AI OPTIMIZATION OF THE EXOTHERMIC REACTION OF ETHYLENE OXIDE WITH WATER

2021 ◽  
pp. 2150033
Author(s):  
Khaled A. Al-Utaibi ◽  
Ayesha sohail ◽  
Andleeb Zafar ◽  
Rana Talha ◽  
Sadiq M. Sait
Keyword(s):  
Mathematical Model ◽  
Analytical Solution ◽  
Ethylene Oxide ◽  
Ethylene Glycol ◽  
Exothermic Reaction ◽  
Plug Flow ◽  
Material Balance ◽  
Chemical Species ◽  
Future Research ◽  
The Mathematical Model

A computational framework, for the numerical approximation of the exothermic reaction of ethylene oxide (EO) with water, to form ethylene glycol is presented in this paper. Ethylene Glycol also known as Mono-ethylene Glycol (MEG), is a diol with a boiling of 198[Formula: see text]C and conventionally produced through hydrolysis of ethylene oxide which is obtained through the oxidation of ethylene. It is used as an excellent automobile coolant as the 1:1 ratio mixture of MEG with Water boils at 129[Formula: see text]C and freezes at [Formula: see text]C. Other than its use as an antifreeze, it is also used as a reagent during the production of polyester fibers, pharmaceutics, cosmetics, hydraulic fluids, printing inks, explosives, polyesters and paint solvents. The mathematical model presented here, consists of an energy balance and a material balance system, described in an axisymmetric coordinate system. The optimized resulting values using the artificial intelligence approach are summarized in this paper. We derive an analytical solution. The analytical solution for the mathematical model equations is in general not possible for this model but it may be possible to derive an analytical solution to this mathematical model if we consider the equation for the conservation of material (chemical species) as a formulation for plug flow and isothermal conditions. Noteworthy findings are reported in this paper for future research.

scholarly journals Computer Simulation of the King's Cross Fire: Effect of Radiative Heat Transfer on Fire Spread

1991 ◽  
Vol 205 (3) ◽  
pp. 201-208 ◽  
Author(s):  
W M G Malalasekera ◽  
F Lockwood
Keyword(s):  
Mathematical Model ◽  
Radiative Heat ◽  
Health And Safety ◽  
Fire Spread ◽  
Future Research ◽  
Full Description ◽  
Department Of Health ◽  
Underground Fire ◽  
The Mathematical Model ◽  
Good Agreement

A mathematical model has been applied to simulate model experiments of the 1987 King's Cross underground fire by the Department of Health and Safety Executive. The predicted growth of the fire is compared with the experimental data and in particular the predicted and measured times to ‘flashover’ are compared. The comparisons show exceptional agreement which, in part, may be fortuitous due to the need to facilitate the prediction of the early stages of the growth with the aid of an experimentally estimated fire strength. The good agreement nonetheless is also due to the full description of the radiation transfer which is a feature of the mathematical model. It is concluded that the flashover phenomenon that occurred at King's Cross was thermal radiation driven and that future research should be devoted to modelling the details of fire spread across a combustible surface.

MATHEMATICAL MODELLING FOR FISH FEED FORMULATION OF MYSTUS NEMURUS SP. CATFISH: OPTIMIZING GROWTH AND NUTRIENTS REQUIREMENTS

2018 ◽  
Vol 80 (6) ◽  
Author(s):  
Nur Aidya Hanum Aizam ◽  
Rabiatul Adawiyah Ibrahim ◽  
Raphael Lee Kuok Lung ◽  
Pang Yen Ling ◽  
Aidilla Mubarak
Keyword(s):  
Mathematical Model ◽  
Nutrient Composition ◽  
Future Research ◽  
Fish Feed ◽  
Research Directions ◽  
Feed Formulation ◽  
Future Research Directions ◽  
The Cost ◽  
The Mathematical Model ◽  
Mystus Nemurus

This study integrates mathematical model in the plan of producing a fish feed formulation by reducing the total cost without neglecting the nutrient requirements. This study focuses on producing the perfect combination of fish feed for Mystus nemurus sp. catfish in different stages of life. The mathematical model developed will consider their required nutrients in each stage, the cost of each ingredient and the amount of nutrients to be consumed (nutrient composition of fish feed ingredients). This research employs AIMMS mathematical software to assist with the computation. The results from this study obtain a much better combination of different ingredients compared to available commercial pellets in terms of nutrient composition and production cost. The combinations yield much cheaper costs yet boosts up the nutrient consumptions, which is an eye-opener for independent local fish farmers. Thorough discussion on utilizing the results with future research directions will also be included.

scholarly journals A Mathematical Model of Epidemics—A Tutorial for Students

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1174 ◽  
Author(s):  
Yutaka Okabe ◽  
Akira Shudo
Keyword(s):  
Mathematical Model ◽  
Analytical Solution ◽  
Analytical Solutions ◽  
Sir Model ◽  
Exact Analytical Solutions ◽  
The Mathematical Model ◽  
Epidemic Diseases

This is a tutorial for the mathematical model of the spread of epidemic diseases. Beginning with the basic mathematics, we introduce the susceptible-infected-recovered (SIR) model. Subsequently, we present the numerical and exact analytical solutions of the SIR model. The analytical solution is emphasized. Additionally, we treat the generalization of the SIR model including births and natural deaths.

