Design Of Mathematical Model Research Articles

Experimental Analysis of Small Solar Unmanned Aerial Vehicle to Predict Aerodynamic Performance

Various studies have been done in recent years on unmanned solar-powered aircraft for non-stop flight at a specified location or area. However, if a solar-powered unmanned aerial vehicle (UAV) can achieve a non-stop flight around the world, it may lead to the possibility of a pseudolite (i.e., pseudo-satellite) operation. These solar UAVs capable of operating as a satellite enable sustainable aviation that provides cheaper communication accessibility. Recently, we have developed a mathematical model for solar UAVs that was followed by the fabrication of a solar UAV model. Both the mathematical design model and the prototype model have been published. Thus, this work aims to determine the actual flight performance characteristics of the fabricated solar UAV. In this work, the bench and flight tests of the prototype solar and non-solar UAV model were compared in terms of aerodynamic characteristics and performance. These characteristics are determined using the flight test data and then compared with simulation data using a mathematical design model published earlier. Both accelerated and un-accelerated methods have been applied to predict the polar drag curve, and a distinct band of data obtained for both UAV prototypes. The predicted zero-lift drag coefficients were similar to the theoretical prediction in these UAVs.

Minimum Cost for Reinforced Concrete Rectangular Beams with Parabolic Haunches

El objetivo de esta investigacion es presentar un modelo matematico para el diseno optimo de trabes de seccion transversal rectangular con cartelas parabolicas bajo el criterio de costo minimo tomando en cuenta el costo del concreto y costo de acero de refuerzo, y considerando las ecuaciones del reglamento (ACI 318S-19). Este modelo presenta las ecuaciones para dos tipos de cargas: Carga uniformemente distribuida y Carga concentrada localizada en cualquier parte de la trabe. Dos ejemplos han sido desarrollados por el modelo propuesto para ambos casos. Los resultados muestran que las trabes prismaticas para los dos casos tienen un costo total, un volumen total y un peso total mayor con respecto a las trabes no prismaticas. Por lo tanto, las trabes no prismaticas son mas economicas, tienen menos volumen y tambien tienen menos peso con respecto a las trabes prismaticas.

Mathematical Modeling of Reversible Bimolecular Catalyzed Transesterification Reaction Kinetics for PKO and Methanol synthesis

Continuous appraisal for alternative renewable energy sources particularly for bio-diesel production is a great concern to engineers and scientist globally. Actually, vegetable oils and C1 to C3 alcohol group alkali catalyzed transesterification reaction leads to bio-diesel production. The aspect of developing reaction time and disappearance rate (-RA) mathematical models for effective various reactor types design seems impassive. Hence, in this work the authors developed a unified reaction time and disappearance rate (-RA) predictive models as a function of reactants and product reaction rate constants (K1 K2), molar masses (MW), conversion (XA), fractional volume change (ɛ) and density (ρ) dimensions using partial fraction and by parts integration methods. The developed models were simulated with Matlab codes programming approach exploiting the kinetics parameters of PKO , Methanol and biodiesel. The results of the reaction time (t) at equilibrium, none equilibrium and disappearance rate (-RɛA) show dependable relationship with the stipulated dimensions and were quite compatible with those of inferential laboratory physicochemical data reported. Thus;

H∞ CONTROL DESIGN OF A MULTITANK SYSTEM

This paper considers MATLAB® modeling and simulation of H∞ controller and its realization on the Multitank System. The first task is to study the physical plant of the laboratory Multitank System and to apply a given mathematical model for optimal controller design. The general objective of the derived regulator is to reach and stabilize the level in the tanks by an adjustment of the pump operation or/and valves settings. Finally, it is necessary to simulate the obtained closed-loop system and to test its workability.

A novel cascade heating system for waste heat recovery in the combined heat and power plant integrating with the steam jet pump

Waste heat utilization is an essential approach for improving the energy utilization efficiency of the combined heat and power (CHP) plant and a significant low-carbon way to achieve clean urban heating. To recover the excess exhaust steam heat of the CHP plant with the high back-pressure turbine (CHP-HBP), this paper proposed a novel heating system integrated with the steam jet pump (SJP). The EBSILON software was applied for modeling the proposed thermal system and analyzing the thermal performance of the CHP-HBP heating system under different operating conditions. On this basis, the coupled component-system design solution was proposed by combining the 1-D mathematical design model of the SJP with the heating system performance. Compared with the conventional system, under the design condition, the exhaust steam recovery rate and the heating capacity of the novel system had a significant increment of 8.66% and 31.8 MW with the same power output. Meanwhile, the total exergy loss and standard coal consumption rate for electricity generation of the novel system reduced by 5.74 MW and 6.77 g/kWh, respectively, with about 2.32% improvement in electricity generation efficiency. The critical parametric influence analysis on the overall performance showed that the novel system has better adaptability with some fluctuations of turbine back-pressure, supply/return water temperatures, and heating load. Under off-designed conditions, the recovery rate of the exhaust steam of the novel system was 5–20% higher than that of the conventional system, and the coal consumption rate and electricity generation efficiency both performed better. In all, the proposed system provided a promising method for the effective utilization of waste heat in the field of clean heating and the energy system optimization and integration for the coal-fired CHP plants.

