Analytical Study of Natural Convection in a Cavity With Volumetric Heat Generation

2005 ◽  
Vol 128 (2) ◽  
pp. 176-182 ◽  
Author(s):  
Mandar V. Joshi ◽  
U. N. Gaitonde ◽  
Sushanta K. Mitra
Keyword(s):  
Natural Convection ◽  
Heat Generation ◽  
Analytical Study ◽  
Vertical Component ◽  
Governing Equations ◽  
Biharmonic Equations ◽  
Aspect Ratios ◽  
Vertical Walls ◽  
Volumetric Heat Generation ◽  
Good Agreement

An analytical study has been conducted for natural convection in a cavity of different aspect ratios with uniform volumetric heat generation. Two different boundary conditions are investigated for the cavity, viz., all walls are isothermal; two horizontal walls are adiabatic and two vertical walls are isothermal. A stream function vorticity formulation is used where the variables are expanded in terms of Rayleigh number, defined as Ra=gβh5q‴∕ανk. The governing equations are reduced, to biharmonic equations, and these biharmonic equations are solved using one of the methods, available in the literature. It is observed that the horizontal component of velocity is smaller than the vertical component near the center and the vertical walls of the cavity. The results for velocity profiles are compared with the simulations obtained from Fluent and they are found to be in good agreement.

Analytical Study of Natural Convection in a Cavity With Volumetric Heat Generation

Volume 1 ◽  
2004 ◽  
Author(s):  
Mandar V. Joshi ◽  
U. N. Gaitonde ◽  
Sushanta K. Mitra
Keyword(s):  
Natural Convection ◽  
Aspect Ratio ◽  
Heat Generation ◽  
Central Region ◽  
Analytical Study ◽  
Vertical Direction ◽  
Maximum Temperature ◽  
Small Aspect Ratio ◽  
Governing Equations ◽  
Volumetric Heat Generation

A semi-analytical method for natural convection in a two dimensional rectangular enclosure, with uniform volumetric heat generation, having insulated horizontal boundaries, and isothermal vertical boundaries, has been studied here. In this method, the governing equations for natural convection, have been solved under the assumption that for a cavity with small aspect ratio, the flow in the central region of the cavity is only in the vertical direction. It is found that for the cavities with small aspect ratio, the temperature in central region of the cavity is nearly constant along the horizontal direction. However, there is a uniform temperature gradient in the vertical direction, which can be related to the maximum temperature in conduction. The velocity profiles and temperature profiles obtained in the present work, are compared with the numerical simulations by Fluent and a fair agreement is found between these results.

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.

Heat and Mass Transfer during Drying of Clay Ceramic Materials: A Three-Dimensional Analytical Study

2017 ◽  
Vol 10 ◽  
pp. 93-106 ◽  
Author(s):  
M.K. Teixeira de Brito ◽  
D.B. Teixeira de Almeida ◽  
A.G. Barbosa de Lima ◽  
L. Almeida Rocha ◽  
E. Santana de Lima ◽  
...  
Keyword(s):  
Mass Transfer ◽  
Heat And Mass Transfer ◽  
Analytical Study ◽  
Separation Of Variables ◽  
Three Dimensional ◽  
Ceramic Materials ◽  
Governing Equations ◽  
Convective Boundary ◽  
Good Agreement

This work aims to study heat and mass transfer in solids with parallelepiped shape with particular reference to drying process. A transient three-dimensional mathematical model based on the Fick ́s and Fourier ́s Laws was developed to predict heat and mass transport in solids considering constant physical properties and convective boundary conditions at the surface of the solid. The analytical solution of the governing equations was obtained using the method of separation of variables. The study was applied in the drying of common ceramic bricks. Predicted results of the heating and drying kinetics and the moisture and temperature distributions inside the material during the process, are compared with experimental data and good agreement was obtained. It has been found that the vertices of the solid dry and heat first. This provokes thermal and hydric stresses inside the material, which may compromise the quality of the product after drying.

Comparative Numerical Simulation of Natural Convection in a Porous Horizontal Cylindrical Annulus

2014 ◽  
Vol 670-671 ◽  
pp. 613-616 ◽  
Author(s):  
Jabrane Belabid ◽  
Abdelkhalek Cheddadi
Keyword(s):  
Natural Convection ◽  
Numerical Study ◽  
Saturated Porous Medium ◽  
Published Data ◽  
Governing Equations ◽  
Alternating Direction Implicit ◽  
Cylindrical Annulus ◽  
Alternating Direction ◽  
Concentric Cylinders ◽  
Good Agreement

This work presents a numerical study of the natural convection in a saturated porous medium bounded by two horizontal concentric cylinders. The governing equations (in the stream function and temperature formulation) were solved using the ADI (Alternating Direction Implicit) method and the Samarskii-Andreev scheme. A comparison between the two methods is conducted. In both cases, the results obtained for the heat transfer rate given by the Nusselt number are in a good agreement with the available published data.

Numerical Study of Three-Dimensional Oscillatory Natural Convection at Low Prandtl Number in Rectangular Enclosures

2000 ◽  
Vol 123 (1) ◽  
pp. 77-83 ◽  
Author(s):  
Shunichi Wakitani
Keyword(s):  
Natural Convection ◽  
Prandtl Number ◽  
Numerical Study ◽  
Three Dimensional ◽  
Width Ratio ◽  
Three Dimensional Flow ◽  
Longitudinal Vortices ◽  
Aspect Ratios ◽  
Vertical Walls ◽  
Prandtl Numbers

Numerical investigations are presented for three-dimensional natural convection at low Prandtl numbers (Pr) from 0 to 0.027 in rectangular enclosures with differentially heated vertical walls. Computations are carried out for the enclosures with aspect ratios (length/height) 2 and 4, and width ratios (width/height) ranging from 0.5 to 4.2. Dependence of the onset of oscillation on the Prandtl number, the aspect ratio, and the width ratio is investigated. Furthermore, oscillatory, three-dimensional flow structure is clarified. The structure is characterized by some longitudinal vortices (rolls) as well as cellular pattern.

