Applications of Numerical Simulation of Solar Cooker Type Box With Multi-Step Inner Reflector

Solar Energy ◽  
2003 ◽  
Author(s):  
H. Terre´s-Pen˜a ◽  
P. Quinto-Diez
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Numerical Methods ◽  
Thermal Conversion ◽  
Numerical Results ◽  
Kutta Method ◽  
Runge Kutta Method ◽  
Energetic Analysis ◽  
The Mathematical Model ◽  
Solar Rays

It is shown a mathematical model of a solar box cooker with multi-step inner reflector and the numerical results for two applications has been analyzed. These applications are 1. Numerical simulation of operation of solar box cooker with multi-step inner reflector in Tanta, Egypt and 2. Numerical simulation of solar box cooker with multi-step inner reflector for 10 hours of operation. In the case 1, is analyzed a solar box cooker constructed and evaluated in Tanta, Egypt [1]. The experimental results that was obtained are compared with the numerical results that was obtained for the mathematical model. The case 2, is an evaluation of numerical results that was obtained for the operation of 10 hours for solar box cooker constructed in the Laboratorio de Ingenieri´a Te´rmica e Hidra´ulica Aplicada (LABINTHAP) in Me´xico City. [4] The solar box cooker is integrated by a covert that was made with double glass, this is use with two purposes, reduce the loss heat convection with outer and to generated the greenhouse effect with inner of cooker. In the inner of cooker there are a mirrors arrangement in inclined position (inner reflectors) placed in angles of 30°, 45° and 75°, these helped to reflex the solar rays in direction to the cook recipient. The recipient also received the solar rays in the upper part (lid). The mathematical model that was obtained from energetic analysis, is formed for five differential equations system no linear and the fourth Runge-Kutta method is used to resolve it. The numerical solution of the equations system is obtained with a computational software in C++. This work is a contribution to the application of numerical methods and computational for development of the solar energy used in thermal conversion equipments. The use of these techniques to solve the mathematical model is important to contribute in the evaluation and design of solar box cookers with multi-step inner reflector.

Enhancement the Solar Still Performance Using Chimney Exhaust Gases

2021 ◽  
Author(s):  
Hamdy Hassan
Keyword(s):  
Mathematical Model ◽  
Theoretical Study ◽  
Saline Water ◽  
Kutta Method ◽  
Solar Still ◽  
Climate Conditions ◽  
Exhaust Gases ◽  
Runge Kutta Method ◽  
The Impact ◽  
The Mathematical Model

Abstract In this paper, a theoretical study is presented on enhancement of the solar still performance by using the exhaust gases passing inside a chimney under the still basin. The impact of the exhaust gases temperature on the solar still temperature, productivity, and efficiency are considered. The performance of solar still with chimney is compared with that of conventional solar still. The study is carried out under the hot and climate conditions of Upper Egypt. A complete transient mathematical model of the physical model including the solar still regions temperatures, productivity, and heat transfer between the solar still and the exhaust gases are constructed. The mathematical model is solved numerically by using fourth-order Runge-Kutta method and is programmed by using MATLAB. The mathematical model is validated using an experimental work. The results show that the solar still saline water temperature increases and productivity with using and rising the exhaust gases. Furthermore, the impact of using exhaust gases on the still performance in winter is greater than in summer. using chimney exhaust gases at 75 °C and 125 °C enhances the daily freshwater yield of the conventional still by more than three times and about six times in winter, respectively, and about two and half times and more than three times in summer, respectively.

scholarly journals Analisis Kontrol Optimal Pada Model Matematika Penyebaran Pengguna Narkoba Dengan Faktor Edukasi

2020 ◽  
Vol 17 (2) ◽  
pp. 238-248
Author(s):  
Resmawan ◽  
M Eka ◽  
Nurwan ◽  
N Achmad
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Optimal Control ◽  
Drug Users ◽  
Minimum Principle ◽  
Runge Kutta Method ◽  
Runge Kutta ◽  
Model Drug ◽  
And Control ◽  
The Mathematical Model

ABSTRACT This paper discusses the mathematical model of drug users with education. Optimal control theory was used on this model with education as a control to achieve the goal of minimizing the number of drug users. The optimal control problem was analyzed using Pontryagin’s minimum principle and performed numerical simulation by using a 4th-order Runge-Kutta method. Based on the numerical simulation, there was a change in the number in each population which caused the population with education to increase, and control with education resulted in the reduced number of drug users. Keywords: Optimal control; mathematical model; drug users; education   ABSTRAK Artikel ini membahas tentang model matematika penyebaran pengguna narkoba dengan faktor edukasi. Teori kontrol optimal diterapkan pada model ini dengan pemberian kontrol berupa edukasi dengan tujuan untuk meminimumkan jumlah pengguna narkoba. Kontrol optimal dianalisis menggunakan Prinsip Minimum Pontryagin dan dilakukan simulasi numerik dengan menggunakan metode Runge-Kutta orde 4. Berdasarkan simulasi diperoleh bahwa terjadi perubahan jumlah di tiap populasi dan mengakibatkan jumlah populasi dengan edukasi bertambah, serta pemberian kontrol dengan edukasi mengakibatkan jumlah pengguna narkoba berkurang. Kata kunci       : Kontrol optimal; model matematika; pengguna narkoba; edukasi

