothermal Vertical Flat Plate With a Uniform Heat Flux at the Surface

2007 ◽  
Author(s):  
Patrick H. Oosthuizen ◽  
Jane T. Paul
Keyword(s):  
Heat Flux ◽  
Nusselt Number ◽  
Vertical Plate ◽  
Three Dimensional ◽  
Uniform Heat Flux ◽  
Heated Plate ◽  
Dimensional Flow ◽  
Uniform Heat ◽  
Two Dimensional Flow ◽  
The Mean

Natural convective flow over a vertical plate with a uniform heat flux over its surface has been numerically studied. When the plate is wide compared to its height the flow can be adequately modeled by assuming two-dimensional flow. However, when the width of the plate is relatively small compared to its height, the heat transfer coefficient can be considerably greater than that predicted by these two-dimensional flow results. The Nusselt number distribution over a narrow vertical plate, with a uniform heat flux at the plate surface, has been numerically determined. This heated plate is embedded in a plane adiabatic surface, the surface of the adiabatic surface being in the same plane as the heated plate. It has been assumed that the fluid properties are constant except for the density change with temperature which gives rise to the buoyancy forces, this having been treated by using the Boussinesq approach. It has also been assumed that the flow is symmetrical about the vertical centre-plane of the plate. The solution has been obtained by numerically solving the full three-dimensional form of the governing equations, these equations being written in dimensionless form. The solution has the Rayleigh number, the dimensionless plate width and the Prandtl number as parameters. Results have been numerically determined for a relatively wide range of Rayleigh numbers and dimensionless plate widths for a Prandtl number of 0.7. The dimensionless plate width has been found to have a significant influence on the mean Nusselt number for the plate when the plate is narrow and the Rayleigh number is low. The conditions under which three dimensional flow effects can be neglected have been deduced and an empirical equation for the mean Nusselt number for narrow plates with a uniform surface heat flux has been derived from the numerical results.

Three Dimensional Numerical Simulation of Gas Heat Transfer in Rectangular Microchannels

2010 ◽  
Author(s):  
Xiaohong Yan ◽  
Qiuwang Wang
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Heat Flux ◽  
Aspect Ratio ◽  
Wall Temperature ◽  
Three Dimensional ◽  
Uniform Heat Flux ◽  
Flux Boundary Condition ◽  
Uniform Heat ◽  
Heat Flux Boundary Condition

Rectangular microchannel is the typical component of the micro heat exchangers and micro heat sinks. Three-dimensional compressible Navier-Stokes equations are solved for gas flow and heat transfer in microchannels under uniform heat flux boundary condition. The numerical methodology is based on the control volume SIMPLE scheme. It is found that the heat removal characteristic for compressible flow is better than the incompressible flow and it is not suitable to use conventionally defined Nu to measure the heat transfer characteristic for compressible heat transfer. The effect of the aspect ratio (width to height) on the cross-sectional averaged wall temperature and the Nu is negligible under the uniform heat flux boundary condition. However, the local uniformity of the wall temperature is significantly influenced by the aspect ratio. The square cross-section exhibits the best local uniformity of the wall temperature.

A Numerical Study of Three-Dimensional Natural Convection in a Low Aspect Ratio Horizontal Enclosure With a Uniform Heat Flux on the Lower Surface

1999 ◽  
Author(s):  
Patrick H. Oosthuizen
Keyword(s):  
Heat Flux ◽  
Rayleigh Number ◽  
Prandtl Number ◽  
Numerical Study ◽  
Lower Surface ◽  
Horizontal Surface ◽  
Uniform Heat Flux ◽  
Cross Sectional ◽  
Vertical Side ◽  
Uniform Heat

Abstract Flow in a rectangular enclosure with a square horizontal cross-section and with a uniform heat flux applied across the lower horizontal surface and with the upper horizontal surface cooled to a uniform low temperature has been numerically studied. The vertical side-walls of the enclosure are adiabatic. It has been assumed that the flow is laminar and that the fluid properties are constant except for the density change with temperature which gives rise to the buoyancy forces. The unsteady form of the governing equations, written in terms of the vector potential and vorticity vector functions and expressed in dimensionless form, have been solved using a finite-difference procedure based on the equations. The solution was started with no flow in the enclosure. The solution, in general, has the following parameters: the heat flux Rayleigh number Raq, the Prandtl number and the size A of the square cross-sectional shape compared to the height of the enclosure. Results have only been obtained for a Prandtl number of 0.7. Results for values of A between 0.5 and 3 for various relatively low and moderate values of Rayleigh number (up to 40000) have been obtained. The results have been used to determine the effect of A on the value of Raq below which there is no fluid motion in the enclosure and to examine the various flow patterns that arise as the value of Raq is increased with various values of A. The effect of A on the variation of the mean dimensionless lower surface temperature with Ra has also been examined.

Transient Natural Convection Slip Flow in a Vertical Microchannel Heated at Uniform Heat Flux

2008 ◽  
Author(s):  
Bernardo Buonomo ◽  
Oronzio Manca
Keyword(s):  
Heat Flux ◽  
Nusselt Number ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Mass Flow Rate ◽  
Knudsen Number ◽  
Flow Rate ◽  
Wall Temperature ◽  
Uniform Heat Flux ◽  
Vertical Microchannel

Miniaturization of devices has received a rapid expansion in the last years and a great attention of research activities is given to microflow due to its new applications of microfluidic systems and components. In the present paper a transient investigation on natural convection in parallel-plate vertical microchannels is carried out numerically. The vertical microchannel is considered asymmetrically or symmetrically heated at uniform heat flux. The first-order model for slip velocity and jump temperature is assumed in microscale conditions. The analysis is performed in laminar boundary layer assumption for different values for different values of Knudsen number, Rayleigh number and the ratio of wall heat flux in order to evaluate their effects on wall temperatures, mass flow rate and Nusselt number. Wall temperature overshoots are detected for the different conditions. These values increase increasing the Knudsen number, Kn, at high Rayleigh number, Ra, whereas for lower Ra the lowest wall temperature are obtained for Kn = 0.05. Mass flow rate increases increasing Kn whereas Nusselt number decreases increasing Kn.

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