Computational Analysis of Laminar Natural Convection in Rectangular Enclosures of Different Aspect Ratios With Different Heating Conditions

2012 ◽  
Author(s):  
Mosfequr Rahman ◽  
Charles Walker ◽  
Gustavo Molina ◽  
Valentin Soloiu
Keyword(s):  
Heat Flux ◽  
Natural Convection ◽  
Rayleigh Number ◽  
Temperature Gradient ◽  
Aspect Ratio ◽  
Heat Generation ◽  
Internal Heat ◽  
Internal Heat Generation ◽  
External Temperature ◽  
Aspect Ratios

Natural convection in rectangular enclosures is found in many real-world engineering applications. Included in these applications are the energy efficient design of buildings, operation and safety of nuclear reactors, solar collector design, passive energy storage, heat transfer across multi-pane windows, thermo-electric refrigeration and heating devices, and the design-for-mitigation of optical distortion in large-scale laser systems. A common industrial application of natural convection is free air cooling without the aid of fans and can happen on small scales such as computer chips to large scale process equipment. The enclosure phenomena can loosely be organized into two large classes: (1) horizontal enclosures heated from below and (2) vertical enclosures heated from the side. In addition to temperature gradient convection strength within the enclosure can vary due to the existence of heat sources with different strength. Numerical simulations are conducted for free convective flow of air with or without internal heat generation in two-dimensional rectangular enclosures of different aspect ratios. The objective of this numerical study is to investigate the effects of external temperature gradient, internal heat generation and aspect ratio (AR) of enclosure (ratio of the length of the isothermal walls to their separation distance), in free convective laminar flow of a fluid. Two-dimensional rectangular enclosures of different aspect ratio (1, 2, 4, 6, 8, and 10) with two adiabatic side walls and isothermal bottom (hot) and top (cold) walls are considered for the first configuration. Whereas for the second configuration, two adiabatic top and bottom walls, isothermal left side (cold) and right side (hot) walls are considered. Two principal parameters considered for the flow of fluid are the external Rayleigh number, RaE, which represents the effect due to the differential heating of the isothermal walls, and the internal Rayleigh number, RaI, which represents the strength of the internal heat generation. The effect of external temperature gradient and aspect ratio on natural convection has been observed by varying the value of external Rayleigh number (RaE) equal to 2×104, 2×105, and 2×106 and keeping the internal Rayleigh number constant (RaI = 2×105). Similarly, the effect of internal heat generation and aspect ratio on natural convection has been observed by varying the value of internal Rayleigh number (RaI) equal to 2×104, 2×105, and 2×106 and keeping the external Rayleigh number constant (RaE = 2×105). Significant changes in flow patterns and isotherms have been observed for all cases. Also the variation of average heat flux ratio (convective heat flux/corresponding conduction heat flux) along the hot and cold walls, and the convection strength have been calculated for all cases. It is found that the aspect ratio has a significant effect in fluid flow and heat transfer in the enclosures. The average heat flux ratio and the strength of convection increase with aspect ratio as the enclosure shape changes square (AR = 1) to shallow (AR > 1).

Effect of Wall Conduction on the Stability of a Fluid in a Rectangular Region Heated from Below

1972 ◽  
Vol 94 (4) ◽  
pp. 446-452 ◽  
Author(s):  
Ivan Catton
Keyword(s):  
Lateral Wall ◽  
Rectangular Region ◽  
Slip Boundary Conditions ◽  
Slip Boundary ◽  
Aspect Ratios ◽  
Usual Manner ◽  
Vertical Walls ◽  
The Stability ◽  
The Galerkin Method ◽  
Good Agreement

The initiation of natural convection in a fluid confined above and below by rigid, perfectly conducting surfaces and laterally by vertical walls of arbitrary thermal conductivity which form a rectangle is examined. The linearized perturbation equations are obtained in the usual manner and reduced to an eigenvalue problem. The Rayleigh number is the eigenvalue and is a function of the lateral-wall conductance and horizontal plan form (aspect ratios). The problem associated with satisfying the no-slip boundary conditions on all surfaces is surmounted by using the Galerkin method. Results are compared with experiments and shown to be in good agreement.

scholarly journals NUMERICAL ANALYSIS OF THE NATURAL CONVECTION IN HORIZONTAL ANNULI AT LOW AND MODERATE Ra

2006 ◽  
Vol 5 (2) ◽  
pp. 58
Author(s):  
E. L. M. Padilla ◽  
R. Campregher ◽  
A. Silveira-Neto
Keyword(s):  
Natural Convection ◽  
Three Dimensional ◽  
Staggered Grid ◽  
Governing Equations ◽  
Concentric Cylinders ◽  
Wide Range ◽  
Horizontal Annuli ◽  
Rayleigh Numbers ◽  
The Heat Transfer Coefficient ◽  
Good Agreement

The natural convection at low and moderate Rayleigh numbers (Ra) incylindrical horizontal annuli with imposed temperatures in both surfaces isnumerically studied. This flow inside concentric cylinders classic configuration has a wide range of practical and technological applications, which justifies its growing studies efforts. In this work, the governing equations are discretized by the volume finite technique over a staggered grid, with second-order accuracy in space and time. The flow pattern is presented by several Rayleigh numbers, with an analysis of the heat transfer coefficient and flow properties. Furthermore, a three-dimensional field is shown at a moderate Ra number. The results showed a good agreement with the experimental data.

Sign in / Sign up

Export Citation Format

Share Document