Natural convection flows in a trapezoidal enclosure with uniform and non-uniform heating of bottom wall (original) (raw)
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International Journal of Heat and Mass Transfer, 2008
A penalty finite element analysis with bi-quadratic elements is carried out to investigate the effects of uniform and non-uniform heating of inclined walls on natural convection flows within a isosceles triangular enclosure. Two cases of thermal boundary conditions are considered; case I: two inclined walls are uniformly heated while the bottom wall is cold isothermal and case II: two inclined walls are non-uniformly heated while the bottom wall is cold isothermal. The numerical solution of the problem is presented for various Rayleigh numbers (Ra), (10 3 6 Ra 6 10 6) and Prandtl numbers (Pr), (0:026 6 Pr 6 1000). It has been found that at small Prandtl numbers, geometry does not have much influence on flow structure while at Pr ¼ 1000, the stream function contours are nearly triangular showing that geometry has considerable effect on the flow pattern. In addition, the presence of multiple circulations are observed for small Pr ðPr ¼ 0:026Þ which causes wavy distribution of local Nusselt number. It is observed that non-uniform heating produces greater heat transfer rates at the center of the walls than the uniform heating; 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 dominant regimes, power law correlations between average Nusselt number and Rayleigh numbers are presented for specific Prandtl numbers.
Natural convection flows in porous trapezoidal enclosures with various inclination angles
International Journal of Heat and Mass Transfer, 2009
Simulations were carried out using penalty finite element analysis with bi-quadratic elements to investigate the influence of uniform and non-uniform heating of bottom wall within a trapezoidal enclosure of various inclination angles ðuÞ. Parametric study has been carried out for a wide range of Rayleigh number ðRaÞ ð10 3 6 Ra 6 10 6 Þ, Prandtl number ðPrÞ ð0:026 6 Pr 6 988:24Þ and Darcy number ðDaÞ ð10 À3 6 Da 6 10 À5 Þ. Numerical results are presented in terms of stream functions, isotherm contours and Nusselt numbers. The heat transfer is primarily due to conduction at lower values of Darcy number ðDaÞ and convection dominant heat transfer is observed at higher Da values. The intensity of circulation increases with increase in Darcy number. Increase in the intensity of circulations and larger temperature gradient are also observed with increase in u from 0°to 45°especially at larger Pr and Ra. Non-uniform heating of the bottom wall produces greater heat transfer rate at the center of the bottom wall than uniform heating at all Rayleigh and Darcy numbers, but average Nusselt number is lower for non-uniform heating. Local heat transfer rates are found to be relatively greater for u ¼ 0 . It is observed that the local heat transfer rate at the central portion of bottom wall is larger for non-uniform heating case. Average Nusselt number plots show higher heat transfer rates at the bottom wall for u ¼ 0 as compared to u ¼ 45 and u ¼ 30 .
Natural Convection in Trapezoidal Enclosure Heated Partially from Below
Natural convection in a trapezoidal enclosure with partial heating from below and symmetrical cooling from the sides has been investigated numerically. The heating is simulated by a centrally located heat source on the bottom wall, and four different values of the dimensionless heat source length, 1/5, 2/5, 3/5, 4/5 are considered. The laminar flow field is analyzed numerically by solving the steady, two-dimensional incompressible Navier-Stokes and energy equations. The Cartesian velocity components and pressure on a collocated (non-staggered) grid are used as dependent variables in the momentum equations discretized by finite volume method; body fitted coordinates are used to represent the trapezoidal enclosure, and grid generation technique based on elliptic partial differential equations is employed. SIMPLE algorithm is used to adjust the velocity field to satisfy the conservation of mass. The range of Rayleigh number is (10 3 ≤ Ra ≤10 5 ) and Prandtl number is 0.7. The results show that the average Nusselt number increases with the increases of the source length.
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.
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 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.
Study of Natural Convection Flows in a Tilted Trapezoidal Enclosure with Isoflux Heating From Below
Laminar steady state natural convection in a two-dimensional symmetrical trapezoidal enclosure has been studied using a finite element method. In this investigation, the top wall is considered adiabatic, both inclined sidewalls are maintained at a constant cold temperature and an isoflux heat source is provided at the bottom surface. The pressure-velocity form of the Navier-Stokes equations and energy equation are used to represent the mass, momentum and energy conservations of the fluid medium in the enclosure. Galerkin weighted residual method of finite element formulation with triangular mesh elements is employed. The fluid investigated here is air of Prandtl number fixed at 0.7. The Rayleigh number is varied from 10^3 to 10^6 while the sidewall inclination angle is varied from -15° to 45°. The results are presented in terms of streamline and isotherm plots as well as the variation of average Nusselt number with Rayleigh number for different base wall tilt angles of 0°, 15°, and 30°. The results show that the average Nusselt number increases with the increase of Rayleigh number and the effect of the sidewall inclination angle on heat transfer is significantly reduced at higher Rayleigh number. Effects of sidewall inclination angle on convection heat transfer characteristics decrease with the increase of base wall tilt angle at higher Rayleigh number and Rayleigh number equal to 10^5 can be considered as a critical limit for the present.
International Journal of Heat and Mass Transfer, 2012
Natural convection in trapezoidal cavities, especially those with two internal baffles in conjunction with an insulated floor, inclined top surface, and isothermal left-heated and isothermal right-cooled vertical walls, has been investigated numerically using the Element based Finite Volume Method (EbFVM). In numerical simulations, the effect of three inclination angles of the upper surface as well as the effect of the Rayleigh number (Ra), the Prandtl number (Pr), and the baffle's height (H b ) on the stream functions, temperature profiles, and local and average Nusselt numbers has been investigated. A parametric study was performed for a wide range of Ra numbers (10 3 6 Ra 6 10 6 ) H b heights (H b = H ⁄ /3, 2H ⁄ /3, and H ⁄ ), Pr numbers (Pr = 0.7, 10 and 130), and top angle (h) ranges from 10 to 20. A correlation for the average Nusselt number in terms of Pr and Ra numbers, and the inclination of the upper surface of the cavity is proposed for each baffle height investigated.
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.
The present work is aimed to study has been carried out of natural convection in a square enclosure with non-uniformly heated bottom wall and square shape heated block with different Prandtl numbers of 0.71, 1.0 and 1.5 has been investigated numerically. The horizontal bottom wall of the square cavity was non-uniformly heated and inner square shape heated block kept at T h while the side walls of the cavity were maintained at a cold temperature T c with T h >T c and upper wall is adiabatic. Finite element method was employed to solve the dimensionless governing equations of continuity, momentum and energy of the problem. Using the developed code, a parametric study was performed, and the effects of the Rayleigh number and the different Prandtl number on the fluid flow and heat transfer inside the square enclosure were investigated. The obtained results showed that temperature distribution and flow pattern inside the square enclosure depended on both strength of the magnetic field and Rayleigh number. For all cases two counter rotating eddies were formed inside the square enclosure. The magnetic field is decreased with the intensity of natural convection and flow velocity. Also it was found that for higher Rayleigh numbers a relatively stronger field was needed to decrease the heat transfer through natural convection.