Slow mixed convection in rectangular containers

Shankar, P. N.; Meleshko, V. V.; Nikiforovich, Eugene

doi:10.1017/s0022112003006256

Cited by 5 publications

(8 citation statements)

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“…Furthermore, the velocity fields forŨ = 0.01,Ũ = 0.001, andŨ = 0.0001 are given in Figure 12. These results are physically reasonable since a larger driving velocity produces a bigger upper eddy, which is similar to the analytical results of Shankar et al [29].…”

Section: Mixed Convection In a Rectangular Cavitysupporting

confidence: 91%

“…In these figures, we can see that the fields are very reasonable, even close to the singular corners. Furthermore, Figure 8 is very similar to the result 398 C.-C. TSAI AND T.-W. HSU obtained by Shankar et al [29]. On the other hand, Figure 9 illustrates the difference norm of the velocities calculated by the enriched MFS and MoS, which shows a general agreement between these two solutions.…”

Section: Natural Convection In a Rectangular Cavitysupporting

confidence: 87%

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A meshless numerical method for solving slow mixed convections in containers with discontinuous boundary data

Tsai

Hsu

2011

Numerical Methods in Fluids

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SUMMARYThis paper describes the formulations of the method of fundamental solutions (MFS), which is a famous meshless numerical method representing a sought solution by a series of fundamental solutions to solve slow mixed convections in containers with discontinuous boundary data. In the derivations, the fundamental solutions were obtained by using the Hörmander operator decomposition technique. All the velocities, temperatures, pressures, stresses and thermal fluxes corresponding to the fundamental solutions were addressed explicitly in tensor forms. Although the MFS is highly accurate for smooth boundary data, its convergence becomes poor when it is applied to problems with discontinuous boundary data. To compensate for this drawback, we enriched the MFS by adding the local discontinuous solutions to the series of fundamental solutions. This enriched MFS was applied to solve the benchmark problems of a lid-driven cavity and natural convection in rectangular containers. In addition, the numerical solutions were compared with the analytical solutions. Then, the meshless numerical method was further utilized to solve mixed convections in a triangular cavity and a cavity with a cosine-shaped bottom. These numerical results demonstrated the applicability of the enriched MFS to two-dimensional mixed convections in containers with discontinuous boundary data.

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Section: Mixed Convection In a Rectangular Cavitysupporting

confidence: 91%

Section: Natural Convection In a Rectangular Cavitysupporting

confidence: 87%

A meshless numerical method for solving slow mixed convections in containers with discontinuous boundary data

Tsai

Hsu

2011

Numerical Methods in Fluids

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“…They investigated the effects of Richardson number and the length of the heat source on the fluid flow and heat transfer. Shankar et al [28] presented analytical solution for mixed convection in cavities with very slow lid motion. The convection process has been shown to be governed by an inhomogeneous biharmonic equation for the stream function.…”

Section: Literature Reviewmentioning

confidence: 99%

Analysis of Mixed Convection in a Lid Driven Trapezoidal Cavity

Mamun¹,

Tanim²,

Rahman³

et al. 2011

Convection and Conduction Heat Transfer

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“…The scalars can then determined by a least squares procedure in minimizing the errors in satisfying the no slip boundary conditions on the cylinder walls [6,7,10]. We note that since the four sets of eigenfunctions deal with different boundary data, the four expansions can be determined independently of one another.…”

Section: The Solution Of the Boundary Value Problem For The Inhomogenmentioning

confidence: 99%

“…The dimensionless equations of continuity, momentum, energy and state in the Boussinesq approximation can then be written down as [4,10,12] …”

Section: An Application: Three-dimensional Natural Convection In a Cymentioning

confidence: 99%

Axial eigenfunctions and inhomogeneous solutions for the three-dimensional Stokes system with an application to natural convection in a cylinder

Shankar

2005

Z. angew. Math. Phys.

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This paper presents two contributions to the analysis of three-dimensional slow viscous flows in cylinders of circular section. First the vector axial eigenfunctions for this geometry, namely those that satisfy homogeneous boundary conditions on the flat end walls, are derived. Secondly a method is presented to find particular solutions to the inhomogeneous Stokes equations in this geometry. These new results, together with some results obtained earlier, are used to analyse slow natural convection in a vertical cylinder completely filled with a viscous liquid. The fluid motion is generated by the differential heating of the walls of the cylinder. The natural convection flow field is shown to be a superposition of an inhomogeneous field, the fields generated by the vector eigenfunctions and a Stokes flow field. A by-product of this work has been the identification of constraints on the boundary data that have to be satisfied in order for the eigenfunction expansions to work; this knowledge will be useful when attempts are made to prove the completeness of these Stokes flow eigenfunctions.

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Slow mixed convection in rectangular containers

Abstract: Journal of Fluid Mechanics, vol. 471 (2002), pp. 203–217

Cited by 5 publications

References 0 publications

A meshless numerical method for solving slow mixed convections in containers with discontinuous boundary data

A meshless numerical method for solving slow mixed convections in containers with discontinuous boundary data

Analysis of Mixed Convection in a Lid Driven Trapezoidal Cavity

Axial eigenfunctions and inhomogeneous solutions for the three-dimensional Stokes system with an application to natural convection in a cylinder

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