Thermoplastic Composites: Modelling Melting, Decomposition and Combustion of Matrix Polymers

In thermoplastic composites, the polymeric matrix upon exposure to heat may melt, decompose and deform prior to burning, as opposed to the char-forming matrices of thermoset composites, which retain their shape until reaching a temperature at which decomposition and ignition occur. In this work, a theoretical and numerical heat transfer model to simulate temperature variations during the melting, decomposition and early stages of burning of commonly used thermoplastic matrices is proposed. The scenario includes exposing polymeric slabs to one-sided radiant heat in a cone calorimeter with heat fluxes ranging from 15 to 35 kW/m2. A one-dimensional finite difference method based on the Stefan approach involving phase-changing and moving boundary conditions was developed by considering convective and radiative heat transfer at the exposed side of the polymer samples. The polymers chosen to experimentally validate the simulated results included polypropylene (PP), polyester (PET), and polyamide 6 (PA6). The predicted results match well with the experimental results.

The Solvability of Mixed Value Problem for the First and Second Approximations of One-Dimensional Nonlinear System of Moment Equations with Microscopic Boundary Conditions

The paper gives a derivation of a new one-dimensional non-stationary nonlinear system of moment equations, that depend on the flight velocity and the surface temperature of an aircraft. Maxwell microscopic condition is approximated for the distribution function on moving boundary, when one fraction of molecules reflected from the surface specular and another fraction diffusely with Maxwell distribution. Moreover, macroscopic boundary conditions for the moment system of equations depend on evenness or oddness of approximation $${f}_{k}(t,x,c)$$ f k ( t , x , c ) , where $${f}_{k}(t,x,c)$$ f k ( t , x , c ) is partial expansion sum of the molecules distribution function over eigenfunctions of linearized collision operator around local Maxwell distribution. The formulation of initial and boundary value problem for the system of moment equations in the first and second approximations is described. Existence and uniqueness of the solution for the above-mentioned problem using macroscopic boundary conditions in the space of functions $$C\left(\left[0,T\right];{L}^{2}\left[-a,a\right]\right)$$ C 0 , T ; L 2 - a , a are proved.

Nonlinear Moving Boundary Model of Low-Permeability Reservoir

At present, there are two main methods for solving oil and gas seepage equations: analytical and numerical methods. In most cases, it is difficult to find the analytical solution, and the numerical solution process is complex with limited accuracy. Based on the mass conservation equation and the steady-state sequential substitution method, the moving boundary nonlinear equations of radial flow under different outer boundary conditions are derived. The quasi-Newton method is used to solve the nonlinear equations. The solutions of the nonlinear equations with an infinite outer boundary, constant pressure outer boundary and closed outer boundary are compared with the analytical solutions. The calculation results show that it is reliable to solve the oil-gas seepage equation with the moving boundary nonlinear equation. To deal with the difficulty in solving analytical solutions for low-permeability reservoirs and numerical solutions of moving boundaries, a quasi-linear model and a nonlinear moving boundary model were proposed based on the characteristics of low-permeability reservoirs. The production decline curve chart of the quasi-linear model and the recovery factor calculation chart were drawn, and the sweep radius calculation formula was also established. The research results can provide a theoretical reference for the policy-making of development technology in low-permeability reservoirs.

Heat and mass transfer in non-coaxial rotation of radiative MHD Casson carbon nanofluid flow past a porous medium

The heat and mass transfer of a radiative Casson nanofluid with single-wall and multi-wall carbon nanotubes in a non-coaxial rotating frame is analyzed in this article. The effects of thermal radiation, magnetic field and porosity are considered. Casson human blood is used to suspend both types of carbon nanotubes. The governed dimensional momentum, energy and concentration equations associated with initial and moving boundary conditions are converted into dimensionless expression by applying appropriate dimensionless variables. The exact solutions are determined by solving the dimensionless governing partial differential equations using the Laplace transform method. The obtained solutions are verified by comparing the present results with the published results. The validity of the solutions is assured since a precise agreement between the results is accomplished. The variation of the skin friction, Nusselt number, and Sherwood number for various values of the embedded parameters are presented in tables. The impacts of embedded parameters on the velocity, temperature and concentration profiles are illustrated in graphs. The distribution of the velocity and temperature is enhanced by the nanoparticles volume fraction but a reverse effect is observed for concentration profile. The radiation parameter has amplified the velocity and temperature of the Casson nanofluid. The emergence of porosity effect has aided to the smoothness of fluid flow but the presence of magnetic field reports the opposite effect on the velocity.

A Multigrid Dynamic Bidirectional Coupled Surface Flow Routing Model for Flood Simulation

Surface flow routing is an important component in hydrologic and hydrodynamic research. Based on a literature review and comparing the different coupling models (the hydrologic model and hydrodynamic model), a multigrid dynamic bidirectional coupled surface flow routing model (M-DBCM), consisting of diffusion wave equations (DWEs) and shallow water equations (SWEs), is proposed herein based on grids with different resolutions. DWEs were applied to obtain runoff routing in coarse grid regions to improve the computational efficiency, while the DWEs and SWEs were bidirectionally coupled to detail the flood dynamics in fine grid regions to obtain good accuracy. In fine grid zones, the DWEs and SWEs were connected by an internal moving boundary, which ensured the conservation of mass and momentum through the internal moving boundary. The DWEs and SWEs were solved by using the time explicit scheme, and different time steps were adopted in regions with different grid sizes. The proposed M-DBCM was validated via three cases, and the results showed that the M-DBCM can effectively simulate the process of surface flow routing, which had reliable computational efficiency while maintaining satisfactory simulation accuracy. The rainfall runoff in the Goodwin Creek Watershed was simulated based on the proposed M-DBCM. The results showed that the discharge hydrographs simulated by the M-DBCM were closer to the measured data, and the simulation results were more realistic and reliable, which will be useful in assisting flood mitigation and management.