Numerical Investigation of Natural Convection Flow in a Trapezoidal Cavity with Non-uniformly Heated Triangular Block Embedded Inside (original) (raw)
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Numerical Analysis on MHD Natural Convection within Trapezoidal Cavity Having Circular Block
In this paper, we have studied MHD natural convection within trapezoidal cavity having circular block with uniformly heated bottom wall with inclination angles (ф). To investigate the effects of uniform heating with the circular block a Galerkin finite element method is studied and also used for solving the Navier-Stokes equations for different angles Φs. Here left and right walls are considered as cold and upper wall is considered as thermal insulated in a trapezoidal cavities. Rayleigh number (Ra) from 10 3 to 10 5 , Hartmann number (Ha = 20) and Prandtl number (Pr) from 0.026 to 0.7 with various tilt angles Ф = 45 0 , 30 0 and 0 0 (square) are concerned with the fluid. By different sets of governing equations along with the corresponding boundary conditions are used to set the physical problems. Results are shown in terms of streamlines, isotherms, heat flux and heat transfer rates for different Ra and Pr. It is seen that for different angles Φs conduction dominant region changes for different Pr when Ra increases. Local and average nusselt numbers are also used for heat transfer analysis for different irrespective Φs.
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.
International Journal of Heat and Mass Transfer, 2008
A penalty finite element analysis with bi-quadratic elements is performed to investigate the influence of uniform and non-uniform heating of bottom wall on natural convection flows in a trapezoidal cavity. In the present investigation, bottom wall is uniformly and non-uniformly heated while two vertical walls are maintained at constant cold temperature and the top wall is well insulated. Parametric study for the wide range of Rayleigh number (Ra), 10 3 6 Ra 6 10 5 and Prandtl number (Pr), 0:07 6 Pr 6 100 shows consistent performance of the present numerical approach to obtain the solutions in terms of stream functions and the temperature profiles. For certain values of the parameters studied in the above range, a symmetry is observed while representing the flow patterns in terms of stream functions. Non-uniform heating of the bottom wall produces greater heat transfer rate at the center of the bottom wall than uniform heating case for all Rayleigh numbers but average Nusselt number shows overall lower heat transfer rate for non-uniform heating case. The power law correlations between average Nusselt number and Rayleigh numbers are presented. The effect of Prandtl number in the variation of local and average Nusselt numbers is more significant for Prandtl numbers in the range 0.07-0.7 than 10-100.
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.
AIP Conference Proceedings
The phenomenon of natural convective flow being there with magnetic field in a trapezoidal cavity with cold triangular obstacle for different leaning angles ф (ф = 0 0 , 30 0 , 45 0) has been studied in this work numerically. The horizontal wall of the cavity is considered as non-uniformly heated while the upper wall of the cavity is thermal insulated and other side walls are at a cold temperature. Finite element technique of Galerkin weighted residual method (GWRM) is used to solve the principal partial differential equations. The numerical calculations are worked out for magnetic field parameter, such as, Hartmann number, Ha (0≤Ha≤200), which is used to find the effects on flow and temperature field and the study is also executed for other buoyancy parameters Rayleigh number, Ra (10 3 ≤Ra≤10 6) and Prandtl number, Pr = 0.7 and also for diverse orientations or rotations (0 0 ≤rot≤90 0) of cold triangular obstacle of the cavity. The obtained results are demonstrated in terms of streamlines, isotherms, heat transfer rates as well as local and average Nusselt numbers affected by the rotations of cold triangular obstacle and also aforesaid parameters.
Thermal Behavior of the Natural Convection of Air Confined in a Trapezoidal Cavity
2021
The thermal behavior of air by natural convection in a confined trapezoidal cavity, one of the walls of which is subjected to a constant heat flow in hot climates, has been analyzed numerically. The heat and mass transfers are carried out by the classical equations of natural convection. These equations are discretized using the Finite Difference Method and the algebraic systems of equations thus obtained are solved with the Thomas and Gauss algorithms. We analyze the influence of the number Ra = 10 − 10 on the current and isothermal lines as well as the effects of the aspect ratio A = l / H and the angle of inclination φ. In particular, we have shown that convective exchanges in the cavity are preponderant for high Ra numbers. Also we have watches the increase in the values of the isothermal lines and the decrease in the intensity of the streamlines for the low values of A and of the angle φ.
Effects of porosity and heat generation on free convection in a porous trapezoidal cavity
Thermal Science, 2019
The problem of laminar free convection in a trapezoidal enclosure, filled with a fluidsaturated porous medium and with internal heat generation has been investigated using a penalty finite element analysis. The enclosure bottom wall is heated at a constant temperature and the top wall is subjected to a constant cold temperature whereas the left inclined wall is considered to be non-isothermal and the right inclined wall is isothermally cooled. The effects of the porosity of the medium and heat generation on the isotherms and streamlinesare investigated. The rate of heat transfer from the walls of the cavity is examined as well. The Prandtl number of the fluid is chosen to be 0.7 (air) whereas the value of the Rayleigh number is selected to be 105.
International Communications in Heat and Mass Transfer, 2021
The aim of the present paper is to study the steady state natural convection in a square porous enclosure using a thermal non-equilibrium model for the heat transfer between the fluid and the solid phases. The analysis assumes that the porous medium is homogeneous and isotropic. The present study also assumes the non-Darcy model of natural convection in porous media. It is assumed that the heat generation is only in solid phase. Two dimensional steady convection in a cavity bounded by isothermal walls at constant temperatures has been studied numerically by adopting a two-temperature model of microscopic heat transfer. Such a model, which allows the fluid and solid phases not to be in local thermal equilibrium, is found to modify the flow behaviour and heat transfer rates. Knowledge of this behaviour is very important for the design of the many engineering applications.
MIXED CONVECTION ANALYSIS IN TRAPEZOIDAL CAVITY WITH A MOVING LID
International Journal of Mechanical and Materials Engineering (IJMME), 2010
Mixed convection heat transfers in a two-dimensional trapezoidal cavity with constant heat flux at the heated bottom wall while the isothermal moving top wall in the horizontal direction has been studied numerically. Control Volume based finite volume method (FVM) has been used to discretize the governing differential equations. The pressure- velocity coupling in the governing equations is achieved by using the well known SIMPLE method for numerical computations. A second order upwind differencing scheme is to be used for the formulation of the coefficients in the finite-volume equations. All computations are to be done for a range of Richardson number, Ri from 0.1 to 10 and the aspect ratio, A are to be changed from 0.5 to 2 for a fluid having Prandtl number equal to 0.71 (air). First the optimum configuration of the trapezoidal cavity has been obtained by changing the inclination angle, γ of the side walls. Then the effect of Richardson number, aspect ratio, and Rotation angle, Φ (30°, 45° and 60°) of the optimum trapezoidal cavity has been studied by changing the desired parameter. Results have been presented in the form of streamline and isotherm plots as well as the variation of the Nusselt number at the heat source surface under different conditions. The results shows that with increasing Ri, the heat transfer rate increases as natural convection dominates. The rotational angle of the trapezoidal cavity and the direction of the lid motion affect the heat transfer rate significantly. Optimum heat transfer rate is obtained at aiding flow condition having higher values of Ri.
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.