Velocity–vorticity formulation for 3D natural convection in an inclined enclosure by BEM

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In this paper we focus on the determination of vorticity boundary conditions for the solution of Navier-Stokes equations in velocity-vorticity form. Boundary element method is used to calculate the vorticity boundary conditions on an arbitrary curved surface. The method is used in an in-house fluid and heat transfer solver.Results of simulations of flow and heat transfer of nanofluids are presented. We consider a heated elliptical cylinder in a cooled cubic enclosure where natural convection develops. Steady laminar regime is considered with Rayleigh number values up to a million. Al 2 O 3 nanofluid is considered, as well as pure water for validation purposes. Properties of the nanofluid are considered to be constant throughout the domain and are estimated using models for different nanoparticle volume fractions (0.1 and 0.2).The results show highest heat transfer enhancement in the conduction dominated flow regime, where the enhanced thermal properties of nanofluids play an important role. When convection is the dominant heat transfer mechanism, using nanofluids yields a smaller increase in heat transfer efficiency.

Section: Numerical Proceduresmentioning

confidence: 99%

Nanofluid natural convection around a cylinder by BEM

Ravnik¹,

Škerget²,

Yeigh³

2015

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“…In our previous work (Ravnik et al [14,16,17]) we have developed and used wavelet compression and sparse approximation techniques aimed at reducing the computational requirements of our BEM based flow solver (Škerget et al [18,19], Ravnik et al [15]). The methods were aimed at the steady Laplace kernel and the following conclusions were found: the methods are successful in lowering the computational requirements and scale nearly linearly.…”

Section: Numerical Experimentsmentioning

confidence: 99%

Wavelet compression of parabolic diffusion integral kernels

Ravnik¹,

Škerget²

2014

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In this paper we examine the properties of steady and unsteady diffusion fundamental solutions in the framework of fast BEM. The fundamental solutions and their kernels form integral kernels in boundary integral equations. The properties of these kernels define the relationship between CPU time and storage gain versus the accuracy of sparse approximations in fast BEM.We show that, when solving a diffusion type problem, using unsteady fundamental solutions is advantageous over steady fundamental solutions. We examine the behaviour of fundamental solutions to show why the unsteady fundamental solution is better for fast BEM. Furthermore, we confirm the theoretical findings by simulation of viscous fluid flow and heat transfer. We consider steady cases, where a false transient approach is used so unsteady diffusion fundamental solutions may be employed. Finally, we examine cases of increasing non-linearity, to highlight that these findings apply to strongly nonlinear problems as well.

“…Taking into account (21) and the results of Ravnik et al [9] the integral form of the vorticity transport equation without derivatives of field functions, for the j-th component of vorticity, is…”

Section: Boundary-domain Integral Formulationmentioning

confidence: 99%

Simulation of ferrofluids by BEM

Ravnik¹,

Škerget²

2012

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In this paper the Boundary element method (BEM) was applied to simulate viscous flow of ferrofluids under the influence of a homogenous external magnetic field. We present a derivation of the boundary integral form of the vorticity transport equation, which includes magnetic body force terms. Furthermore, discretization and numerical solution of the coupled flow and heat transfer problems are presented.The derived numerical model has been used to study the effect of a homogenous external magnetic field on the natural convection of ferrofluids in a differentially heated enclosure. We established that the effects are negligible for magnetic Rayleigh numbers less or equal to the flow Rayleigh number. On the other hand, the magnetic body force changes the flow field significantly and contributes to the instability of the flow.