Torus-Like Balloons

2020 ◽  
Vol 56 ◽  
pp. 59-65
Author(s):  
Ivïalo M. Mladenov ◽  
Keyword(s):  
Mathematical Model ◽  
Analytical Solution ◽  
Elliptic Integrals ◽  
Deployable Structures ◽  
The Future ◽  
The Mathematical Model

The concepts for inflatable deployable structures have been under development and evaluation for many years. Strangely enough only the Mylar balloon up to now has been described adequately. Here we provide the mathematical model and its analytical solution for the torus-like balloons. Their characteristics and shapes are described explicitly in terms of elliptic integrals. The obtained results are commented shortly and the possible directions for the related studies in the future are outlined.

scholarly journals On the Sodium Concentration Diffusion with Three-Dimensional Extracellular Stimulation

2011 ◽  
Vol 2011 ◽  
pp. 1-19 ◽  
Author(s):  
Luisa Consiglieri ◽  
Ana Rute Domingos
Keyword(s):  
Mathematical Model ◽  
Boundary Condition ◽  
Analytical Solution ◽  
Parabolic Equations ◽  
Three Dimensional ◽  
Sodium Concentration ◽  
Dynamical Boundary Condition ◽  
Sodium Diffusion ◽  
The Mathematical Model ◽  
Concentration Diffusion

We deal with the transmembrane sodium diffusion in a nerve. We study a mathematical model of a nerve fibre in response to an imposed extracellular stimulus. The presented model is constituted by a diffusion-drift vectorial equation in a bidomain, that is, two parabolic equations defined in each of the intra- and extra-regions. This system of partial differential equations can be understood as a reduced three-dimensional Poisson-Nernst-Planck model of the sodium concentration. The representation of the membrane includes a jump boundary condition describing the mechanisms involved in the excitation-contraction couple. Our first novelty comes from this general dynamical boundary condition. The second one is the three-dimensional behaviour of the extracellular stimulus. An analytical solution to the mathematical model is proposed depending on the morphology of the excitation.

scholarly journals Analysis of the non-stationary mathematical model of a simple hydraulic network with a centrifugal pump

Vestnik IGEU ◽  
2020 ◽  
pp. 64-70
Author(s):  
V.A. Naumov
Keyword(s):  
Mathematical Model ◽  
Analytical Solution ◽  
Centrifugal Pump ◽  
Similarity Criteria ◽  
Dimensionless Form ◽  
Maximum Volume ◽  
Stationary Flows ◽  
Variable Level ◽  
Hydraulic Network ◽  
The Mathematical Model

Simple hydraulic networks with a centrifugal pump are not only part of complex networks, but are also widely used in Autonomous water supply and Sewerage systems. The mathematical model of simple networks taking into account the variable level of liquid in reservoirs includes the well-known Bernoulli equation for non-stationary flows. Published works on this problem do not take into account the non-stationary nature of the flow due to the variable liquid level. The conditions for using the quasi-stationary model are not discussed. Similarity criteria for the issue were not found. The purpose of the study is to analyze the non-stationary mathematical model of the object, including the definition of criteria for similarity of the problem and their impact on the solution. The well-known equations of fluid quantity balance and Bernoulli for non-stationary flows with smoothly changing characteristics were used as a mathematical model of a simple hydraulic network. The pressure characteristic of a centrifugal pump is approximated by a well-established dependence in the form of a square three-member. The system of differential equations was reduced to a dimensionless form. Analytical and numerical methods were used to solve the problem. The analysis of the mathematical model of pumping liquid by a centrifugal pump in a hydraulic network with a variable level was carried out. The dimensionless form of the system of equations allowed us to determine three similarity criteria for the problem, including the analog of the Struhal number Str. The analytical solution to the Cauchy problem is found in the quasi-stationary formulation (Str = 0). The solution of the problem in the full statement is obtained by the numerical method. The results of the study of the influence of similarity criteria on the solution are presented. The dimensionless flow rate of the liquid decreases with increasing Str values. In this case, the maximum volume of liquid and the time to reach it increases. Increasing the values of the other two criteria leads to an increase in both the flow rate and the maximum volume of the liquid. The analytical solution in the quasi-rational formulation can be used only for Str < 0,1. The results obtained can be used in the design of Autonomous Water supply and Sewerage systems. Further research for the non-self-similar area of hydraulic resistance and for variable fluid viscosity is promising.

scholarly journals Modelling and PID control system integration for quadcopter DJI F450 attitude stabilization

