A finite element free convection model for the side wall heated cavity

Ismail, Kamal Abdel Radi; Scalon, Vicente Luiz

doi:10.1016/s0017-9310(99)00225-2

Cited by 18 publications

(10 citation statements)

References 20 publications

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“…The constant temperature lines and flow patterns shown in Figs. 7 and 8 for the Raleigh numberZ10 5 , respectively.The analysis of the results indicated that there are good agreements between the present solution and the benchmark solution[11].…”

supporting

confidence: 51%

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Development of an integrated model for airflow in building spaces

Farhanieh

Sattari

2006

Renewable Energy

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supporting

confidence: 51%

“…The top and bottom walls are insulated. This problem has studied as a benchmark to verification of the results by previous researchers [7,11]. …”

Section: Problemmentioning

confidence: 94%

Development of an integrated model for airflow in building spaces

Farhanieh

Sattari

2006

Renewable Energy

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“…Validation for natural convection in absence of magnetic field and surface radiation is done by comparing the average Nusselt number of present study with extensive benchmark results, those available in literature [1,[40][41][42]. The comparisons are presented in Table 2.…”

Section: Grid Sensitivity Study and Validationmentioning

confidence: 99%

A Numerical Investigation of Surface Radiation Interaction With Magneto-Convection of an Electrically Conducting Fluid Imposed With a Transverse Magnetic Field

Jena

Mahapatra

2014

Heat Transfer Engineering

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In the present study, analysis has been performed to investigate the surface radiation effect on hydro-magnetic buoyant convection of an electrically conducting fluid in a differentially heated cavity. The fluid is enclosed within a gray chamber and imposed with a uniform magnetic field orthogonal to the vertical cross-sectional plane of the chamber. Numerical solution is done by control volume integration. A modified Marker and Cell method is used for the solution of the governing equation for flow transport. A gradient-dependent consistent hybrid upwind scheme of second order is used for discretization of the convective terms. The transport equation for surface radiation is solved using a net radiation method. Cross-string method is used to compute the view factor. Comprehensive studies on the controlling parameters that affect the flow and heat transfer characteristics are delineated. The results are presented in tabular and graphical form. The heat transfer and flow characteristics are depicted in form of isotherms and streamlines revealing the concealed physics of a complex phenomenon.

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“…where the non-dimensional parameters are defined as Rayleigh number Ra = g$ATL 3 /ar> and Prandtl number Pr = υ/α. In Eq.…”

Section: Governing Equations and Boundary Conditionsmentioning

confidence: 99%

“…Additionally, De Vahl Davis [2] presented a benchmark solution of 2D natural convective problem in a square cavity and revealed results for different Rayleigh numbers. Irrespective of model used to handle the natural convection in a square cavity, Ismail and Scalon [3] described a finite element analysis of 2D natural convection in a cavity over a wide range of L/H aspect ratios varying from 0.1 to 1.0.…”

Section: Introductionmentioning

confidence: 99%

Velocity-Vorticity Formulation for 2D Natural Convection in an Inclined Cavity by the DQ Method

Liao

Young

et al. 2007

J. mech.

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The aim of this paper attempts to apply the differential quadrature (DQ) method for solving twodimensional natural convection in an inclined cavity. The velocity-vorticity formulation is used to represent the mass, momentum, and energy conservations of the fluid medium in an inclined cavity. We employ a coupled technique for four field variables involving two velocities, one vorticity and one temperature components. In this method, the velocity Poisson equation, continuity equation, vorticity transport equation and energy equation are all solved as a coupled system of equations so as to we are capable of predicting four field variables accurately. The main advantage of present approach is that coupling the velocity and the vorticity equations allows the determination of the boundary values implicitly without requiring the explicit specification of the vorticity values at the boundary walls. A natural convection in a cavity with different angle of inclinations for Rayleigh number equal to 10 3 , 10 4 , 10 5 and 10 6 and H/L aspect ratios varying from 1 to 3 is investigated. It is shown that with the use of the present algorithm the benchmark results for temperature and flow fields could be obtained using a coarse mesh grid.

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A finite element free convection model for the side wall heated cavity

Cited by 18 publications

References 20 publications

Development of an integrated model for airflow in building spaces

Development of an integrated model for airflow in building spaces

A Numerical Investigation of Surface Radiation Interaction With Magneto-Convection of an Electrically Conducting Fluid Imposed With a Transverse Magnetic Field

Velocity-Vorticity Formulation for 2D Natural Convection in an Inclined Cavity by the DQ Method

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