Effect of the Temperature Difference Aspect Ratio on Natural Convection in a Square Cavity for Nonuniform Thermal Boundary Conditions

2007 ◽  
Vol 129 (12) ◽  
pp. 1723-1728 ◽  
Author(s):  
M. Sathiyamoorthy ◽  
Tanmay Basak ◽  
S. Roy ◽  
N. C. Mahanti
Keyword(s):  
Nusselt Number ◽  
Natural Convection ◽  
Aspect Ratio ◽  
Temperature Difference ◽  
Heat Transfer Process ◽  
Bottom Wall ◽  
Maximum Temperature ◽  
Convection Flow ◽  
Square Cavity ◽  
Thermal Boundary Conditions

The present numerical investigation deals with steady natural convection flow in a closed square cavity when the bottom wall is sinusoidal heated and vertical walls are linearly heated, whereas the top wall is well insulated. In the nonuniformly heated bottom wall maximum temperature TH attains at the center of the bottom wall. The sidewalls are linearly heated, maintained at minimum temperature Tc at top edges of the sidewalls and at temperature Th at the bottom edges of the sidewalls, i.e., Tc≤Th≤TH. Nonlinear coupled PDEs governing the flow have been solved by the penalty finite element method with biquadratic rectangular elements. Numerical results are obtained for various values of Prandtl number (Pr)(0.01≤Pr≤10) and temperature difference aspect ratio A=[(Th−Tc)∕(TH−Tc)](0≤A≤1) for higher Raleigh number Ra=105. Results are presented in the form of streamlines, isotherm contours, local Nusselt number, and the average Nusselt number as a function of temperature difference aspect ratio A. The overall heat transfer process is shown to be tuned efficiently with suitable selection of A.

Effects of Thermal Boundary Conditions on Entropy Generation During Natural Convection in a Differentially Heated Square Cavity

2010 ◽  
Author(s):  
Ram Satish Kaluri ◽  
Tanmay Basak ◽  
A. R. Balakrishnan
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Boundary Conditions ◽  
Entropy Generation ◽  
Bottom Wall ◽  
Convection Flow ◽  
Uniform Heating ◽  
Square Cavity ◽  
Fluid Friction ◽  
Thermal Boundary Conditions

Natural convection is a widely occurring phenomena which has important applications in material processing, energy storage devices, electronic cooling, building ventilation etc. The concept of ‘entropy generation minimization’, which is a thermodynamic approach for optimization, may be very useful in designing efficient thermal systems. In the current study, entropy generation in steady laminar natural convection flow in a square cavity is studied with following isothermal boundary conditions: (1) Bottom wall is uniformly heated (2) Bottom wall is sinusoidally heated. The side walls are maintained cold and the top wall is maintained adiabatic. The thermal boundary condition in non-uniform heating case (case 2) is such that the dimensionless average temperature of the bottom wall is equal to that of uniform heating case (case 1). The prime objective of this work is to investigate the influence of uniform and non-uniform heating on entropy generation. The governing mass, momentum and energy equations are solved using Galerkin finite element method. Streamlines, isotherms, contour maps of entropy generation due to heat transfer and fluid friction are studied for Pr = 0.01 (molten metals) and 7 (water) in range of Ra = 103–105. Detailed analysis on the effect of uniform and non-uniform thermal boundary conditions on entropy generation due to heat transfer and fluid friction has been presented. Also, the average Bejan’s number which indicates the relative dominance of entropy generation due to heat transfer or fluid friction and the total entropy generation are studied for each case.

Natural convection flow in a vertical micro-annulus with time-periodic thermal boundary conditions

2018 ◽  
Vol 14 (5) ◽  
pp. 1064-1081
Author(s):  
Basant Kumar Jha ◽  
Michael O. Oni
Keyword(s):  
Nusselt Number ◽  
Natural Convection ◽  
Boundary Conditions ◽  
Skin Friction ◽  
Convection Flow ◽  
Natural Convection Flow ◽  
Content Type ◽  
Thermal Boundary Conditions ◽  
The Impact ◽  
Time Periodic

PurposeThe purpose of this paper is to investigate the impact of time-periodic thermal boundary conditions on natural convection flow in a vertical micro-annulus.Design/methodology/approachAnalytical solution in terms of Bessel’s function and modified Bessel’s function of order 0 and 1 is obtained for velocity, temperature, Nusselt number, skin friction and mass flow rate.FindingsIt is established that the role of Knudsen number and fluid–wall interaction parameter is to decrease fluid temperature, velocity, Nusselt number and skin friction.Research limitations/implicationsNo laboratory practical or experiment was conducted.Practical implicationsCooling device in electronic panels, card and micro-chips is frequently cooled by natural convection.Originality/valueIn view of the amount of works done on natural convection in microchannel, it becomes interesting to investigate the effect that time-periodic heating has on natural convection flow in a vertical micro-annulus. The purpose of this paper is to examine the impact of time-periodic thermal boundary conditions on natural convection flow in a vertical micro-annulus.

