scholarly journals Numerical study of a modified Trombe wall solar collector system

2009 ◽  
Vol 13 (1) ◽  
pp. 195-204 ◽  
Author(s):  
Snezana Dragicevic ◽  
Miroslav Lambic
Keyword(s):  
Mathematical Model ◽  
Numerical Study ◽  
Operational Parameters ◽  
Collector System ◽  
Fast Running ◽  
Simulation Techniques ◽  
Solar Radiation Intensity ◽  
Trombe Wall ◽  
Solar Wall ◽  
The Mathematical Model

The paper presents numerical analysis of efficiency of the modified Trombe wall with forced convection. The analyzed system comprises a double glass glazing, and a massive wall with opening and central channel in it. In order to increase the efficiency, a fan is provided at the bottom vent of the wall. It is more advanced as compared with simple Trombe solar wall with a relatively low thermal resistance, which is taken as a reference in experimental analysis. The mathematical model, composed for the massive solar wall efficiency, is usually very complicated and assessment of the thermal behavior requires the use of thermal simulation techniques. This paper presents steady-state and one-dimensional mathematical model for simplified analysis of thermal efficiency of modified Trombe solar wall. The results from presented model were analyzed to predict the effects of variations in the operational parameters on the solar wall efficiency: solar radiation intensity, air velocity in the entrance duct, and room air temperature. The results have been compared with the available experimental study, and the comparison has shown satisfactory agreement. The obtained results have be used for simple and fast running design tools that designers can use in the early phases of the design process for approximate calculations of efficiency of the passive solar heating systems.

Theoretical Study on Thermal Performance of Trombe Wall Combined with Solar Air Collector

2012 ◽  
Vol 512-515 ◽  
pp. 208-213
Author(s):  
Yu Bie ◽  
Fang Zhou ◽  
Ming Fu Hu ◽  
Qian Peng ◽  
Wen Yuan Mao ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Thermal Performance ◽  
Air Flow ◽  
Flow Channel ◽  
C Programming ◽  
Solar Air Collector ◽  
Trombe Wall ◽  
Collecting Efficiency ◽  
Solar Wall ◽  
The Mathematical Model

A thermal performance mathematical model of Trombe wall combined with solar air collector was established on the base of thermodynamics and fluid dynamics analysis. Then we solved the mathematical model by means of calculating program based on C programming language. The calculating results show the influence law of the area ratio of air opening to air flow channel (Ao/Af ) and the thickness of air flow channel affected on the heat collecting efficiency of solar wall. With the increasing of Ao/Af , the efficiency increases firstly, then increases more slowly, and finally comes to steady. The thickness also affects the efficiency in the same way. Though the results still need a further validation by experiments, they are initially proved correct by the qualitative analysis. The theoretical model can be a tool for the structural optimization of the Trombe wall combined with solar air collector.

scholarly journals A mathematical model of common-cold epidemics on Tristan da Cunha

1971 ◽  
Vol 69 (3) ◽  
pp. 423-433 ◽  
Author(s):  
B. J. Hammond ◽  
D. A. J. Tyrrell
Keyword(s):  
Mathematical Model ◽  
Common Cold ◽  
Average Duration ◽  
Model Parameters ◽  
Epidemic Threshold ◽  
Tristan Da Cunha ◽  
Simulation Techniques ◽  
Time Courses ◽  
The Mathematical Model ◽  
Computer Simulation Techniques

SUMMARYRecords of seven common-cold outbreaks on the island of Tristan da Cunha are compared with the corresponding time courses given by the mathematical model of Kermack & McKendrick (1927) and with an alternative model that directly involves a constant average duration of individual infection. Using computer simulation techniques the latter model is shown to be preferred and is then closely matched to the field data to obtain values for the model parameters. Consideration is then given to the intensity of epidemics predicted by the model and to the distribution of the actual epidemics relative to the theoretical epidemic threshold.

