scholarly journals Numerical investigation of natural convection heat transfer in a symmetrically cooled square cavity with a thin fin on its bottom wall

2014 ◽  
Vol 18 (4) ◽  
pp. 1119-1132 ◽  
Author(s):  
Saeid Jani ◽  
Mostafa Mahmoodi ◽  
Meysam Amini ◽  
Jafar Jam
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Constant Temperature ◽  
Convection Heat Transfer ◽  
Bottom Wall ◽  
Square Cavity ◽  
Remarkable Effect ◽  
Simpler Algorithm ◽  
The Right ◽  
Volume Method

In the present paper, natural convection fluid flow and heat transfer in a square cavity heated from below and cooled from sides and the ceiling with a thin fin attached to its hot bottom wall is investigated numerically. The right and the left walls of the cavity, as well as its horizontal top wall are maintained at a constant temperature Tc, while the bottom wall is kept at a constant temperature Th ,with Th > Tc. The governing equations are solved numerically using the finite volume method and the couple between the velocity and pressure fields is done using the SIMPLER algorithm. A parametric study is performed and the effects of the Rayleigh number and the length of the fin on the flow pattern and heat transfer inside the cavity are investigated. Two competing mechanisms that are responsible for the flow and thermal modifications are observed. One is the resistance effect of the fin due to the friction losses which directly depends on the length of the fin, whereas the other is due to the extra heating of the fluid that is offered by the fin. It is shown that for high Rayleigh numbers, placing a hot fin at the middle of the bottom wall has more remarkable effect on the flow field and heat transfer inside the cavity.

The effect of viscous dissipation on natural convection in a square cavity

2019 ◽  
Vol 5 (3) ◽  
pp. 118-130 ◽  
Author(s):  
Pavel T. Zubkov ◽  
Eduard I. Narygin
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Viscous Dissipation ◽  
Convection Heat Transfer ◽  
Dissipation Function ◽  
Initial Condition ◽  
Square Cavity ◽  
Conservation Of Energy ◽  
Left Wall ◽  
The Right

This article studies the natural convection of a viscous, incompressible fluid in a square cavity in a gravitational field. The temperature of vertical walls is constant. The temperature of the left wall is higher than temperature of the right wall; the horizontal walls are considered thermally insulated. The initial condition for the temperature of a fluid in a square caviry is the constant and equals the temperature of the right wall. The initial condition for the velocity is zero. We consider only those cases where the obtained flow in the cavity is laminar. All thermophysical characteristics are assumed constant, except for one when the motion equation accounts for the gravity. Mathematical model is the Boussinesq approximation but the equation of conservation of energy contains Rayleigh dissipation function.<br> In this article, the authors have researched the effect of viscous dissipation on natural convection heat transfer in square field. The results show that viscous dissipation significantly affects the heat transfer through the cavity. This problem was solved with the finite volume method by algorithm SIMPLER for Pr=1, Gr=10<sup>4</sup>, and 10<sup>−5</sup>≤Ec≤10<sup>−3</sup>.

Laminar Natural Convection Heat Transfer in a Differentially Heated Square Cavity Due to a Thin Fin on the Hot Wall

2003 ◽  
Vol 125 (4) ◽  
pp. 624-634 ◽  
Author(s):  
Xundan Shi ◽  
J. M. Khodadadi
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Computational Study ◽  
Convection Heat Transfer ◽  
Square Cavity ◽  
Left Wall ◽  
Flow Modification ◽  
Laminar Natural Convection ◽  
Rayleigh Numbers ◽  
Blockage Effect

A finite-volume-based computational study of steady laminar natural convection (using Boussinesq approximation) within a differentially heated square cavity due to the presence of a single thin fin is presented. Attachment of highly conductive thin fins with lengths equal to 20, 35 and 50 percent of the side, positioned at 7 locations on the hot left wall were examined for Ra=104,105,106, and 107 and Pr=0.707 (total of 84 cases). Placing a fin on the hot left wall generally alters the clockwise rotating vortex that is established due to buoyancy-induced convection. Two competing mechanisms that are responsible for flow and thermal modifications are identified. One is due to the blockage effect of the fin, whereas the other is due to extra heating of the fluid that is accommodated by the fin. The degree of flow modification due to blockage is enhanced by increasing the length of the fin. Under certain conditions, smaller vortices are formed between the fin and the top insulated wall. Viewing the minimum value of the stream function field as a measure of the strength of flow modification, it is shown that for high Rayleigh numbers the flow field is enhanced regardless of the fin’s length and position. This suggests that the extra heating mechanism outweighs the blockage effect for high Rayleigh numbers. By introducing a fin, the heat transfer capacity on the anchoring wall is always degraded, however heat transfer on the cold wall without the fin can be promoted for high Rayleigh numbers and with the fins placed closer to the insulated walls. A correlation among the mean Nu, Ra, fin’s length and its position is proposed.

