Laminar natural convection in an inclined complicated cavity with spatially variable wall temperature (original) (raw)
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Laminar natural convection in an inclined cavity with a wavy wall
International Journal of Heat and Mass Transfer, 2002
In the present work, a numerical study of the effect of a hot wavy wall of a laminar natural convection in an inclined square cavity, differentially heated, was carried out. This problem is solved by using the partial differential equations, which are the vorticity transport, heat transfer and stream function in curvilinear co-ordinates. The tests were performed for different inclination angles, amplitudes and Rayleigh numbers while the Prandtl number was kept constant. Two geometrical configurations were used namely one and three undulations.
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.
In the present study, natural convection problem has been solved in a cavity having three flat walls and the right vertical wall consisting of one undulation and three undulations. The two vertical and bottom walls are cold walls maintained at a fixed temperature whereas the top wall is heated with spatially varying temperature distribution. Air has been taken as the working fluid with Pr =0.71. This problem is solved by SIMPLE algorithm with deferred QUICK scheme in curvilinear coordinates. A wide range of Rayleigh number (10 3 to 10 6) has been chosen for this study. For small Ra, the heat transfer was dominated by conduction across the fluid layers. With increase of Ra, the process began to be dominated by convection. In the presence of undulation the peak point of the heat rejection (negative local Nusselt number) in the right wall increases by 5.54% than left wall for Ra = 10 4. The three undulations case had maximum heat transfer to the uppermost undulation compared to that of the one undulation case.
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.
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.
International Journal of Heat and Mass Transfer, 2007
The turbulent natural convection of air flow in a confined cavity with two differentially heated side walls is investigated numerically up to Rayleigh number of 10 12 . The objective of the present work is to study the effect of the inclination angle and the amplitude of the undulation on turbulent heat transfer. The low-Reynolds-number k-e, k-x, k-x-SST RANS models and a coarse DNS are used and compared to the experimental benchmark data of Ampofo and Karayiannis [F. Ampofo, T.G. Karayiannis, Experimental benchmark data for turbulent natural convection in an air filled square cavity, Int. J. Heat Mass Transfer 46 ]. The k-x-SST model is then used for the following test-cases as it gives the closest results to experimental data and coarse DNS for this case. The mean flow quantities and temperature field show good agreement with coarse DNS and measurements, but there are some slight discrepancies in the prediction of the turbulent statistics. Also, the numerical results of the heat flux at the hot wall are over predicted. The strong influence of the undulation of the cavity and its orientation is well shown. The trend of the local heat transfer is wavy with different frequencies for each undulation. The turbulence causes an increase in the convective heat transfer on the wavy wall surface compared to the square cavity for high Rayleigh numbers. A correlation of the mean Nusselt number function of the Rayleigh number is also proposed for the range of Rayleigh numbers of 10 9 -10 12 .
Effect of Aspect Ratio on Natural Convection in a Cavity with Wavy Walls
Acta Physica Polonica A, 2015
In this study, flow characteristics and natural convection in a cavity with two wavy walls is studied numerically. The wavy walls of the cavity are isothermal and at different temperatures while other straight walls are adiabatic. The fluid considered inside the cavity is air having Prandtl number of 0.71. A parametric study is conducted for various aspect ratios (1 ≤ AR ≤ 5), Rayleigh numbers (10 3 ≤ RaH ≤ 10 6) and inclination angles (0 • ≤ θ ≤ 180 •). Streamlines, isotherms and local and mean Nusselt numbers are presented to show the effect of the investigated parameters on the flow field and heat transfer.
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.
The present work is focused on the numerical modeling of steady laminar natural convection flow in a modified square enclosure with an inclined triangular top wall filled with air (Pr=0.71).The vertical right side wall is considered isothermal while the vertical left side wall is considered wavy with zero, one, two and three undulations respectively and subjected to a uniform heat flux. The upper inclined triangular wall and the lower flat wall are supposed to be perfectly insulated. The Rayleigh number ranging from 10 3 to 10 6 .The amplitude of the wavy wall is taken from 0 to 0.075 in steps of 0.025 and different heights of the triangular top wall have been considered for the present work. Various sets of governing equations are utilized to represent the physical problem and are non-dimensionalized and then solved numerically subjected to appropriate boundary conditions by using a finite volume method and the numerical solution is proved to be grid independent. Comparisons with p...
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.