A comprehensive analysis of natural convection in a trapezoidal cavity with magnetic field and cooled triangular obstacle of different orientations (original) (raw)
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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.
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The present study is conducted to investigate heat and fluid flow patterns based on heatline concept for free convection within trapezoidal cavity with uniformly and non-uniformly heated bottom wall under magnetic field. The left and right (side) walls are cold and top wall is kept thermal insulated. The consequent mathematical model is governed by the coupled equations of mass, momentum and energy and solved by employing Galerkin weighted residual method of finite-element technique. A wide range of pertinent parameters such as Rayleigh numbers (10 3 ≤ Ra ≤10 5 ) and Hartmann number (Ha = 50) and Prandtl numbers (0.026 ≤ Pr ≤ 1000) with inclination angles (ф) are considered in the present study. In addition, the free convection regime is occurred due to buoyancy forces. Various characteristics such as streamlines, isotherms, total heat flux or heat function and heat transfer rate in terms of the local Nusselt number (NuL), average Nusselt number (Nuav) are investigated for the afore...
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The present research was developed to find out the effect of heated cylinder configurations in accordance with the magnetic field on the natural convective flow within a square cavity. In the cavity, four types of configurations—left bottom heated cylinder (LBC), right bottom heated cylinder (RBC), left top heated cylinder (LTC) and right top heated cylinder (RTC)—were considered in the investigation. The current mathematical problem was formulated using the non-linear governing equations and then solved by engaging the process of Galerkin weighted residuals based on the finite element scheme (FES). The investigation of the present problem was conducted using numerous parameters: the Rayleigh number (Ra = 103–105), the Hartmann number (Ha = 0–200) at Pr = 0.71 on the flow field, thermal pattern and the variation of heat inside the enclosure. The clarifications of the numerical result were exhibited in the form of streamlines, isotherms, velocity profiles and temperature profiles, lo...
Numerical Heat Transfer, Part A: Applications, 2017
In this paper double diffusive natural convection in a square cavity in the presence of external magnetic field has been studied numerically by Galerkin's weighted residual finite element method using velocity-vorticity formulation. Simulation results are reported for 0 < Ha < 200, buoyancy ratio, 2 < N < 2, 104 < Ra < 106 and field inclination angle varying from 00 to 3600 for different fluid systems, namely gas, water, and liquid Gallium. Results indicate that the streamline pattern is greatly influenced by the direction and intensity of magnetic field and at Ra = 1.0e5, the increase in Ha from 0 to 30 has resulted in a decrease in Nusselt number and Sherwood number by about 72% and 78% respectively. The inclination angle has played an important role in the suppression of heat and mass transfer, maximum suppression is experienced at Θ = 45 and 270 while minimum is recorded at Θ = 135 and 315. Liquid Gallium showed the least response to change in magnetic field intensity compared to other two fluids.
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This work was carried out in collaboration between all authors. Author MSH designed the physical model, wrote the literature review, carried out simulation work, wrote the first draft of the manuscript and did the analysis of the study. Author MAA provided the idea of the problem, helped to match the program, checked the overall write up, figures, numerical results and data. Author LSA discussed the idea of the problem, checked the numerical results and the whole manuscript. All authors read and approved the final manuscript.
Effect of a Magnetic Field on Buoyancy-Driven Convection in Differentially Heated Square Cavity
IEEE Transactions on Magnetics, 2009
Steady, laminar, natural-convection flow in the presence of a magnetic field in a cavity heated from left and cooled from right is considered. In our formulation of the governing equations, mass, momentum, energy and induction equations are applied to the cavity. To solve the governing differential equations a finite volume code based on PATANKAR's SIMPLER method is utilized. Numerical predictions are obtained for a wide range of Rayleigh number (Ra) and Hartmann number (Ha) at the Prandtl number Pr = 0 733. When the magnetic field is relatively strengthened, the thermal field resembles that of a conductive distribution, and the fluid in much of the interior is nearly stagnant. Further, when the magnetic field is weak and the Rayleigh number is high, the convection is dominant and vertical temperature stratification is predominant in the core region. However, for sufficiently large Ha, the convection is suppressed and the temperature stratification in the core region diminishes. The numerical results show that the effect of the magnetic field is to decrease the rate of convective heat transfer and the average Nusselt number decreases as Hartmann number increases. The results are presented for Rayleigh number from 10 4 up to 10 6 and are in form of streamlines, isotherms, and Nusselt number for various Rayleigh and Hartman numbers.
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Combined effect of free and forced convection i.e. mixed convection occurs in many heat transfer devices, such as the cooling system of a nuclear power plant, large heat exchangers, cooling of electronic equipment, ventilation and heat or pollution agent clearance. In this thesis under the title “Finite Element Analysis on Magneto-hydrodynamic Mixed Convection Flow in a Triangular Enclosure”, two problems have been studied. The relative direction between the buoyancy force and the externally forced flow is important. In the case the fluid is externally forced to flow as the buoyancy force, the mode of heat transfer is termed combined forced and natural convection. The studies as well as depending on various flow and geometrical conditions are abstracted below. Initially, the effect of conduction in mixed convection flow in a triangular enclosure has been investigated numerically. The left vertical wall which is moving from the bottom corner of the cavity is kept at a uniform constan...
The influence of thermal radiation and heat generation on an unsteady two-dimensional natural convection flow in an inclined enclosure heated from one side and cooled from the adjacent side under the influence of a magnetic field using staggered grid finite-difference technique has been studied. The governing equations have been solved numerically for streamlines, isotherms, local Nusselt numbers and the average Nusselt number for various values of thermal radiation and heat generation parameters by considering three different inclination angles and magnetic field directions, keeping the aspect ratio fixed. The results indicate that the flow pattern and temperature fields are significantly dependent on the above mentioned parameters. It is found that magnetic field suppresses the convection flow and its direction influences the flow pattern which results in the appearance of inner loop and multiple eddies.
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.
AIP Conference Proceedings, 2016
In the present study the effect of natural convection in a rectangular cavity with three square shape heated block is focused in this numerical is studied. The horizontal bottom wall and three square blocks are temperature T h while the left and right vertical walls and horizontal top wall are temperature T c with T h >T c. The governing equations along with appropriate boundary conditions for the present problem are first transformed into a non-dimensional form and the resulting non linear system of partial differential equations are then solved numerically using Galerkin's finite element method. Parametric studies of the fluid flow and heat transfer in the enclosure are performed for magnetic parameter Hartmann number Ha, Prandtl number Pr and Rayleigh number Ra. The streamlines, isotherms and average Nusselt number at the hot wall and average temperature of the fluid in the enclosure are presented for the parameters. The numerical results indicate that the Hartmann number and Rayleigh number have strong influence on the streamlines and isotherms. On the other hand Prandtl has little effect on the stream line and isotherm plots. Finally, the mentioned parameters have significant effect on average Nusselt number at the hot wall and average temperature of the fluid in the cavity.