Numerical Study of Natural Convection of Air in an Inclined Square Enclosure (original) (raw)
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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 an inclined square enclosure with a partition attached to its cold wall
International Journal of Heat and Mass Transfer, 1989
Natural convection in an inclined differentially heated square enclosure containing internally heated fluid has been investigated numerically using the Galerkin finite element method. The horizontal walls are adiabatic, while the side walls are isothermal but kept at different temperatures. Flow and heat transfer characteristics through isotherms, streamlines and average Nusselt numbers have been presented for the external Rayleigh number 10 3 to 10 6 , internal Rayleigh number 10 5 to 10 8 and inclination angles 0º to 30º. The obtained computational results indicate that the strength of the convective currents depends on the internal energy. Heat removal rate is optimized at zero inclination angle for relatively weak external heating mode for all values of internal energy.
Natural convection in inclined partitioned enclosures
Heat and Mass Transfer, 2006
The problem of steady, laminar, natural convective flow of a viscous fluid in an inclined enclosure with partitions is considered. Transverse gradient of temperature is applied on the two opposing regular walls of the inclined enclosure while the other walls are maintained adiabatic. The problem is formulated in terms of the vorticity-stream function procedure. A numerical solution based on the finite volume method is obtained. Representative results illustrating the effects of the enclosure inclination angle and the degree of irregularity on the contour maps of the streamlines and temperature are reported and discussed. In addition, results for the average Nusselt number at the heated wall of the enclosure and the difference of extreme stream-function values are presented and discussed for various Rayleigh numbers, inclination angles and dimensionless partition heights.
The Influence of Inclination Angle on Natural Convection in a Rectangular Enclosure
2013
An experimental work was conducted to investigate the influence of inclination angle on natural heat transfer in a rectangular enclosure. The enclosure length was (100 cm) with a square cross section (10×10 cm). All the enclosure surfaces were insulated except the upper surface, where half of it was cooled and the other half was heated. The tests were done for three inclination angles (15 o , 45 o and 75 o ), three mass flow rates (0, 0.0275 and 0.062 kg/sec) and five heat fluxes (4.92, 19.2, 39.96, 69.6 and 108 W/m2) for (1.95×10 5 ≤ Ra ≤ 4.96×10 6 ). It was found that the highest Nu x was at (x/L=0.33) where the highest heat transfer occurred between the hot air and the cold surface (high temperature difference). It was also found that as the inclination angle increased, the Nu x and Nu increased. This is because the falling cold air disrupted the rising hot air which led to an increase in the heat transfer between the hot air and the cold surface. Increasing the mass flow rate an...
Anbar Journal of Engineering Sciences, 2017
Laminar natural convection heat transfer and fluid flow due to the heating from below at variable heat source length inside two dimensional enclosure has been analyzed numerically in this study. The enclosure has filled with air as a working fluid. The vertical inclined walls of the enclosure are maintained at lower temperature while the remaining walls are insulated. The value of Rayleigh number from (1x10 3 ≤ Ra ≤ 4x10 4), the inclination angle at (γ = 0 o , 22.5 o , 45 o) and dimensionless heat source length at (S = 1 and 0.5). The continuity, momentum and energy equations have been applied to the enclosure and solved by using finite difference method. The results showing that the average Nusselt number increases with the increasing of the heating source length and decreases with the increasing in an inclination angle of the vertical walls.
Natural Convection in an Inclined Square Enclosure Containing Internal Energy Sources
Natural convection in an inclined differentially heated square enclosure containing internally heated fluid has been investigated numerically using the Galerkin finite element method. The horizontal walls are adiabatic, while the side walls are isothermal but kept at different temperatures. Flow and heat transfer characteristics through isotherms, streamlines and average Nusselt numbers have been presented for the external Rayleigh number 10^3 to 10^6, internal Rayleigh number 10^5 to 10^8 and inclination angles 0º to 30º. The obtained computational results indicate that the strength of the convective currents depends on the internal energy. Heat removal rate is optimized at zero inclination angle for relatively weak external heating mode for all values of internal energy.
Energies
This paper proposes an analytical model for natural convection in a closed rectangular enclosure filled by a fluid, with imposed heat fluxes at the vertical walls and adiabatic horizontal walls. The analytical model offers a simplified, but easy to handle, description of the temperature and velocity fields. The predicted temperature, velocity, and pressure fields are shown to be in agreement with those obtained from a reliable numerical model. The Nusselt numbers for both the analytical and numerical solutions are then calculated and compared, varying both the aspect ratio of the enclosure and the Rayleigh number. Based on the comparisons, it is possible to assess the dependence of the reliability of the analytical model on the aspect ratio of the enclosure, showing that the prediction error rapidly decreases with the increase of the enclosure slenderness.
11.The Influence of the Angle of Inclination on Laminar Natural Convection in a Square Enclosure
This paper discusses the results obtained by the numerical modeling of natural convection in a water-filled two-dimensional square enclosure inclined to the horizontal. Here, the top and bottom walls of the cavity are considered adiabatic, left vertical wall is maintained at a constant low temperature and the right vertical wall is maintained at a constant high temperature. The aim is to investigate the effects of angle of inclination on the flow patterns. We use the Krylov subspace method, GMRES, to solve the discretized formulation of the governing equations. At the validation stage, our results are in good agreement with those reported in the literature. Results are presented in the form of velocity vector and isotherm plots as well as the variation of the average Nusselt number for different angles of inclination.
Natural convection in a Square Enclosure with Partially Active Vertical Wall
MATEC Web of Conferences, 2020
Steady, laminar, natural convection flow in a square enclosure with partially active vertical wall is considered. The enclosure is filled with air and subjected to horizontal temperature gradient. Finite volume method is used to solve the dimensionless governing equations. The physical problem depends on three parameters: Rayleigh number (Ra =103-106), Prandtl number (Pr=0.71), and the aspect ratio of the enclosure (A=1). The active location takes two positions in the left wall: top (T) and middle (M). The main focus of the study is on examining the effect of Rayleigh number on fluid flow and heat transfer rate. The results including the streamlines, isotherm patterns, flow velocity and the average Nusselt number for different values of Ra. The obtained results show that the increase of Ra leads to enhance heat transfer rate. The fluid particles move with greater velocity for higher thermal Rayleigh number. Also by moving the active location from the top to the middle on the left ve...