NATURAL CONVECTION OF AIR IN A SQUARE CAVITY A BENCH MARK NUMERICAL SOLUTION (original) (raw)
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 ...
Numerical investigation of natural convection in a cavity using an open geometry
This paper presents a numerical investigation of airflow in an open geometry. The case under consideration is a room with two opposite and decentred openings which create a strong potential for ventilation. The building's characteristic dimensions are the following: H=2.50 m height and W=6.50 m width. A temperature difference between the walls and the outside air is fixed, resulting in a characteristic Rayleigh number (Ra) ranging from 10 5 to 10 7 . This room model proceeds from a benchmark exercise "ADNBATI"
A Study on Natural Convection of Air in a Square Cavity with Partially Thermally Active Side Walls
Open Journal of Fluid Dynamics, 2017
In this present work, we study heat transfer in a confined environment. We have to determine the thermal and dynamics fields of the cavity while observing the effect of the Rayleigh number which depends on the characteristics of the fluid and the temperatures imposed. The behavior of boundary layers in natural convection is analyzed along this square cavity. The central halves of its vertical walls are heated at different temperatures. The left active part is at a higher temperature than the one on the right wall. The remaining inactive parts and the horizontal walls (upper and lower) are adiabatic. The thermal and dynamic modeling of two-dimensional problem was done using a calculation code Fortran 90 and a visualization software ParaView based on the finite volume method. The equations governing this phenomenon of unsteady flow have thus been solved. This allows the modeling of both air flow and heat transfer with a numerical stabilization of the solution. So, we have presented our results of numerical simulations using a visualization tool. The results show the different velocity and temperature curves, velocity vectors and isotherms in laminar flow regime.
Natural Convection in a Square Cavity with Spatial SideWall Temperature Variation
Numerical Heat Transfer Part A-applications, 2006
Laminar natural convection in a two-dimensional square cavity filled with a pure air (Pr ¼ 0.71) is studied numerically in the present article with nonuniform side-wall temperature. The heated vertical wall is assumed to have spatial sinusoidal temperature variations about a constant mean value, which is higher than the cold side-wall temperature, while the top and the bottom walls are adiabatic. A finite-volume method is used to solve numerically the nondimensional governing equations in the vorticity-stream function formulation. The effects of the amplitude and the wave number of the heated side-wall temperature variation on the natural convection in the cavity are investigated. It is found that the average Nusselt number varies based on the hot-wall temperature. It increases with an increase in the amplitude, while the maximum average Nusselt number occurs at the wave number of k ¼ 0.7 for Rayleigh number range 10 3 Ra 10 6 . It is found that the values of maximum fluid circulation occur at a similar wave number, which produces maximum heat transfer for small values of Ra, while it occurs at higher values of wave number at high Ra.
Numerical simulations have been undertaken for the benchmark problem of natural convection flow in a square cavity. The control volume method is used to solve the conservation equations for laminar and turbulent Rows for a series of Rayleigh numbers (Ra) reaching values up to 10". The k--E model has been used for turbulence modelling with and without logarithmic wall functions. Uniform and non-uniform (stretched) grids have been employed with increasing density to guarantee accurate solutions, especially near the walls for high Ra-values. AD1 and SIP solvers are implemented to accelerate convergence. Excellent agreement is obtained with previous numerical solutions, while some discrepancies with others for high Ra-values may be due to a possibly different implementation of the wall functions. Comparisons with experimental data for heat transfer (Nusselt number) clearly demonstrates the limitations of the standard k--E model with logarithmic wall functions, which gives significant overpredictions.
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
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.
Numerical study of double-diffusive natural convection in a square cavity
International Journal of Heat and Mass Transfer, 1992
Steady-state thermosolutal convection in a square cavity filled with air, submitted to horizontal temperature and concentration gradients, is studied numerically. In the first series of numerical simulations, the influence of solutal buoyancy force on heat or mass transfer rate is investigated : Lewis and thermal Rayleigh numbers are kept constant (Le = 1. Ra, = lo'), solutal Rayleigh number is varied (Ra, = lo'-5 x 10'). The second series deals with the influence of Lewis number on fluid motion for heat transfer driven flow (RaT = lo', Ra, = 0) and mass transfer driven flow (Ra, = 0, Ra, = 10') configurations. Lewis number is varied from 0.3 to 5. Correlations are obtained between heat and mass transfer rates and the non-dimensional numbers characterizing both phenomena.
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.