THERMAL RESPONSE OF OPEN-CELL POROUS MATERIALS: A NUMERICAL STUDY AND MODEL ASSESSMENT (original) (raw)
The evaluation of effective material properties in heterogeneous materials (e.g., composites or multicomponent structures) has direct relevance to a vast number of applications, including nuclear fuel assembly, electronic packaging, municipal solid waste, and others. The work described in this paper is devoted to the numerical verification assessment of the thermal behavior of porous materials obtained from thermal modeling and simulation. Two-dimensional, steady state analyses were conducted on unit cell nano-porous media models using the finite element method (FEM). The effective thermal conductivity of the structures was examined, encompassing a range of porosity. The geometries of the models were generated based on ordered cylindrical pores in six different porosities. The dimensionless effective thermal conductivity was compared in all simulated cases. In this investigation, the method of manufactured solutions (MMS) was used to perform code verification, and the grid convergence index (GCI) is employed to estimate discretization uncertainty (solution verification). The system response quantity (SRQ) under investigation is the dimensionless effective thermal conductivity across the unit cell. Code verification concludes an approximately second order accurate solver. It was found that the introduction of porosity to the material reduces effective thermal conductivity, as anticipated. This approach can be readily generalized to study a wide variety of porous solids from nano-structured materials to geological structures. NOMENCLATURE a = apparent order of accuracy A = area α = porosity ε = error g = characteristic function G = conductance matrix GCI = grid convergence index Γ = computational domain boundary h = mesh number H = characteristic mesh size k = thermal conductivity K = thermal conductivity matrix L = cell length and width n = boundary normal vector N = total count N = shape function ω = relaxation coefficient Ω = computational domain p = order of accuracy P = vertex heat load vector q = heat flux q = heat flux vector Q = volumetric heat generation R = void radius ρ = energy balance residual ρ = energy balance residual vector s = unit direction sign T = temperature T = triangle vertex temperature vector U = approximate numerical uncertainty w = interpolation weight x = x-coordinate y = y-coordinate Subscripts a = approximate b = bulk eff = effective ext = extrapolated h = mesh number i = index j = index MMS = manufactured solution n = normal
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