Wind Energy Conversion: The Potential of a Novel Ducted Turbine for Residential and Commercial Applications

2013 ◽  
Author(s):  
N. Goudarzi ◽  
W. D. Zhu ◽  
H. Bahari
Keyword(s):  
Mathematical Model ◽  
Wind Power ◽  
Flow Behavior ◽  
Experimental Tests ◽  
Simulation Techniques ◽  
Ducted Turbine ◽  
Grid Applications ◽  
Commercial Applications ◽  
Four Quadrant ◽  
The Mathematical Model

A novel ducted turbine, referred to as a Wind Tower, for capturing wind power in either residential or commercial scale applications is studied theoretically and experimentally. A mathematical model is developed to predict the flow behavior inside the tower and a velocity coefficient is defined to correct the results at different test conditions. A wind tower prototype, including a four-quadrant-peak wind-catcher rooftop, a tower, a nozzle, and a turbine, is designed and fabricated. The captured wind power values from the mathematical model and the preliminary experimental tests are compared. While the mathematical model provides a good estimation of the output power in some cases, more precise experimental tests and simulation techniques are required to improve the mathematical model in some other cases. Significant changes in the output wind speed due to pressure differences created by the surrounding environment, the tower height, and the number of nozzles are observed. The advantages of being maintenance free, reliable, and sustainable, together with its special design that eliminates bird/bat mortality make the Wind Tower a promising solution for residential, commercial, and even off-grid applications.

A Numerical Study on Integral Solar Air Collector

2013 ◽  
Vol 860-863 ◽  
pp. 146-150
Author(s):  
Fu Sheng Dong ◽  
Ming Fu Hu ◽  
Xiao Chun Huang
Keyword(s):  
Mathematical Model ◽  
Solar Radiation ◽  
Thermal Efficiency ◽  
Radiation Intensity ◽  
Numerical Study ◽  
One Dimension ◽  
Inlet Temperature ◽  
Solar Radiation Intensity ◽  
Solar Air Collector ◽  
Matlab Programming

A mathematical modeling method was devoted to study the thermal performance of integral solar air collector. A mathematical model of heat transfer was set up based on one-dimension assumptions at first, and then numerical solution was brought out by using finite-difference method under one-dimension steady heat exchange. Through the MATLAB programming, the approximate solutions for the local air temperature and thermal efficiency were obtained at the quasi-steady state. After calculation, the influence of air inlet velocity, inlet temperature, solar radiation intensity and height of flow channel on the performance of collector was analyzed. It is discovered that the mathematical model is reasonable, the thermal efficiency decreases with temperature of inlet air increasing and increases with air velocity increasing, on which the solar radiation intensity have little influence. Depth of the channel and optimum flow both have a best value.

Calculations of three-dimensional viscous flow in a multiblade centrifugal fan by modelling blade forces

2003 ◽  
Vol 217 (3) ◽  
pp. 287-297 ◽  
Author(s):  
S-J Seo ◽  
K-Y Kim ◽  
S-H Kang
Keyword(s):  
Mathematical Model ◽  
Turbulent Flows ◽  
Numerical Study ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Centrifugal Fan ◽  
Complex Flows ◽  
Flow Through ◽  
Volume Method ◽  
The Mathematical Model

A numerical study is presented for Reynolds-averaged Navier-Stokes analysis of three-dimensional turbulent flows in a multiblade centrifugal fan. Present work aims at development of a relatively simple analysis method for these complex flows. A mathematical model of impeller forces is obtained from the integral analysis of the flow through the impeller. A finite volume method for discretization of governing equations and a standard k-ɛ model as turbulence closure are employed. For the validation of the mathematical model, the computational results for velocity components, static pressure, and flow angles at the exit of the impeller were compared with experimental data. The comparisons show generally good agreement, especially at higher flow coefficients.

scholarly journals Modeling of electricity production by wind power stations of Ukraine

2021 ◽  
Vol 280 ◽  
pp. 09010
Author(s):  
Volodymyr Podhurenko ◽  
Yulii Kutsan ◽  
Oleg Getmanets ◽  
Volodymyr Terekhov
Keyword(s):  
Mathematical Model ◽  
Wind Power ◽  
Black Sea ◽  
Energy Production ◽  
Electricity Production ◽  
Operational Parameters ◽  
Black Sea Region ◽  
Power Stations ◽  
The North ◽  
The Mathematical Model

Based on the results of actual multi-year measurements of wind speeds, numerical calculations have been made of the forecast energy productions of 43 megawatt-high power stations of the leading world producers in the wind conditions of the North Black Sea region of Ukraine. The established correlation between the annual energy production of wind power station (WPS) and its basic parameters (nameplate capacity, diameter of the rotor and hub height) allowed to develop a mathematical model of the forecast annual energy production of WPS. The calculations for the mathematical model are well in line with the operational parameters of the generation. The mathematical model makes it possible to quickly and reliably select (or design) the optimal wind turbine for industrial wind power in the North Black Sea, thus taking a significant step in reducing the energy dependency, environmental protection and the transition to energy-efficient and environmentally friendly technologies enabling Ukraine to reach the level of advanced states in the development of wind energy.