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.

Numerical analysis of natural convection heat transfer and entropy generation in a porous quadrantal cavity

2019 ◽  
Vol 29 (12) ◽  
pp. 4826-4849 ◽  
Author(s):  
Shantanu Dutta ◽  
Arup Kumar Biswas ◽  
Sukumar Pati
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Natural Convection ◽  
Convection Heat Transfer ◽  
Bottom Wall ◽  
Natural Convection Heat Transfer ◽  
Convection Heat ◽  
Uniform Temperature ◽  
Content Type ◽  
Temperature Heating

Purpose The purpose of this paper is to analyze the natural convection heat transfer and irreversibility characteristics in a quadrantal porous cavity subjected to uniform temperature heating from the bottom wall. Design/methodology/approach Brinkmann-extended Darcy model is used to simulate the momentum transfer in the porous medium. The Boussinesq approximation is invoked to account for the variation in density arising out of the temperature differential for the porous quadrantal enclosure subjected to uniform heating on the bottom wall. The governing transport equations are solved using the finite element method. A parametric study is carried out for the Rayleigh number (Ra) in the range of 103 to 106 and Darcy number (Da) in the range of 10−5-10−2. Findings A complex interaction between the buoyant and viscous forces that govern the transport of heat and entropy generation and the permeability of the porous medium plays a significant role on the same. The effect of Da is almost insignificant in dictating the heat transfer for low values of Ra (103, 104), while there is a significant alteration in Nusselt number for Ra ≥105 and moreover, the change is more intense for larger values of Da. For lower values of Ra (≤104), the main contributor of irreversibility is the thermal irreversibility irrespective of all values of Da. However, the fluid friction irreversibility is the dominant player at higher values of Ra (=106) and Da (=10−2). Practical implications From an industrial point of view, the present study will have applications in micro-electronic devices, building systems with complex geometries, solar collectors, electric machinery and lubrication systems. Originality/value This research examines numerically the buoyancy driven heat transfer irreversibility in a quadrantal porous enclosure that is subjected to uniform temperature heating from the bottom wall, that was not investigated in the literature before.

scholarly journals Comparison of the Finite Volume and Lattice Boltzmann Methods for Solving Natural Convection Heat Transfer Problems inside Cavities and Enclosures

2014 ◽  
Vol 2014 ◽  
pp. 1-15 ◽  
Author(s):  
M. Goodarzi ◽  
M. R. Safaei ◽  
A. Karimipour ◽  
K. Hooman ◽  
M. Dahari ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Natural Convection ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Lattice Boltzmann ◽  
Convection Heat Transfer ◽  
Natural Convection Heat Transfer ◽  
Convection Heat ◽  
Square Enclosure ◽  
Volume Method

Different numerical methods have been implemented to simulate internal natural convection heat transfer and also to identify the most accurate and efficient one. A laterally heated square enclosure, filled with air, was studied. A FORTRAN code based on the lattice Boltzmann method (LBM) was developed for this purpose. The finite difference method was applied to discretize the LBM equations. Furthermore, for comparison purpose, the commercially available CFD package FLUENT, which uses finite volume Method (FVM), was also used to simulate the same problem. Different discretization schemes, being the first order upwind, second order upwind, power law, and QUICK, were used with the finite volume solver where the SIMPLE and SIMPLEC algorithms linked the velocity-pressure terms. The results were also compared with existing experimental and numerical data. It was observed that the finite volume method requires less CPU usage time and yields more accurate results compared to the LBM. It has been noted that the 1st order upwind/SIMPLEC combination converges comparatively quickly with a very high accuracy especially at the boundaries. Interestingly, all variants of FVM discretization/pressure-velocity linking methods lead to almost the same number of iterations to converge but higher-order schemes ask for longer iterations.

Sign in / Sign up

Export Citation Format

Share Document