Research on Numerical Simulation of Quad Bundle Conductor on Galloping

2013 ◽  
Vol 457-458 ◽  
pp. 23-27
Author(s):  
Xue Ping Zhan ◽  
Kuan Jun Zhu ◽  
Cao Lan Liu ◽  
Bin Liu ◽  
Jun Zhang ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Finite Element Method ◽  
Finite Element ◽  
Numerical Results ◽  
Kutta Method ◽  
Aerodynamic Parameter ◽  
Runge Kutta Method ◽  
Simulation Results ◽  
Runge Kutta ◽  
Element Method

The models of the multi-bundled conductors are constructed by finite element method in this paper. The numerical results are given by using the 4th order Runge-Kutta method considering aerodynamic parameter of sub-conductor. The simulation results are obtained on galloping of quad bundle conductors with the different span. Thus some effective numerical results of quad twin bundle conductor can provide a useful reference for anti-galloping design.

scholarly journals Comparison of Numerical Simulation of Epidemiological Model between Euler Method with 4th Order Runge Kutta Method

2021 ◽  
Vol 2 (1) ◽  
pp. 37-44
Author(s):  
Rizky Ashgi
Keyword(s):  
Numerical Simulation ◽  
Numerical Methods ◽  
Sir Model ◽  
Euler Method ◽  
Kutta Method ◽  
System Of Differential Equations ◽  
Runge Kutta Method ◽  
Global Pandemic ◽  
The World ◽  
Runge Kutta

Coronavirus Disease 2019 has become global pandemic in the world. Since its appearance, many researchers in world try to understand the disease, including mathematics researchers. In mathematics, many approaches are developed to study the disease. One of them is to understand the spreading of the disease by constructing an epidemiology model. In this approach, a system of differential equations is formed to understand the spread of the disease from a population. This is achieved by using the SIR model to solve the system, two numerical methods are used, namely Euler Method and 4th order Runge-Kutta. In this paper, we study the performance and comparison of both methods in solving the model. The result in this paper that in the running process of solving it turns out that using the euler method is faster than using the 4th order Runge-Kutta method and the differences of solutions between the two methods are large.

scholarly journals A numerical solution by alternative Legendre polynomials on a model for novel coronavirus (COVID-19)

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Elham Hashemizadeh ◽  
Mohammad Ali Ebadi
Keyword(s):  
Mathematical Model ◽  
Numerical Solution ◽  
Legendre Polynomials ◽  
Algebraic System ◽  
The Novel ◽  
Kutta Method ◽  
System Of Differential Equations ◽  
Runge Kutta Method ◽  
Novel Coronavirus ◽  
The Mathematical Model

Abstract Coronavirus disease (COVID-19) is an infectious disease caused by a newly discovered coronavirus. This paper provides a numerical solution for the mathematical model of the novel coronavirus by the application of alternative Legendre polynomials to find the transmissibility of COVID-19. The mathematical model of the present problem is a system of differential equations. The goal is to convert this system to an algebraic system by use of the useful property of alternative Legendre polynomials and collocation method that can be solved easily. We compare the results of this method with those of the Runge–Kutta method to show the efficiency of the proposed method.

Numerical Study of the Dynamics of Particles Motion with Different Sizes from Coal-Based Thermal Power Plant

2019 ◽  
Vol 20 (2) ◽  
pp. 223-241 ◽  
Author(s):  
Alibek Issakhov ◽  
Ruslan Bulgakov ◽  
Yeldos Zhandaulet
Keyword(s):  
Experimental Data ◽  
Numerical Simulation ◽  
Mathematical Model ◽  
Power Plant ◽  
Thermal Power Plant ◽  
Thermal Power ◽  
Numerical Results ◽  
Simulation Results ◽  
Turbulent Models ◽  
The Mathematical Model

AbstractIn this paper, the propagation of particles with different sizes from a coal-based thermal power plant was investigated. It was found that the deterioration of the environment is due to the release of a large amount of SOx, NOx and the volatile particles of Suspended Particulate Matter and Respirable Suspended Particles matter, which cause human and animal diseases. This paper presents the numerical simulation results of air pollution by particles which having different sizes from thermal power plants in real sizes using a 3D model. For the adequacy of the mathematical model, a test problem was solved using different turbulent models. To assess the applicability of the mathematical model, the numerical algorithm and the choice of the optimal turbulent model, experimental data and numerical results of other authors were used. The obtained numerical simulation results are in good agreement with the experimental results and the numerical results of other authors. And to obtain more accurate numerical results for the experimental data for turbulent models ($k - \varepsilon $,$k - \omega $), there were certain corresponding boundary conditions for kinetic energy. Also, profiles of all flow characteristics were compared with and without particles and some effects of the particle on the flow were identified.

