Discovering governing equations via moving horizon learning: the case of reacting systems

AIChE Journal ◽  
2022 ◽  
Author(s):  
Fernando Lejarza ◽  
Michael Baldea
Keyword(s):  
Governing Equations ◽  
Reacting Systems

On Local and Global Species Conservation Errors for Nonlinear Ecological Models and Chemical Reacting Flows

2015 ◽  
Author(s):  
M. K. Mudunuru ◽  
M. Shabouei ◽  
K. B. Nakshatrala
Keyword(s):  
Numerical Solutions ◽  
Species Conservation ◽  
Chemical Species ◽  
Chemical Kinetic ◽  
Benchmark Problems ◽  
Governing Equations ◽  
Non Linear ◽  
Chemically Reacting Systems ◽  
Oscillatory Chemical ◽  
Reacting Systems

Advection-controlled and diffusion-controlled oscillatory chemical reactions appear in various areas of life sciences, hydrogeological systems, and contaminant transport. In this conference paper, we analyze whether the existing numerical formulations and commercial packages provide physically meaningful values for concentration of the chemical species for two popular oscillatory chemical kinetic schemes. The first one corresponds to the chlorine dioxide-iodine-malonic acid reaction while the second one is a simplified version of Belousov-Zhabotinsky reaction of a non-linear chemical oscillator. The governing equations for species balance are presented based on the theory of interacting continua. This results in a set of coupled non-linear partial differential equations. Obtaining analytical solutions is not practically viable. Moreover, it is well-known in literature that if the local dynamics becomes complex, the range of possible dynamic behavior in the presence of diffusion and advection becomes practically unlimited. We resort to numerical solutions, which are obtained using two popular stabilized formulations: Streamline Upwind/Petrov Galerkin and Galerkin/Least Squares. In order to make the computational analysis tractable, an estimate on the range of system-dependent parameters is obtained based on model reduction performed on the strong-form of the governing equations. Finally, we quantify the errors in satisfying the local and global species balance for various realistic benchmark problems. Through these representative numerical examples, we shall demonstrate the need and importance of developing locally conservative non-negative numerical formulations for chaotic and oscillatory chemically reacting systems.

Unsteady MHD Free Convective Heat and Mass Transfer Flow Past a Vertical Porous Plate in the Presence of Radiation and Chemical Reaction

2017 ◽  
Vol 6 (10) ◽  
pp. 116
Author(s):  
J. Buggaramulu ◽  
M. Venkatakrishna ◽  
Y. Harikrishna
Keyword(s):  
Mass Transfer ◽  
Heat And Mass Transfer ◽  
Convective Heat ◽  
Chemical Reaction ◽  
Porous Plate ◽  
Physical Parameters ◽  
Governing Equations ◽  
Vertical Porous Plate ◽  
Flow Past ◽  
Transfer Flow

The objective of this paper is to analyze an unsteady MHD free convective heat and mass transfer boundary flow past a semi-infinite vertical porous plate immersed in a porous medium with radiation and chemical reaction. The governing equations of the flow field are solved numerical a two term perturbation method. The effects of the various parameters on the velocity, temperature and concentration profiles are presented graphically and values of skin-frication coefficient, Nusselt number and Sherwood number for various values of physical parameters are presented through tables.

Propagation and Reflection of Plane Waves in a Rotating Magneto-Elastic Fibre-Reinforced Semi Space with Surface Stress

2020 ◽  
Vol 22 (4) ◽  
pp. 939-958
Author(s):  
Indrajit Roy ◽  
D. P. Acharya ◽  
Sourav Acharya
Keyword(s):  
Surface Stress ◽  
Incident Angle ◽  
Plane Waves ◽  
Three Dimensional ◽  
Elastic Fibre ◽  
Amplitude Ratios ◽  
Governing Equations ◽  
Rotation Surface ◽  
Wave Velocities ◽  
Magnetic Field Rotation

AbstractThe present paper investigates the propagation of quasi longitudinal (qLD) and quasi transverse (qTD) waves in a magneto elastic fibre-reinforced rotating semi-infinite medium. Reflections of waves from the flat boundary with surface stress have been studied in details. The governing equations have been used to obtain the polynomial characteristic equation from which qLD and qTD wave velocities are found. It is observed that both the wave velocities depend upon the incident angle. After imposing the appropriate boundary conditions including surface stress the resultant amplitude ratios for the total displacements have been obtained. Numerically simulated results have been depicted graphically by displaying two and three dimensional graphs to highlight the influence of magnetic field, rotation, surface stress and fibre-reinforcing nature of the material medium on the propagation and reflection of plane waves.

