This study is focused on numerical modeling of evolution of ablated plume in laser furnace. The temperature of catalyst particles embedded in plume is crucial for the formation of carbon nanotubes from gaseous carbon. The proposed model includes compressible Euler equations combined with a multispecies formulation for concentration of chemical components describing the plume expansion into surrounding gas. To obtain the thermal behavior of catalyst particles the Eulerian solver has been combined with Lagrangian tracking of catalyst particles. The chamber pressure, geometry of the carbon target, plume emerging velocity, and the time interval between injections of the plume dramatically affect the thermal behavior of catalyst particles. The results of modeling have shown that the increase of plume injection velocity raises the temperature of particles but also increases the oscillations of particles temperature. The low chamber pressure helps to avoid temperature oscillations of catalyst particles because the plume moves far behind strong reflected shock waves; however, complex motion of particles at the vicinity of slip lines causes temperature oscillations. Whereas previous studies were focused on the evolution of a single plume, this study shows that the dynamics and thermal regime of multiple plumes are different from those of a single plume. NomenclatureC 1 , C 2 = mass concentration (mass fraction) of plume material and furnace gas c(x, t) = freezing speed in relaxing total variation diminishing scheme c ∞ = speed of sound in undisturbed furnace gas E = total energy per volume unit volume e = internal energy per unit mass F, G = components of flux vector h = total entalpy J = Jacobian L = furnace length M = Mach number p = pressure R = furnace radius R 1 , R 2 = gas constants of plume material and furnace gas (r, x) = two-dimensional cylindrical coordinates S = source term T = temperature t = time U, V = contravariant velocity components u, v = Cartesian velocity components W 1 , W 2 = characteristic variables γ = ratio of specific heats, 1.4 ρ = density ς, η = generalized curvilinear coordinates

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In this work, numerical solutions of the two-dimensional Navier-Stokes and Euler equations using explicit MacCormack method on multi-block structured mesh are presented for steady state and unsteady state compressible fluid flows. The multi-block technique and generalized coordinate system are used to develop a numerical solver which can be applied for a large range of compressible flow problems on complex geometries without modifying the governing equations and numerical method. Besides that the numerical method is based on a finite difference approach and the generalized coordinates introduced allow the application of the boundary conditions easily. The subsonic flow over a backward facing step and supersonic flow over a curved ramp are presented, and the results are compared with the experimental and numerical data.

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The finite element method (FEM) has become one of the most important and useful engineering tools for engineers and scientists in the last three decades. Finite element method is considered very powerful and efficient tool in solving partial differential equations. Seeking for exact solution of some engineering applications, such as fluid flow problems, is still a challenging task to overcome. Based on this, finite element method can be used to model such problems and it is possible to obtain solution near to the exact one. In the present study, FEM is employed to discretize the governing equations for a viscous incompressible fluid flow around a circular cylinder inside a 2D channel. The fluid flow is described by the Navier-Stokes equations. There are many methods to tackle these equations. However, minding computational speed the choice is for a simple method called Chorin's projection method for discretizing the Navier-Stokes equations. Results are presented for two different meshes and is shown that the elements density have some significant influence in the results. Also, there is an apparent effect on Cd and Cl calculation on the cylinder.

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he Thermomass theory is based on the relationship mass-energy of Einstein, i.e., the heat has mass-energy duality, behaving as energy in processes where its conversion occurs in another form of energy, and behaving as mass in heat transfer processes. The mathematical model stablished by the Thermomass model falls within the class of problems called models non-Fourier heat conduction. The present work aims to analyze the thermal responses provided by Thermomass theory of nanofilms submitted to a very fast heating process using two different heat sources (laser pulses). During the process of analysis, the equations are written in conservation law, put into dimensionless form and discretized in the way that a high-order TVD scheme is used on to provide accurate and reliable numerical simulations for obtaining the thermal responses predicted by the Thermomass model. The results show that the Thermomass theory predicted a heterogeneous temperature distribution with elevated temperature peaks. The thermal responses obtained from this model may prevent the thermal damage caused by technologies of the processing and manufacturing of elements based on high-power laser applications.