Natural convection in inclined partitioned enclosures (original) (raw)
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.
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.
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...
“Effects Of Heat Source Location On Natural Convection In A Square Cavity”
2012
Natural convection in a closed square cavity has occupied the centre stage in many fundamental heat transfer analysis which is of prime importance in certain technological applications. Infact buoyancy driven convection in a sealed cavity with differentially heated isothermal walls is a prototype of many industrial applications such as energy efficient buildings, operation and safety of nuclear reactor and convective heat transfer associated with electronic cooling equipment. The internal flow problems are considerably more complex than external ones. In electronic systems normally the heat generating bodies exist within the cavity. The effect of the presence of heat source on the mass flow rate and heat transfer is considered in present case for investigation. In order to verify the methodology of using fluent, the commercial software, the available problem in the literature is verified for parametric study on the location of heat source and its strength is considered for study. In present work, the given source is split into two parts and its effect on the flow rate and heat transfer is studied. An attempt is made for the best location of the heat source in the cavity so that it can be used in the electronic equipment generating heat.
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.
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.
Numerical Study of Natural Convection of Air in an Inclined Square Enclosure
International Journal of Materials, Mechanics and Manufacturing, 2013
Natural convection of air in an inclined square enclosure was numerically investigated. The left and right walls of the enclosure were maintained at the uniform hot and cold temperatures, respectively, while the top and bottom walls were adiabatic. The enclosure was filled with real air, a compressible Newtonian fluid. The finite volume method was employed to discretize the partial differential equations of airflow in the enclosure. The angles of the inclination of a square enclosure giving the maximum average Nusselt numbers are 110 o for Ra = 110 3 and 130 o for 310 3 Ra 110 4 .
Natural Convection in Inclined two Dimensional Rectangular Cavities
Conference: ASME Fluids Engineering Division 2009 Summer Conference, Vail, Colorado, USA, Volume: Paper No. FEDSM2009-78566; available online: ASME digital library, 2009
ABSTRACT: Steady two-dimensional natural convection in fluid filled cavities has been investigated numerically. The conservation equations of mass, momentum and energy governing the motion of a Newtonian Boussinesq fluid have been numerically solved using the finite volume technique. The computations were performed for three cavity height based Rayleigh numbers 10 (Exponent 4), 10 (Exponent 5) and 10 (Exponent 6). In all of the numerical experiments, the channel is heated from below and cooled from the top with insulated side-walls and the inclination angle is varied. The simulations have been carried out for several aspect ratios. For the case of the square cavity the calculated values are in excellent agreement with previously published benchmark results. The effects of the inclination of the cavity to the horizontal, with the angle varying from 0 to 180 and the initial start up conditions were investigated in turn for each aspect ratio. The inclination and the “initial” assumed conditions have a significant effect on the flow patterns, temperature distributions and the heat transfer rates. In particular it is found that the average Nusselt number exhibits discontinuities for rectangular cavities and that the occurrence of the discontinuity with angle of inclination is strongly influenced by the assumed start up field in the steady calculations in much the same way as the hysteresis effect that was identified by other workers.
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 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
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.
International Journal of Heat and Mass Transfer, 1995
Abstraet--Steady natural convection in an enclosure heated from below and symmetrically cooled from the sides is studied numerically, using a streamfunction-vorticity formulation. The Allen discretization scheme is adopted and the discretized equations were solved in a line by line basis. The Rayleigh number based on the cavity height is varied from 103 to 10 7. Values of 0.7 and 7.0 for the Prandtl number are considered. The aspect ratio L/H (length to height of the enclosure) is varied from 1 to 9. Boundary conditions are uniform wall temperature and uniform heat flux. For the range of the parameters studied, a single cell is observed to represent the flow pattern. Numerical values of the Nusselt number as a function of the Rayleigh number are reported, and the Prandtl number is found to have little influence on the Nusselt number. A scale analysis is presented in order to better understand the phenomenon.
