Laminar Natural Convection Study in a Quadrantal Cavity Using Heater on Adjacent Walls (original) (raw)
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In this paper, we analyze the fluid flow and heat transfer characteristics inside a two dimensional quadrantal cavity filled with air. The cavity is heated non-uniformly from the bottom wall and the vertical wall is cooled to a constant temperature while the curved wall is thermally insulated. Finite element method is used to solve the transport equations. The results are illustrated in the form of streamlines, isotherms, local Nusselt number and average Nusselt number. It reveals that the local Nusselt number at the bottom wall follows a sinusoidal variation and moreover at some location, the Nusselt number is negative because of the imposed temperature distribution on the wall. It further reveals that the mechanism of heat transfer is conduction at lower values of Rayleigh number, while heat transfer is due to convection at higher values of Rayleigh number.
Journal of Naval Architecture and Marine Engineering, 2011
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.
International Journal of Heat and Mass Transfer, 2005
Natural convection in two-dimensional enclosure with three flat and one wavy walls is numerically investigated. One wall is having a sinusoidal temperature profile. Other three walls including the wavy wall are maintained at constant cold temperature. This problem is solved by SIMPLE algorithm with deferred QUICK scheme in curvilinear co-ordinates. The tests were carried out for different inclination angles, amplitudes and Rayleigh numbers while the Prandtl number was kept constant. The geometrical configurations considered were namely one, two and three undulations.
Numerical Simulation of Natural Convection in a Square Cavity with Two Partitions and Two Fluids
International Review of Mechanical Engineering (IREME), 2018
The present work enlightens the study of laminar natural convection in an isosceles right-angled triangular cavity filled with water. The bottom wall of the cavity contains a caterpillar (C)-curve shape wavy wall, having different width (w = 0.20b, 0.25b, 0.33b and 0.50b) and aspect ratio (d) with 0 6 d 6 0.15. Vertical and incline walls of the cavity are considered individually and together for cooling purpose. The physical model is solved to examine the effect of constrained parameters such as hot wall profiles, configurations of cold walls and Rayleigh number (10 5-10 7) on the fluid flow and heat transfer. The study is carried out numerically by commercially available software FLUENT 6.3. The deviation in the flow pattern and temperature profile is displayed by streamlines and isotherms contours whereas the variation in heat transfer rate is presented by local and average Nusselt number. It is found from the investigation that the heat transfer rate is enhanced significantly for caterpillar curved shape wavy wall than the flat hot wall. Moreover, the rate of heat transfer is varied profoundly with the location of cold walls.
Laminar natural convection in inclined rectangular cavities with a localized heat source
Alexandria Engineering Journal, 2013
The paper investigates numerically laminar natural convection in inclined rectangular cavities with a localized heat source. A mathematical model was constructed where the conservation equations governing the mass, momentum, and thermal energy together with their boundary conditions were solved. The calculation grid used in the solution is investigated to determine the best grid spacing, the required number of iterations, and other parameters which affect the accuracy of the generated solutions. The numerical method and computer program were tested for the case of pure conduction to assure validity and accuracy of the numerical method. The numerical investigation used air as the fluid and covered Rayleigh numbers based on scale length, s/A ranging from 10 2 to 10 6 , aspect ratio from 0.5 to 5, position ratio from 0.25 to 0.75, heater size ratio from 0.25 to 1, and the tilt angle measured from horizontal was varied from 0 to 180°. The results are presented graphically in the form of streamline and isotherm contour plots. The heat transfer characteristics, velocity profiles, local and average Nusselt numbers were also presented. A correlation was developed which represents the present numerical heat transfer results with an average deviation of less than 11.5%.
Computers & Fluids, 2007
In this article, we present a two-dimensional study of laminar natural convection in porous enclosure. The horizontal walls of the enclosure are thermally insulated , where as the left and right vertical walls are maintained respectively at different temperatures (warm temperature) and (cold temperature).we present the differential equations modeling the phenomenon studied according to Darcy-Brinkman-Forcheimer model. after the dimensionless form of the equation we have four dimensionless numbers : the Prandtl number the thermal Grashof , the aspect ratio A, the Darcy number .The results allowed us to conclude the following: Increasing of Grachof number with a constant Darcy number, so we areThe increase of convection and as a result the increase in flow velocity and heat transfer.at constant of Grachof number whith decreasing of the Darcy number, the medium is impermeable which slow motion of the convection phenomenon. so we are a degradation speed and heat transfer .Finaly We executed the program calculates with the real data of oil reservoir.
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.
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.
IOP Conference Series: Materials Science and Engineering, 2019
Effects of cavity aspect ratios and cavity inclination angles to natural convection in a rectangular cavity are numerically investigated. Investigation is performed at the Rayleigh number (Ra) equal to 104, the cavity aspect ratios from 1 to 50 and the cavity inclination angles from 0 to 180°. Consequently, Heat transfer enhancement or decreasing due to the effects is exposed. In addition, streamline contours in the rectangular cavity are illustrated. Multi-cellular flow figuring on the appropriate conditions is exhibited. A new correlation of the average Nusselt number, the cavity aspect ratio and the cavity inclination angle is formulated at Ra equal to 104.
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.