2020 ◽  
Vol 19 (3) ◽  
pp. 1235
Author(s):  
N. M. Salma ◽  
Khairuddin Osman
Keyword(s):  
Mathematical Model ◽  
Control System ◽  
Pid Control ◽  
System Integration ◽  
Analysis Data ◽  
Euler Method ◽  
Future Research ◽  
Simulink Simulation ◽  
Fast Development ◽  
The Mathematical Model

<p><span style="font-family: Times New Roman;">In this paper we focus on the overall overview of the mathematical modelling of the DJI F450 UAV quadcopter, the hardware and software system integration based on PID control system for the attitude feedback. The parameter specification of the DJI F450 is fed into the mathematical model and implement a basic PID for the system. Future research using the DJI F450 model can benefit from this observation by implementing the modelling and tune in their own variable that varies, such as the overall of their weight. The data of PID control system simulation using the quadcopter frame model type DJI F450 parameter. The mathematical model for the quadcopter modelled DJI F450 is developed using Newton-Euler method. Altitude data for the control system is obtain from the analysis data of the Simulink simulation. The simulation is done using the Simulink toolbox inside the MATLAB software. From this paper, we can more understand the step involves in making a full control system of a quadcopter. The mathematical model for other type of quadcopter model can be implemented using the steps with their own parameter and achieve fast development.</span></p>

scholarly journals Growth of N-dimensional spherical bubble within viscous, superheated liquid: Analytical solution

2019 ◽  
pp. 380-380
Author(s):  
Gamiel Shalaby ◽  
Ali Abu-Bakr
Keyword(s):  
Mathematical Model ◽  
Analytical Solution ◽  
Variable Viscosity ◽  
Superheated Liquid ◽  
Spherical Bubble ◽  
The Mathematical Model

In this paper, we present the study of the bevaiour of spherical bubble in N-dimensions fluid. The fluid is a mixture of vapour and superheated liquid. The mathematical model is formulated in N-dimensions fluid on the basis of continuity and momentum equations, and solved its analytically. The variable viscosity is taken in an account problem. The obtained results show that the radius of bubble increases with the decreasing of the value of N-dimensions.

Modelling of external filter cake profile along the well during drilling

2014 ◽  
Vol 54 (1) ◽  
pp. 319 ◽  
Author(s):  
Azim Kalantariasl ◽  
Abbas Zeinijahromi ◽  
Pavel Bedrikovetsky
Keyword(s):  
Mathematical Model ◽  
Velocity Profile ◽  
Filter Cake ◽  
Thickness Distribution ◽  
Material Balance ◽  
Force Balance ◽  
Predictive Tool ◽  
Physiochemical Properties ◽  
Cake Thickness ◽  
The Mathematical Model

This paper presents a new mathematical model to predict the steady-state external filter cake thickness distribution and velocity profile along the wellbore during overbalanced drilling. Several models have been suggested for the prediction of external cake thickness using the force balance method. Yet, a comprehensive literature survey reveals that electrostatic forces and the permeate force correction factor have been neglected, while both can significantly change the conditions of particle detachment from the cake surface. Torque balance of hydrodynamic (lifting, tangential and permeate drag), gravity and electrostatic (DLVO) forces along with Darcy’s law and material balance is used to investigate the conditions of particle attachment/detachment on the cake surface. The results show strong effects of mud chemistry, particle size, cake permeability, tangential flow velocity, overbalance pressure, and Young’s modulus on the external filter cake thickness and velocity profile. The mathematical model can be applied as a predictive tool for the estimation of filter cake thickness. It allows for the calculation of external filter cake distribution using the physiochemical properties of mud and particles.

A feedback temperature control in a chemical reactor with high inertia of its cooling system

1984 ◽  
Vol 49 (7) ◽  
pp. 1642-1652 ◽  
Author(s):  
Josef Horák ◽  
František Jiráček ◽  
Libuše Ježová
Keyword(s):  
Mathematical Model ◽  
Temperature Control ◽  
Cooling System ◽  
Batch Reactor ◽  
Time Derivative ◽  
Exothermic Reaction ◽  
Chemical Reactor ◽  
The One ◽  
The Mathematical Model ◽  
The Given

In this work we compare simple algorithms for the one-off feedback temperature control of the reaction mixture in a batch reactor during an exothermic reaction. The aim of the control was to maintain the temperature of the mixture within the given range, and simultaneously, to minimize the number of the regulator switchings. The temperature control of the mixture was being performed at conditions when working states of the reactor in an open regulation loop are unstable and when the response of the cooler to regulation is slow. The following control algorithms were compared: P - regulator, PD - regulator and algorithms based on a prediction mathematical model including its adaptive variant. The results indicate that the algorithms based on the mathematical model are more efficient. However, the precision of the control can be diminished due to error in the time derivative of the temperature of the reaction mixture which forms the input to the prediction model. The adaptive variant of the algorithms was advantageous in cases when it was necessary to make up for significant errors in initial estimates of parameters of the prediction mathematical model.

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