On the Influence of Fluctuating Flow Rate Upon the Performance and Behaviour of Isothermal Reacting Systems

1998 ◽  
Vol 63 (6) ◽  
pp. 881-898
Author(s):  
Otakar Trnka ◽  
Miloslav Hartman
Keyword(s):  
Flow Rate ◽  
Gas Flow ◽  
Fluidized Bed Reactor ◽  
Computational Techniques ◽  
Continuous Stirred Tank Reactor ◽  
Gas Flow Rate ◽  
Solid Reaction ◽  
Continuous Stirred Tank ◽  
And Performance ◽  
Reacting Systems

Three simple computational techniques are proposed and employed to demonstrate the effect of fluctuating flow rate of feed on the behaviour and performance of an isothermal, continuous stirred tank reactor (CSTR). A fluidized bed reactor (FBR), in which a non-catalytic gas-solid reaction occurs, is also considered. The influence of amplitude and frequency of gas flow rate fluctuations on reactant concentrations at the exit of the CSTR is shown in four different situations.

scholarly journals A New Analytical Approach for Nonlinear Global Buckling of Spiral Corrugated FG-CNTRC Cylindrical Shells Subjected to Radial Loads

2020 ◽  
Vol 10 (7) ◽  
pp. 2600
Author(s):  
Tho Hung Vu ◽  
Hoai Nam Vu ◽  
Thuy Dong Dang ◽  
Ngoc Ly Le ◽  
Thi Thanh Xuan Nguyen ◽  
...  
Keyword(s):  
Analytical Approach ◽  
Cylindrical Shells ◽  
Equation System ◽  
Functionally Graded ◽  
Governing Equations ◽  
Reinforced Composite ◽  
Global Buckling ◽  
Homogenization Model ◽  
Corrugated Structure ◽  
The Galerkin Method

The present paper deals with a new analytical approach of nonlinear global buckling of spiral corrugated functionally graded carbon nanotube reinforced composite (FG-CNTRC) cylindrical shells subjected to radial loads. The equilibrium equation system is formulated by using the Donnell shell theory with the von Karman’s nonlinearity and an improved homogenization model for spiral corrugated structure. The obtained governing equations can be used to research the nonlinear postbuckling of mentioned above structures. By using the Galerkin method and a three term solution of deflection, an approximated analytical solution for the nonlinear stability problem of cylindrical shells is performed. The linear critical buckling loads and postbuckling strength of shells under radial loads are numerically investigated. Effectiveness of spiral corrugation in enhancing the global stability of spiral corrugated FG-CNTRC cylindrical shells is investigated.

scholarly journals Latent Heat Phase Change Heat Transfer of a Nanoliquid with Nano–Encapsulated Phase Change Materials in a Wavy-Wall Enclosure with an Active Rotating Cylinder

2021 ◽  
Vol 13 (5) ◽  
pp. 2590
Author(s):  
S. A. M. Mehryan ◽  
Kaamran Raahemifar ◽  
Leila Sasani Gargari ◽  
Ahmad Hajjar ◽  
Mohamad El Kadri ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Energy Storage ◽  
Phase Change ◽  
Latent Heat ◽  
Thermal Energy ◽  
Thermal Energy Storage ◽  
Wavy Wall ◽  
Governing Equations ◽  
Stefan Number ◽  
Change Material

A Nano-Encapsulated Phase-Change Material (NEPCM) suspension is made of nanoparticles containing a Phase Change Material in their core and dispersed in a fluid. These particles can contribute to thermal energy storage and heat transfer by their latent heat of phase change as moving with the host fluid. Thus, such novel nanoliquids are promising for applications in waste heat recovery and thermal energy storage systems. In the present research, the mixed convection of NEPCM suspensions was addressed in a wavy wall cavity containing a rotating solid cylinder. As the nanoparticles move with the liquid, they undergo a phase change and transfer the latent heat. The phase change of nanoparticles was considered as temperature-dependent heat capacity. The governing equations of mass, momentum, and energy conservation were presented as partial differential equations. Then, the governing equations were converted to a non-dimensional form to generalize the solution, and solved by the finite element method. The influence of control parameters such as volume concentration of nanoparticles, fusion temperature of nanoparticles, Stefan number, wall undulations number, and as well as the cylinder size, angular rotation, and thermal conductivities was addressed on the heat transfer in the enclosure. The wall undulation number induces a remarkable change in the Nusselt number. There are optimum fusion temperatures for nanoparticles, which could maximize the heat transfer rate. The increase of the latent heat of nanoparticles (a decline of Stefan number) boosts the heat transfer advantage of employing the phase change particles.

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