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A dynamically adaptive lattice Boltzmann method for thermal convection problems

100%

Feldhusen K. , Deiterding R. , Wagner C.

International Journal of Applied Mathematics and Computer Science

2016

tom 26

nr 4

735-747

Utilizing the Boussinesq approximation, a double-population incompressible thermal lattice Boltzmann method (LBM) for forced and natural convection in two and three space dimensions is developed and validated. A block-structured dynamic adaptive mesh refinement (AMR) procedure tailored for the LBM is applied to enable computationally efficient simulations of moderate to high Rayleigh number flows which are characterized by a large scale disparity in boundary layers and free stream flow. As test cases, the analytically accessible problem of a two-dimensional (2D) forced convection flow through two porous plates and the non-Cartesian configuration of a heated rotating cylinder are considered. The objective of the latter is to advance the boundary conditions for an accurate treatment of curved boundaries and to demonstrate the effect on the solution. The effectiveness of the overall approach is demonstrated for the natural convection benchmark of a 2D cavity with differentially heated walls at Rayleigh numbers from 103 up to 108. To demonstrate the benefit of the employed AMR procedure for three-dimensional (3D) problems, results from the natural convection in a cubic cavity at Rayleigh numbers from 103 up to 105 are compared with benchmark results.

Effect of compressibility and suspended particles on thermal convection in a Walters' B' elastico-viscous fluid in hydromagnetics

88%

Sharma R. C. , Aggarwal A. K.

2006

tom Vol. 11, no 2

391-399

A layer of a compressible, electrically conducting Walters' B' elastico-viscous fluid permeated with suspended particles heated from below in the presence of a magnetic field is considered. For the case of stationary convection, the Walters'(model B') elastico-viscous fluid behaves like a Newtonian fluid and the compressibility, magnetic field are found to have stabilizing effects, whereas the suspended particles have a destabilizing effect on the thermal convection. The presence of each - viscoelasticity, magnetic field and suspended particles introduces oscillatory modes in the system which were non-existent in their absence.

Thermal convection in a Walters' (model B') elastico-viscous dusty fluid in hydromagnetics with the effect of compressibility and rotation

63%

Kumar V. , Aggarwal A. K. , Kumar S.

2010

tom Vol. 15, no 1

51-62

A compressible, electrically conducting Walters'B' elastico-viscous fluid heated from below in the presence of a magnetic field and rotation is considered. At stationary convection, Walters' (Model B') elastico-viscous fluid behaves like a Newtonian fluid and compressibility, rotation are found to have a stabilizing effect whereas the suspended particles have a destabilizing effect on the thermal convection and magnetic field has a stabilizing effect under certain conditions. The presence of magnetic field and rotation introduces oscillatory modes in the system which were non-existent in their absence. Graphs have also been plotted by giving some numerical values to the parameters.

Simulation of thermal convection depending on the angle between gravity force and temperature gradient

63%

Jopek H.

2006

tom Vol. 11, nr 1

29-34

In this papers the influence of the angle between the gravity force and the temperature gradient on the convection process is studied and simulated. Free convection is the kind of heat transfer in which the fluid's motion is caused by the volume forces, usually by the gravity force but also due to centrifugal forces or magnetic field's forces. The differences of temperature around the body are connected to differences of density and consequently buoyant force appears. For that reason, in the equations of motion the volume force is substituted by the expression representing the difference in specific weight and bouyancy which is proportional to the difference of density. It is a very common phenomenon that the convection appears in the film of fluid between the surfaces of two different temperatures

A Characterization of the Rivlin-Ericksen Viscoelastic Fluid in the Presence of a Magnetic Field and Rotation

51%

Banyal A. S.

2012

tom Vol. 60, iss. 4

355-355

A layer of Rivlin-Ericksen viscoelastic fluid heated from below is considered in the presence of an uniform vertical magnetic field and rotation. Following the linearized stability theory and normal mode analysis, this paper mathematically establishes the condition for characterizing oscillatory motion, which may be neutral or unstable, for rigid boundaries at the top and bottom of the fluid. It is established that all non-decaying slow motions starting from rest, in the configurations, are necessarily non-oscillatory in the regime TAF 2 + TA 4 + Qp2 2 1; where TA is the Taylor number, Q is the Chandrasekhar number, p2 is the magnetic Prandtl number, and F is the viscoelasticity parameter. This result is important, since it holds for all wave numbers for rigid boundaries of infinite horizontal extension at the top and bottom of the fluid, and the exact solutions of the problem investigated in closed form are not obtainable.