scholarly journals Numerical study of the effect of droplet coagulation intensity on polydisperse aerosol fraction distribution

2021 ◽  
Vol 1 (1) ◽  
pp. 73-80
Author(s):  
D.A. Tukmakov ◽  
Keyword(s):  
Mathematical Model ◽  
Boundary Conditions ◽  
Volume Content ◽  
Fine Particles ◽  
Stokes Equations ◽  
Numerical Study ◽  
Dispersed Phase ◽  
Mass Force ◽  
Carrier Medium ◽  
The Mathematical Model

The paper is devoted to the study of the effect of the intensity of aerosol fluctuations on the dis-tribution of fractions of the dispersed component of the coagulating aerosol. Oscillations of aerosol in closed channel are numerically modeled in operation. To describe the dynamics of the carrier medium, a two-dimensional non-stationary system of Navier-Stokes equations for compressed gas is used. They are written taking into account interfacial power interaction and interfacial heat ex-change. To describe the dynamics of the dispersed phase, a system of equations is solved for each of its fractions. It includes an equation of continuity for the “average density” of the fraction, equa-tions of preservation of spatial components of the pulse and an equation of preservation of thermal energy of the fraction of the dispersed phase of the gas suspension. Phase-to-phase power interac-tion included Archimedes force, attached mass force, and aerodynamic drag force. Heat exchange between the carrier medium-gas and each of the fractions of the dispersed phase was also taken into account. The mathematical model of dynamics of polydisperse aerosol was supplemented by the mathematical model of collision coagulation of aerosol. For the velocity components of the mixture, uniform Dirichlet boundary conditions were set. For the remaining functions of the dynamics of the multiphase mixture, uniform Neumann boundary conditions were set. The equations were solved by the explicit McCormack method with a nonlinear correction scheme that allows to obtain a mono-tone solution. As a result of numerical calculations, it was determined that in the vicinity of the os-cillating piston, an area with an increased content of coarse particles is formed. The coagulation process results in a monotonous increase in volume content of the coarse particle fraction and a mo-notonous decrease in volume content of fine particles. Increasing the intensity of gas fluctuations leads to intensification of the process of coagulation of aerosol droplets.

Mathematical model of oil-containing water purification process in the volume of granulated media

2018 ◽  
Vol 233 (3) ◽  
pp. 879-885
Author(s):  
Valeriy Ivanovich Istomin ◽  
Elena Stanislavovna Solodova ◽  
Viktoria Valer’evna Khlebnikova
Keyword(s):  
Mathematical Model ◽  
Physical Model ◽  
Water Purification ◽  
Theoretical Research ◽  
Purification Process ◽  
Operational Parameters ◽  
Filtering Element ◽  
The Mathematical Model ◽  
First Time ◽  
Further Development

A mathematical model of oil-containing water purification process in the volume of granulated media is developed. On the basis of this model, the purifying ability of filtering unit with granulated coalescing media, which regenerates filtering media in the mode of pseudo liquefaction of granule without disassembling and replacement of filtering element, is studied. In the process of theoretical research, the physical model of oil-containing water purification process in the volume of granulated coalescing media is elaborated. The consistent patterns of the analysed process have gained further development. Due to these patterns, the factors which determine the effectiveneness of purification are established. After realization of the experiment plan for the first time, the mathematical model of a ship’s oil-containing water purification process in the volume of granulated media on the basis of the regression equation has been received. This model allows to calculate the rational constructive and operational parameters of the plant with granulated filter elements.

Study of Macrosegregation Defects Formation Caused by Double Diffusive Convective Flow during Solidification of a Binary Alloy

2009 ◽  
Vol 283-286 ◽  
pp. 340-345 ◽  
Author(s):  
Farid Mechighel ◽  
Mahfoud Kadja ◽  
Mohammed El Ganaoui ◽  
Bernard Pateyron
Keyword(s):  
Mathematical Model ◽  
Finite Volume ◽  
Binary Alloy ◽  
Convective Flow ◽  
Continuum Model ◽  
Numerical Study ◽  
Finite Volume Approach ◽  
The Mathematical Model ◽  
Double Diffusive

Numerical study of both the solidification of the binary alloy Al-4.1%wtCu and macrosegregation defects formation have been carried out. The mixture continuum model was used in the development of the mathematical model representing the solidification phenomena. This model included the conservative equations (mass, momentum, energy and species); these equations were numerically solved by using a finite volume approach.

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