Numerical Analysis of Laminar Natural Convection in a Quadrantal Cavity with Non-uniform heating of Bottom Wall (original) (raw)
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Laminar Natural Convection Study in a Quadrantal Cavity Using Heater on Adjacent Walls
Frontiers in Heat and Mass Transfer, 2013
A numerical analysis of laminar natural convection in a quadrantal cavity filled with water having variable length heaters attached on the adjacent walls have been made to examine heat and fluid flow. Numerical solutions are obtained using a commercial computational fluid dynamics package, FLUENT, using the finite volume method. Effects of the Rayleigh number, Ra, on the Nusselt number, Nu, as well as velocity and temperature fields are investigated for the range of Ra from 10 3 to 10 7 . Computations were carried out for the non-dimensional heater lengths on the vertical wall (m=0.2, 0.4 and 0.6) and horizontal wall (n=0.2, 0.4 and 0.6). It is observed that heat transfer increases with increase in Rayleigh number and the flow strength increases with increase in size of heater on the vertical wall compared to the bottom wall and temperature fields are also affected. In contrast, with increase in size of heater on both side of adjacent walls flow strength does not changes significantly.
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.
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.
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.
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.
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 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.
Study of Natural Convection Heat Transfer in a Closed Wall with Thermal Conditions
Lecture Notes in Mechanical Engineering, 2021
In this study, conjugate natural convection in a square cavity filled with fluids under steady-state condition is numerically investigated with the finite element method. The left side wall is considered as hot wall, and the right wall is considered to be cold. The top and bottom walls are assumed to be adiabatic. Different boundary conditions are introduced on the walls, and a thorough investigation is done in the present study. Numerical simulations have been done for different parameters of Grashof number (10 3-10 7) and Prandtl number. The graph of Nusselt number versus Grashof number and Nusselt number versus Prandtl number is plotted. It is observed that the buoyant forces developed in the cavity due to thermally induced density gradients vary as the value of acceleration due to gravity (g) differs, due to the change in temperature and stream function. Keywords Conjugate natural convection heat transfer Á Square cavity Nomenclature AR aspect ratio (H/L) g acceleration due to gravity (m s −2) H height of square cavity (m) K thermal conductivity (W m −1 K −1) L length of the square cavity (m)
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.