Geometric multigrid technique for solving heat convection-diffusion and phase change problems

Moraga, Nelson O.; Marambio, Marcelo A.; Cabrales, Roberto Carlos

doi:10.1016/j.icheatmasstransfer.2017.08.012

Cited by 14 publications

(3 citation statements)

References 24 publications

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“…The FVM with QUICK was further investigated in [14] in solving NNC with internal rotating heater and cooler. Moraga et al [15] demonstrated the multigrid FVM with a fifth power differentiation scheme for convective transport in the solution of NNC with phase change. A similar numerical approach was also used in the solution of NNC in 3D [16].…”

Section: Introductionmentioning

confidence: 99%

Refined RBF-FD analysis of non-Newtonian natural convection

Rot¹,

Kosec²

2022

Preprint

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In this paper we present a refined RBF-FD solution for a non-Newtonian fluid in a closed differentially heated cavity. The problem at hand is governed by three coupled nonlinear partial differential equations, namely heat transport, momentum transport and mass continuity. The non-Newtonian behaviour is modelled with the Ostwald-de Weele power law and the buoyancy with the Boussinesq approximation. The problem domain is discretised with scattered nodes without any requirement for a topological relation between them. This allows a trivial generalisation of the solution procedure to complex irregular 3D domains, which is also demonstrated by solving the problem in a 2D and 3D geometry mimicking the porous filter. The results in 2D are compared with two reference solutions that use the Finite volume method in a conjunction with two different stabilisation techniques (upwind and QUICK), where we achieved good agreement with the reference data. The refinement is implemented on top of a dedicated meshless node positioning algorithm using piecewise linear node density function that ensures sufficient node density in the centre of the domain while maximising the node density in a boundary layer where the most intense dynamic is expected. The results show that with a refined approach, up to 5 times fewer nodes are needed to obtain the results with the same accuracy compared to the regular discretisation. The paper also discusses the convergence for different scenarios for up to 2 • 10 5 nodes, the behaviour of the flow in the boundary layer, the behaviour of the viscosity and the geometric flexibility of the proposed solution procedure.

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Section: Introductionmentioning

confidence: 99%

Refined RBF-FD analysis of non-Newtonian natural convection

Rot¹,

Kosec²

2022

Preprint

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“…The convection constant or the heat transfer coefficient (hc), is used in thermodynamics to calculate the heat transfer typically occurring by convection. The coefficient is very important parameter in science and engineering [1], [2], [4]- [10]. Dynamic analysis of some thermal systems cannot be done without this parameter and numerical studies of such systems also require using it.…”

Section: Introductionmentioning

confidence: 99%

“…In [10], the effects of the multigrid technique on the accuracy and efficiency in describing convective heat transfer in closed and open cavities with and without liquid-solid phase changes of Newtonian and shear-thinning non-Newtonian fluids are analyzed. In [11], the results of a numerical study of the melting and natural convection in a rectangular enclosure heated with three discrete protruding electronic components which are the heat sources mounted on a conducting vertical plate are given.…”

Section: Introductionmentioning

confidence: 99%

Convection Coefficient Estimation of Still Air Using an Infrared Thermometer and Curve-Fitting

Yener¹,

Yener²,

Mutlu³

2019

Journal of Engineering Technology and Applied Sciences

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The convection coefficient is an important thermal property. In this study, using an infrared thermometer, the convection coefficient of still air is estimated. First, the sample is heated in a sintering oven, then placed on a wood table for obtaining an almost adiabatic boundary, finally its temperature is recorded with respect to time using an infrared thermometer. The data is curve-fitted to find the sample temperature as a function of time. Using the sample's physical dimensions, the specific heat capacity and the mass of the sample, the convection coefficient of still air is estimated.

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