A Study on Natural Convection of Air in a Square Cavity with Partially Thermally Active Side Walls (original) (raw)
Related papers
2013
A numerical study is performed to analyze the steady natural convection phenomena of air in a square cavity with different locations of the heating portion. The heat sources parts in the left, right and bottom walls of the cavity are maintained at a higher temperature Th, whereas the other parts of these sidewalls are kept at a lower temperature Tc. The enclosure’s top wall is kept insulated. The coupled equations of continuity, momentum and energy are solved by a finite volume method. The SIMPLE algorithm is used to solve iteratively the pressurevelocities coupling. The numerical investigations in this analysis is made over a wide range of parameters, Rayleigh number ( ) and dimensionless heater lengths. The effect of three different heating locations on the vertical walls (bottom, Centre, and top) and the local heat source on the bottom wall was evaluated. Results are presented graphically in the form of streamlines, isotherms and also with a velocity profiles and average Nusselt ...
Steady natural convection flows in a square cavity with linearly heated side wall(s)
International Journal of Heat and Mass Transfer, 2007
The present numerical study deals with natural convection flow in a closed square cavity when the bottom wall is uniformly heated and vertical wall(s) are linearly heated whereas the top wall is well insulated. Non-linear coupled PDEs governing the flow have been solved by penalty finite element method with bi-quadratic rectangular elements. Numerical results are obtained for various values of Rayleigh number (Ra) (10 3 6 Ra 6 10 5 ) and Prandtl number (Pr) (0.7 6 Pr 6 10). Results are presented in the form of streamlines, isotherm contours, local Nusselt number and the average Nusselt as a function of Rayleigh number.
Simulation of Natural Convection in a Square Cavity with Partially Heated and Cooled Vertical Walls
Proceeding of 5th Thermal and Fluids Engineering Conference (TFEC)
Natural convection driven by temperature differences between partially heated and cooled vertical walls in a square cavity is studied numerically. Steady or unsteady cellular flow structures and temperature patterns are illustrated along with the evolution of heat transfer rates in terms of Nusselt number. The cavity is filled with fluids of various Prandtl number, including .024 (liquid metal), .71 (air), 6 (water), and 450 (silicon oil). The effect of Prandtl and Rayleigh numbers on the flow regime and heat transfer is established along with two different thermal boundary conditions.
Effects of thermal boundary conditions on natural convection flows within a square cavity
International Journal of Heat and Mass Transfer, 2006
A numerical study to investigate the steady laminar natural convection flow in a square cavity with uniformly and non-uniformly heated bottom wall, and adiabatic top wall maintaining constant temperature of cold vertical walls has been performed. A penalty finite element method with bi-quadratic rectangular elements has been used to solve the governing mass, momentum and energy equations. The numerical procedure adopted in the present study yields consistent performance over a wide range of parameters (Rayleigh number Ra, 10 3 6 Ra 6 10 5 and Prandtl number Pr, 0.7 6 Pr 6 10) with respect to continuous and discontinuous Dirichlet boundary conditions. Non-uniform heating of the bottom wall produces greater heat transfer rates at the center of the bottom wall than the uniform heating case for all Rayleigh numbers; however, average Nusselt numbers show overall lower heat transfer rates for the non-uniform heating case. Critical Rayleigh numbers for conduction dominant heat transfer cases have been obtained and for convection dominated regimes, power law correlations between average Nusselt number and Rayleigh numbers are presented.
NATURAL CONVECTION FLOW IN A SQUARE CAVITY WITH TEMPERATURE DEPENDENT HEAT GENERATION
Unsteady natural convection laminar flows in a square cavity formed by insulated bottom and top walls, uniformly heated left wall and the cooled right wall has been investigated numerically. The governing equations are transformed into non-dimensional form and the resulting partial differential equations are solved applying upwind finite difference method together with Successive Over-Relaxation (SOR) scheme. The effect of the heat generation and the Rayleigh number on streamlines and isotherms as well as on the rate of heat transfer from the heated wall of the cavity are presented.