Glycemia monitoring

1998 ◽  
Vol 2 ◽  
pp. 23-30
Author(s):  
Igor Basov ◽  
Donatas Švitra
Keyword(s):  
Diabetes Mellitus ◽  
Mathematical Model ◽  
Numerical Methods ◽  
Differential Equations ◽  
Blood Sugar ◽  
Self Regulation ◽  
Physiological System ◽  
Non Linear ◽  
The Mathematical Model

Here a system of two non-linear difference-differential equations, which is mathematical model of self-regulation of the sugar level in blood, is investigated. The analysis carried out by qualitative and numerical methods allows us to conclude that the mathematical model explains the functioning of the physiological system "insulin-blood sugar" in both normal and pathological cases, i.e. diabetes mellitus and hyperinsulinism.

MATHEMATICAL ANALYSIS OF THE ENDEMIC EQUILIBRIUM OF MALARIAHYGIENE MODEL

2021 ◽  
Vol 5 (10) ◽  
Author(s):  
Oluwafemi Temidayo J. ◽  
Azuaba E. ◽  
Lasisi N. O.
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
Equilibrium Point ◽  
Reproduction Number ◽  
Endemic Equilibrium ◽  
The Mathematical Model ◽  
Globally Stable ◽  
Well Posed ◽  
The Basic Reproduction Number ◽  
Invariant Principle

In this study, we analyzed the endemic equilibrium point of a malaria-hygiene mathematical model. We prove that the mathematical model is biological and meaningfully well-posed. We also compute the basic reproduction number using the next generation method. Stability analysis of the endemic equilibrium point show that the point is locally stable if reproduction number is greater that unity and globally stable by the Lasalle’s invariant principle. Numerical simulation to show the dynamics of the compartment at various hygiene rate was carried out.

Numerical Simulation of Subsea Cluster Manifold Installation by the Sheave Method

2018 ◽  
Author(s):  
Yu Zhao ◽  
Yingying Wang ◽  
Liwei Li ◽  
Chao Yang ◽  
Yang Du ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Mathematical Model ◽  
South China Sea ◽  
Deep Sea ◽  
High Reliability ◽  
Two Dimensional ◽  
Complex Environment ◽  
Lumped Mass ◽  
Lumped Mass Method ◽  
The Mathematical Model

The sheave installation method (SIM) is an effective and non-conventional method to solve the installation of subsea equipment in deep water (>1000m), which has been developed to deploy the 175t Roncador Manifold I into 1,885 meters water depth in 2002. With the weight increment of subsea cluster manifold, how to solve its installation with the high reliability in the deep sea is still a great challenge. In this paper, the installation of the 300t subsea cluster manifold using the SIM is studied in the two-dimensional coordinate system. The mathematical model is established and the lumped mass method is used to calculate the hydrodynamic forces of the wireropes. Taking into account the complex environment loads, the numerical simulation of the lowering process is carried out by OrcaFlex. The displacement and vibration of the subsea cluster manifold in the z-axis direction and the effective tension at the top of the wireropes can be gotten, which can provide guidance for the installation of the cluster manifold in the South China Sea.

scholarly journals Population Behavior in the Mathematical Model of the Spread of COVID19 Type SEIRS

2021 ◽  
Vol 6 (2) ◽  
pp. 83-88
Author(s):  
Asmaidi As Med ◽  
Resky Rusnanda
Keyword(s):  
Mathematical Modeling ◽  
Numerical Simulation ◽  
Mathematical Model ◽  
Everyday Life ◽  
Applied Mathematics ◽  
Living Things ◽  
Simulation Results ◽  
Parameter Values ◽  
The Mathematical Model ◽  
Disease Free

Mathematical modeling utilized to simplify real phenomena that occur in everyday life. Mathematical modeling is popular to modeling the case of the spread of disease in an area, the growth of living things, and social behavior in everyday life and so on. This type of research is included in the study of theoretical and applied mathematics. The research steps carried out include 1) constructing a mathematical model type SEIRS, 2) analysis on the SEIRS type mathematical model by using parameter values for conditions 1and , 3) Numerical simulation to see the behavior of the population in the model, and 4) to conclude the results of the numerical simulation of the SEIRS type mathematical model. The simulation results show that the model stabilized in disease free quilibrium for the condition  and stabilized in endemic equilibrium for the condition .

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