Temperature Dependence Of Thermophysical Parameters Research Articles

A Numerical Time Integration Procedure for Secondary Dendrite Arm Spacing in Hyper-Peritectic Steel Alloys

AbstractA numerical time integration procedure for the calculation of the secondary dendrite arm spacing (SDAS) in FeC hyper-peritectic alloys is presented, a preferred group of low-carbon casting steel. The procedure incorporates a three-stage thin arm dissolution model, which is solved at each time step using Newton–Raphson iteration. This is coupled to a coarsening model based on the integral forms of the dissolution model, which are solved using Gaussian quadrature, as well as a growth model for solid fraction evolution. The procedure can easily be embedded into numerical models for solidification, in which the space–time evolution of the SDAS is required for determining the dynamic permeability in the mushy zone. Higher order approximations for both growth and solute concentration evolution can easily be incorporated. Temperature dependence of thermophysical parameters is taken into account using inter-dendritic solidification empirical models, and an alloy-specific peritectic reaction constant is used to determine the isothermal peritectic holding time. The procedure is validated against experimental data presented in literature. Various cases of SDAS as a function of local solidification time, cooling rate and carbon composition are investigated. The method is compared to experimental results of SDAS obtained from test castings of a hyper-peritectic steel alloy and can be used to iteratively determine the alloy-specific peritectic reaction constant by comparing the solid fraction evolution during the peritectic reaction with that found from the experimental cooling curve.

Assessing r2SCAN meta-GGA functional for structural parameters, cohesive energy, mechanical modulus, and thermophysical properties of 3d, 4d, and 5d transition metals.

The recent development of accurate and efficient semilocal density functionals on the third rung of Jacob's ladder of density functional theory, such as the revised regularized strongly constrained and appropriately normed (r2SCAN) density functional, could enable rapid and highly reliable prediction of the elasticity and temperature dependence of thermophysical parameters of refractory elements and their intermetallic compounds using the quasi-harmonic approximation (QHA). Here, we present a comparative evaluation of equilibrium cell volumes, cohesive energy, mechanical moduli, and thermophysical properties (Debye temperature and thermal expansion coefficient) for 22 transition metals using semilocal density functionals, including the local density approximation (LDA), Perdew-Burke-Ernzerhof (PBE) and PBEsol generalized gradient approximations (GGAs), and the r2SCAN meta-GGA. PBEsol and r2SCAN deliver the same level of accuracies for structural, mechanical, and thermophysical properties. PBE and r2SCAN perform better than LDA and PBEsol for calculating cohesive energies of transition metals. Among the tested density functionals, r2SCAN provides an overall well-balanced performance for reliably computing cell volumes, cohesive energies, mechanical properties, and thermophysical properties of various 3d, 4d, and 5d transition metals using QHA. Therefore, we recommend that r2SCAN could be employed as a workhorse method to evaluate thermophysical properties of transition metal compounds and alloys in high throughput workflows.

Determination of Temperature Dependence of Thermophysical Parameters in Solids: Numerical Solution of the Problem

Two approaches one presented to determine the thermophysical properties of materials. Necessary experimental data on thermal curves have been extracted by simulation modeling of the heat propagation process based on numerically solving the 1D thermal conductivity equation. The thermal conductivity and thermal diffusivity coefficients have been calculated independently using a method suggested in this study. Comparing our results with data from simulation modeling makes it possible to estimate the calculation accuracy. The suggested method provides a better qualitative and quantitative insight into the thermophysical properties of materials.

Adjoint problems of mechanics of continuous media in gas‐laser cutting of metals

A mathematical model of gas‐laser cutting of metal plates in an inert gas is proposed. The formation and flow of the liquid metal melt film at the cutting front is considered within the framework of incompressible boundary‐layer equations. Based on the resultant analytical solution, a local law of energy conservation on the cutting surface is derived, which takes into account the melt‐film thickness and the temperature dependence of thermophysical parameters of the metal. The problem of the cutting shape and depth is solved in the two‐dimensional formulation. A comparison with experimental data is made in terms of the cutting depth and maximum cutting velocity for carbon and alloy steel.