Natural convection in partially heated square cavity
Mechanics, 2016
T-temperature difference T = Th-Tc, Ra-Rayleigh number greek letters--thermal diffusivity; -thermal expansion coefficient; ε-turbulent energy dissipation rate; -dynamic viscosity; -kinematic viscosity; -fluid density
Natural convection in an enclosed cavity
Journal of Computational Physics, 1984
We are concerned with the problem of buoyancy driven flow in a vertical, rectangular cavity whose vertical sides are at different temperatures and whose horizontal sides are insulated. An application of the dynamic A.D. I. method to obtain nUMerical solutions to this problem is described. For large non-dimensional temperature differences characterized by the Rayleigh number the flow patterns develop strong boundary layers. These boundary layers are resolved by applying the D.A.D.I. method to the discretization of this problem on a non-uniform grid.
Natural convection in a rectangular cavity with wall temperature decreasing at a uniform rate
W�rme - und Stoff�bertragung, 1982
The transient natural convection in a fluid contained in a rectangular enclosure, the wall of which is maintained at a uniform temperature which changes at a steady rate, is approached by a numerical method. Numerical solutions are obtained for Pr = 0.73, 7.3 and 73 and a range of Rayleigh numbers Ra = 102 ~ l0 s. At relatively low Rayleigh numbers the flow is characterized by the development of double cells with flow up the center and down the sidewalls. However it was found that an increase of the Rayleigh number leads to the development of strong secondary circulation on the axis of symmetry of the cavity near the top wall. Thus, as the Rayleigh number is increased the secondary cells grow in size. The effects of the secondary cells on the temperature field and heat transfer coefficients are discussed. Most results are obtained for the case of a square cavity (E ~-2) but the influence of the aspect ratio of the cavity is also studied for E = 1 and 4. Freie Konvektion in reehtwinkeligen Riiumen bei mit der Zeit linear fallenden Wandtemperaturen
Natural convection in cavities containing internal sources
Heat and Mass Transfer, 2000
Numerical predictions are reported for buoyancy-induced circulations in a 2D closed cavity with internal heat sources. Two cases are considered: (A) two vertical plates with uniform heat generation, forming a short vertical channel within the enclosure; and, (B) a rectangular heating block with uniform wall temperature, placed central in the enclosure. Air, with a Prandtl number 0.71, is considered as the working¯uid. The vertical enclosure walls are isothermal, while the horizontal enclosure walls are adiabatic. Results are presented for two values of the Grashof number, one below the stability limit for laminar ow, and one well above it. In those latter cases, the longterm behaviour of the numerical solution is time-dependent, i.e. no steady-state can be reached. Heat transfer results are compared with predictions from standard correlations for isolated surfaces.
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 cooled right wall has been investigated. The governing equations are transformed into a non-dimensional form and the resulting partial differential equations are solved numerically 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 local rate of heat transfer in terms of the local Nusselt number and the average Nusselt number from the heated wall of the cavity are presented.
Natural Convection in a Partitioned Trapezoidal Cavity Heated from the Side
Numerical Heat Transfer, Part A: Applications, 2003
Numerical results are reported for natural convection heat transfer in partially divided trapezoidal cavities representing industrial buildings. Two thermal boundary conditions are considered. In the first, the left short vertical wall is heated while the right long vertical wall is cooled (buoyancy assisting mode along the upper inclined surface of the cavity). In the second, the right long vertical wall is heated while the left short vertical wall is cooled (buoyancy opposing mode along the upper inclined surface of the cavity). The effects of Rayleigh number, Prandtl number, baffle height, and baffle location on the heat transfer are investigated. Results are displayed in terms of streamlines, isotherms, and local and average Nusselt number values. For both boundary conditions, predictions reveal a decrease in heat transfer in the presence of baffles with its rate generally increasing with increasing baffle height and Pr. For a given baffle height, higher decrease in heat transfer is generally obtained with baffles located close to the short vertical wall.