2012
This paper reports a numerical study of flow behaviors and natural convection heat transfer characteristics in an inclined open-ended square cavity filled with air. The cavity is formed by adiabatic top and bottom walls and partially heated vertical wall facing the opening. Governing equations in vorticity-stream function form are discretized via finite-difference method and are solved numerically by iterative successive under relaxation (SUR) technique. A computer program to solve mathematical model has been developed and written as a code for MATLAB software. Results in the form of streamlines, isotherms, and average Nusselt number, are obtained for a wide range of Rayleigh numbers 10 3-10 6 with Prandtl number 0.71 (air) , inclination angles measured from the horizontal direction 0º-60º , dimensionless lengths of the active part 0.4-1 ,and different locations of the thermally active part at the vertical wall. The Results show that heat transfer rate is high when the length of the...
International Journal of Heat and Mass Transfer, 2011
A steady buoyancy-driven flow of air in a partially open square 2D cavity with internal heat source, adiabatic bottom and top walls, and vertical walls maintained at different constant temperatures is investigated numerically in this work. A heat source with 1% of the cavity volume is present in the center of the bottom wall. The cold right wall contains a partial opening occupying 25%, 50% or 75% of the wall. The influence of the temperature gradient between the verticals walls was analyzed for Ra e = 10 3-10 5 , while the influence of the heat source was evaluated through the relation R = Ra i /Ra e , investigated at between 400 and 2000. Interesting results were obtained. For a low Rayleigh number, it is found that the isotherm plots are smooth and follow a parabolic shape indicating the dominance of the heat source. But as the Ra e increases, the flow slowly becomes dominated by the temperature difference between the walls. It is also observed that multiple strong secondary circulations are formed for fluids with a small Ra e whereas these features are absent at higher Ra e. The comprehensive analysis is concluded with horizontal air velocity and temperature plots for the opening. The numerical results show a significant influence of the opening on the heat transfer in the cavity.
Numerical Study of Natural Convection Inside a Square Cavity with Non-uniform Heating from Top
Journal of The Institution of Engineers (India): Series C, 2020
The prime objective of the present numerical study is to analyse buoyancy-driven thermal flow behaviour inside an enclosure with the application of nonlinear heating from top surface which is commonly essential in glass industries. A fluid-filled square cavity with sinusoidal heating from top surface, adiabatic bottom wall and constant temperature side walls is considered here. The thermal flow behaviour has been numerically observed with the help of relevant parameters like stream functions, isotherms and Nusselt number. For the present investigation, Rayleigh number (Ra), Prandtl number (Pr) and heating frequency of the wall (x) are varied from 10 3 to 10 6 , 0.7 to 7 and 0.5 to 2, respectively. It has been noticed from the investigation that flow dynamics drastically alter with Ra, x and Pr. However, the effect of Ra on heat transfer rate has been found to be significantly higher while compared with the influences by x and Pr. Keywords Free convection Á Buoyancy Á Rayleigh number Á Pr number Á Sinusoidal heating Greek letters a Thermal diffusivity (m 2 s-1) b Volumetric expansion coefficient (K-1) q Kinetic viscosity (m 2 s-1) t Density of fluid (kg m-3) h Dimensionless temperature x Heating frequency of the top wall
International Journal of Engineering Science, 2005
A penalty finite element analysis with bi-quadratic rectangular elements is performed to investigate the influence of uniform and non-uniform heating of wall(s) on natural convection flows in a square cavity. In the present investigation, one vertical wall and the bottom wall are uniformly and non-uniformly heated while the other vertical wall is maintained at constant cold temperature and the top wall is well insulated. Parametric study for a wide range of Rayleigh number (Ra), 10 3 6 Ra 6 10 6 and Prandtl number (Pr), 0.2 6 Pr 6 100 shows consistent performance of the present numerical approach to obtain the solutions as stream functions and temperature profiles. Heat transfer rates at the heated walls are presented in terms of local Nusselt number.