scholarly journals Thermal Model for Timber Fire Exposure with Moving Boundary

Materials ◽  
2021 ◽  
Vol 14 (3) ◽  
pp. 574
Author(s):  
Stanislav Šulc ◽  
Vít Šmilauer ◽  
František Wald
Keyword(s):  
Boundary Condition ◽  
Moving Boundary ◽  
Transport Model ◽  
Internal Heat ◽  
Internal Heat Source ◽  
Fire Exposure ◽  
Surface Cracking ◽  
Moving Boundary Condition ◽  
Insulation Effect ◽  
Initial Geometry

Fire exposure of timber leads to charring, surface cracking and timber burnout, shifting the external thermal load deeper into the timber domain. This phenomenon plays its role mainly in situations of longer fire exposure. The majority of current approaches and models assume initial geometry during the whole analysis, leading generally to the overestimation of the insulation effect of the charred layer and to a limited burnout. This paper presents a heat transport model which is supplemented with a moving boundary condition, a criterion for the finite element deactivation and the internal heat source. Comparison with experiments using a constant radiative load testifies that the moving boundary condition becomes important after approximately 10 min of fire exposure and rather leads to a constant charring rate observed in several experiments.

Singular Perturbation Solution for a Two-Phase Stefan Problem in Outward Solidification

2019 ◽  
Author(s):  
Minghan Xu ◽  
Saad Akhtar ◽  
Mahmoud A. Alzoubi ◽  
Agus P. Sasmito
Keyword(s):  
Boundary Condition ◽  
Porous Media ◽  
Analytical Solution ◽  
Singular Perturbation ◽  
Stefan Problem ◽  
Moving Boundary ◽  
Computational Cost ◽  
Perturbation Solution ◽  
Two Phase ◽  
Moving Boundary Condition

Abstract Mathematical modeling of phase change process in porous media can help ensure the efficient design and operation of thermal energy storage and pipe freezing. Numerical methods generally require high computational power to be applicable in practice. Therefore, it is of great interest to develop accurate and reliable analytical frameworks. This study proposes a singular perturbation solution for a two-phase Stefan problem that describes outward solidification in a finite annular space. The problem solves cylindrical heat conduction equations for both solid and liquid phases, with consideration of a moving boundary condition. Perturbation method takes the advantages of small Stefan number as the perturbation parameter, which intrinsically occurs in porous media. Furthermore, a boundary-fixing technique is used to remove nonlinearity in the moving boundary condition. Two different time scales are separately expanded and evaluated to facilitate the construction of a composite asymptotic solution. The analytical solution is verified against a general numerical model using enthalpy method and local volume-averaged thermal properties. The results indicate that the temperature profile of both phases can be well modeled by singular perturbation theory. The analytical solution is found to have similar conclusions to the numerical analysis with much lesser computational cost.

The LBE Simulation and PIV Experimental Study on a Novel Viscous Pump

2005 ◽  
Author(s):  
Fan Yang ◽  
Shuhong Liu ◽  
Jinwei Li ◽  
Yulin Wu
Keyword(s):  
Boundary Condition ◽  
Unsteady Flow ◽  
Cross Sections ◽  
Lattice Boltzmann ◽  
Moving Boundary ◽  
Flow Problem ◽  
Numerical Study ◽  
Reynolds Numbers ◽  
Low Reynolds Numbers ◽  
Moving Boundary Condition

A numerical study and PIV investigation of flow in a novel viscous-based pumping device appropriate for microscale applications is described. The device, essentially consisting of a rotating cylinder eccentrically placed in a channel, is shown to be capable of generating a net flow. The two shape cross-sections of cylinders, the circular and four semi-elliptic lobed contour are studied, which is the steady and unsteady flow problem, respectively. The lattice Boltzmann equation (LBE) simulations at low Reynolds numbers are carried out to study the influence of various geometric parameters, which the results are compared with the PIV experiment ones. The unified solid curved wall boundary condition based on interpolation and the balance of momentum on the wall of the LBE simulation is used in steady and unsteady flow, and the moving boundary condition is also used in the latter. The numerical results indicated that the more effective pumping and better performance is obtained with the decrease of Reynolds number, as well as the increase regular degree of cylinder cross-section.

Solution of Fractional Diffusion Equation with a Moving Boundary Condition by Variational Iteration Method and Adomian Decomposition Method

2010 ◽  
Vol 65 (10) ◽  
pp. 793-799 ◽  
Author(s):  
Subir Das ◽  
Subir Rajeev
Keyword(s):  
Boundary Condition ◽  
Diffusion Equation ◽  
Iteration Method ◽  
Decomposition Method ◽  
Moving Boundary ◽  
Adomian Decomposition Method ◽  
Variational Iteration Method ◽  
Fractional Diffusion ◽  
Adomian Decomposition ◽  
Moving Boundary Condition

In this paper, the approximate analytic solutions of the mathematical model of time fractional diffusion equation (FDE) with a moving boundary condition are obtained with the help of variational iteration method (VIM) and Adomian decomposition method (ADM). By using boundary conditions, the explicit solutions of the diffusion front and fractional releases in the dimensionless form have been derived. Both mathematical techniques used to solve the problem perform extremely well in terms of efficiency and simplicity. Numerical solutions of the problem show that only a few iterations are needed to obtain accurate approximate analytical solutions. The results obtained are presented graphically.

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