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.

scholarly journals Natural convection flow in a square cavity with internal heat generation and a flush mounted heater on a side wall

2011 ◽  
Vol 7 (2) ◽  
pp. 37-50 ◽  
Author(s):  
Md. Mustafizur Rahman ◽  
M. Arif Hasan Mamun ◽  
M. Masum Billah ◽  
Saidur Rahman
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Natural Convection ◽  
Heat Generation ◽  
Vertical Wall ◽  
Heated Wall ◽  
Convection Flow ◽  
Square Cavity ◽  
Natural Convection Flow ◽  
Heater Length

In this study natural convection flow in a square cavity with heat generating fluid and a finite size heater on the vertical wall have been investigated numerically. To change the heat transfer in the cavity, a heater is placed at different locations on the right vertical wall of the cavity, while the left wall is considered to be cold. In addition, the top and bottom horizontal walls are considered to be adiabatic and the cavity is assumed to be filled with a Bousinessq fluid having a Prandtl number of 0.72. The governing mass, momentum and energy equations along with boundary conditions are expressed in a normalized primitive variables formulation. Finite Element Method is used in solution of the normalized governing equations. The parameters leading the problem are the Rayleigh number, location of the heater, length of the heater and heat generation. To observe the effects of the mentioned parameters on natural convection in the cavity, we considered various values of heater locations, heater length and heat generation parameter for different values of Ra varying in the range 102 to 105. Results are presented in terms of streamlines, isotherms, average Nusselt number at the hot wall and average fluid temperature in the cavity for the mentioned parameters. The results showed that the flow and thermal fields through streamlines and isotherms as well as the rate of heat transfer from the heated wall in terms of Nusselt number are strongly dependent on the length and locations of the heater as well as heat generating parameter.DOI: 10.3329/jname.v7i2.3292 

scholarly journals Numerical Investigation of Natural Convection Flow in a Hexagonal Enclosure Having Vertical Fin

2019 ◽  
Vol 11 (2) ◽  
pp. 173-183 ◽  
Author(s):  
M. Fayz -Al- Asad ◽  
M. M. A. Sarker ◽  
M. J. H. Munshi
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Natural Convection ◽  
Transfer Rate ◽  
Numerical Study ◽  
Bottom Wall ◽  
Convection Flow ◽  
Temperature Profiles ◽  
Natural Convection Flow ◽  
Fin Efficiency

Numerical study of natural convection flow in a hexagonal enclosure with a single vertical fin attached to its heated bottom wall has been carried out. Finite element method based Galerkin weighted residual technique is used to solve the governing equation. The horizontal walls of the enclosure are kept at constant high temperature while the inclined walls are kept at constant cold temperature. A vertical heated fin is attached to the hot bottom wall with a length  at a position  from the left surface having thickness . The Prandlt number for the flow inside the enclosure is 0.71. The results of the problem are presented in graphical and tabular forms and discussed. The fin efficiency and temperature distribution were examined. The numerical results indicate the strong influence of the mentioned parameters on the flow structure and heat transfer as well as temperature. A set of graphical results are presented in terms of streamlines, isotherms contour, temperature profiles, velocity profiles, local Nusselt number and average Nusselt number. The obtained results indicated that the heat transfer rate increases with the increase of Rayleigh number in a hexagonal enclosure. The results are validated comparing with the published works.

scholarly journals Natural convection in tilted square cavities with triangular shaped top cold wall

1970 ◽  
Vol 39 (1) ◽  
pp. 30-39 ◽  
Author(s):  
Tamanna Sultana ◽  
Sumon Saha ◽  
Goutam Saha ◽  
Md Quamrul Islam
Keyword(s):  
Heat Transfer ◽  
Finite Element ◽  
Nusselt Number ◽  
Natural Convection ◽  
Numerical Study ◽  
Constant Heat Flux ◽  
Heat Transfer Process ◽  
Bottom Wall ◽  
Grashof Number ◽  
Inclination Angles

A numerical study of natural convection in a tilted square cavity with heated horizontal base and cold upper wall is presented. The present study is based in such a configuration where the top triangular wall of two different shapes is maintained at a constant low temperature. A constant heat flux source whose length is 20% of the total length of the cavity is discretely embedded at the left corner of the bottom wall. The remaining part of the bottom wall and the two sidewalls are considered to be adiabatic. The study includes computations for inclination angles of the cavity from 0° to 45°, where the Grashof number, Gr varies from 103 to 106. The Penalty finite element method has been used to see the effects of inclination angles and Grashof number on heat transfer process in the cavity. Results are presented in the form of streamline and isotherm plots as well as the variation of the average Nusselt number. Observation shows the significant effect of different triangular top surface on the heat transfer characteristics at the higher Grashof number and inclination angle. Keywords: Natural convection, Penalty finite element, Nusselt number, Isoflux heating. doi:10.3329/jme.v39i1.1831 Journal of Mechanical Engineering, vol. ME39, No. 1, June 2008 30-39  

Natural Convection in Rectangular Cavities at Various Aspect Ratios and Inclinations With Isothermal Sidewalls and Constant Flux Heat Source on the Bottom Wall

2004 ◽  
Author(s):  
M. A. R. Sharif ◽  
Taqui-ur-Rahman Mohammed
Keyword(s):  
Natural Convection ◽  
Heat Source ◽  
Heat Transfer Process ◽  
Bottom Wall ◽  
Maximum Temperature ◽  
Bottom Surface ◽  
Source Surface ◽  
Constant Flux ◽  
Aspect Ratios ◽  
Inclination Angles

Natural convection in rectangular cavities is studied numerically using a finite volume based computational procedure. In many applications, especially for cooling of electronic components, a natural convection configuration is encountered where the heat source is at the bottom surface and the sidewalls are at colder temperature while the top wall can be considered adiabatic. The present study is based on such a configuration where a constant flux heat source is symmetrically embedded at the bottom wall. The non-heated parts of the bottom wall are considered adiabatic. The study includes computations for cavities at various aspect ratios, ranging from 0.5 to 2, and inclination angles of the cavity from 0° to 30°. The Grashof number is varied from 103 to 106. The effects of aspect ratio and inclination angles on the heat transfer process are analysed. Results are presented in the form of streamline and isotherm plots as well as the variation of the average Nusselt number and maximum temperature at the heat source surface under different conditions.

Unsteady MHD natural convection flow of a nanofluid inside an inclined square cavity containing a heated circular obstacle

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
M. A. Mansour ◽  
Rama Subba Reddy Gorla ◽  
Sadia Siddiqa ◽  
A. M. Rashad ◽  
T. Salah
Keyword(s):  
Nusselt Number ◽  
Natural Convection ◽  
Average Nusselt Number ◽  
Convection Flow ◽  
Square Cavity ◽  
Natural Convection Flow ◽  
Symmetric Pattern ◽  
Inclined Cavity ◽  
The Right ◽  
Good Agreement

Abstract The phenomena of unsteady magnetohydrodynamics (MHD) natural convection flow in an inclined square cavity filled with nanofluid and containing a heated circular obstacle at its center with heat generation/absorption impact are examined numerically. The cavity’s right and left walls are maintained at low temperatures, while the remaining walls are adiabatic. The volumetric external force, MHD, is applied across the inclined cavity. A penalty formulation-based finite element method is used to solve the nonlinear set of governing equations iteratively. The numerical scheme and results are validated through a comparison with the benchmark results, and it shows that our solutions are in good agreement with them. The results are shown in terms of contours of streamlines, isotherms, and average Nusselt number. It is observed that MHD alters the streamlines, isotherms, and average Nusselt number and dominates the flow as compared to any other physical parameter. The average Nusselt number is found sensitive to the central obstacle’s size, and it reduces sufficiently when the radius of the inner cylinder increases. For all the parameters, the streamlines’ symmetric pattern holds, such that the anti-clockwise cells on the left side of the cavity have their symmetric clockwise cells on the right side.

Numerical Study of Steady Natural Convection Flow in A Prismatic Enclosure with Strip Heater on Bottom Wall Using Flexpde

2014 ◽  
Vol 7 (1) ◽  
pp. 61-80
Author(s):  
Sana Jaafar Yaseen
Keyword(s):  
Nusselt Number ◽  
Natural Convection ◽  
Numerical Study ◽  
Bottom Wall ◽  
Convection Flow ◽  
Two Dimensional ◽  
Finite Element Software ◽  
Stream Functions ◽  
Vertical Walls ◽  
Temperature And Flow Fields

Laminar natural convection in two-dimensional Prismatic enclosure is studied and analysis numerically. For the enclosure top inclined walls are considered at low temperature, two vertical walls are adiabatic and strip heater at constant high temperature mounted on the bottom enclosure, while the reminder bottom wall kept at low known temperature. The partial differential equations for two dimensional conservation of mass, momentum and energy are solved using finite element software package (FLEXPDE.5). For Rayleigh number varying from 103 to 105 and for constant Prandtal number Pr=0.7 the change in temperature and flow fields (stream functions) were investigated for different heater locations and for different number of heaters. The effect of the number and locations of the strip heaters on local and mean Nusslet number were examined. Results were presented by streamlines, isotherms and Nusselt number and it indicates that the Nusselt number is significantly affected by increasing both Ra and number of heaters. A comparison of the streamlines, isotherms curves and average Nusselt at the same boundary conditions was made with that obtained by Tanmay et al.(7), and showed a good agreement.

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