A mathematical model for optimum design and synthesis of a hybrid electrolyser-fuel cell system: Production of hydrogen and freshwater from seawater

Fossil fuels have earned a reputation as unsustainable sources of energy, due to the release of carbon emissions that are attributable to global warming. To overcome the extensive release of carbon emissions into the environment, different approaches are being explored to produce energy, by replacing non-renewable fuels with renewable energy. Additionally, many countries across the world are emerging as water-scarce countries, due to the vulnerability of freshwater supply. This work, therefore, focuses on the design and synthesis of a hybrid electrolyser-fuel cell system to generate hydrogen and freshwater from seawater. The proposed system is designed to be integrated with a background process that requires both power and water. It has the potential to reduce the burden on freshwater sources and carbon footprint of background processes, as well as produce power. A one-dimensional, mathematical model is developed for a continuous hybrid seawater electrolyser-fuel cell system operated at steady state. The model determines the optimal operating conditions in terms of temperature, current density, electrode thickness and humidity, as well as the performance of the system through the activation overpotential, diffusion overpotential, ohmic overpotential and the open-circuit voltage. GAMS/BARON is used to optimise the hybrid system. Furthermore, a techno-economic evaluation is conducted to determine the viability of the system. Results indicate that an overall power conversion efficiency of 41.2%, and a freshwater recovery rate of 48.2% is achieved.

Axiomatic Design for ‘X’: An Integrated Methodology for Product Design. (Dept. M. ( Production ))

The Axiomatic Design (AD) introduces several benefits for product innovation, but it doesn’t account for all required concerns in product lifecycle. Integrating Design for X (DFX) is proposed here to enhance the results of AD and measure the performance of proposed product designs. The introduced methodology is referred to as Axiomatic Design for X (ADFX). This idea enables adding several design and usage requirements as functional requirements and/or design axioms in addition to design constraints in a flexible framework for product design. Furthermore, this idea can inspire robust mathematical models for product design by agglomerating objective and subjective product requirements. This paper provides a base for other directions in the product design research.

Milk Supply Chain Network Design (SCND)

This study is based on a real-life case study of a SCND of a single milk product (premium milk) of a leading milk producing organization in Odisha. This product is highly perishable in nature; SCND implicates decision-making at a strategic level. Network design is the basis for the efficient operation of supply chain, and consequently, one of the most important problems a supply chain manager has to solve. This study conducts a real-life case-based modeling to address the gap in the area of supply chain network design. The author investigates the milk supply chain network design under preservation technology and propose a generic mathematical model for milk supply chain network design encompassing economic objective. A customized mathematical model is also developed for a leading milk producing organization in Odisha. Both of the models are formulated and solved by using piecewise nonlinear optimization.

Application of mathematical models in design and assessment of sewer network facilities

The application of mathematical models has been expanding in the field of sanitary and environmental engineering. Mathematical models are used in the design and assessment of sewer networks and their facilities. Sewer network models make it possible to create a model of hydraulic and Physico-chemical processes in wastewater flowing through the sewage network. The number of extreme rainfall events is increasing due to climate change. It causes a collapse in the infrastructure of urbanized areas. It is possible to investigate the flow of wastewater under extreme rainfall and to propose measures to eliminate adverse events using mathematical models. Nowadays, it is possible to use modern calculation procedures, which are used to dimension and assess existing facilities. This paper aims to focus on the application of numerical models in the design and assessment of combined sewer overflow chambers. The combined sewer overflow serves to carry away a part of the rain flows from the network to the nearest suitable receiving water body. Their main task is to reduce the uneven load of wastewater treatment plants by rainwater. The combined sewer overflow chambers distribute the inflow into the flow going to the wastewater treatment plant and the lightened flow going to the receiving water. The aim of this paper is to summarize the knowledge of CFD modelling and to get acquainted with the basic principles. In brief, the normal flow describes its simulation using two basic models. Finally, it focuses on the recapitulation of foreign studies and their use in the assessment and design of relief chambers and regulatory objects of the single sewer networks.

Thiol Ligand Adsorption on Gold Nanoparticle Surfaces: Mathematical Models to Predict Optimal Concentration of Heterobifunctional Polyethylene Glycol for Horseradish Peroxidase Immobilization

Gold nanoparticles (GNPs) are often used in numerous applications, including diagnostics, drug delivery and treatment of diseases, given its physical features and excellent biocompatibility, where factors such as dispersion and stability are directly related to the its performance and efficiency. Mathematical models for experimental design can be very useful and contribute to predict optimal functionalization strategies. Therefore, the purpose of this work was to stabilize and functionalize GNPs of 40 nm and 80 nm and determine optimal concentrations of heterobifunctional polyethylene glycols (HS-PEG-NH2 3500 and 7500 g/mol). Mathematical models relating particle diameter, initial concentration and quantification of the polymers adsorbed for both varieties of thiol PEG was predicted. GNP were modified and subjected to the four different strategies employed in this study (strategy I and III with HS-PEG-NH2 3500; II and IV with HS-PEG-NH2 7500). Solutions with concentrations ranging from 30 to 200 ng/ml of enzyme horseradish peroxidase (HRP) were used as an alternative to gauge the efficiency of the evaluated strategies. A superior yield and efficacy of strategies I and II was observed, since the former had a capture capacity of up to 5 times when stabilized for 2 h and up to 6 times for 12 h. Regarding stability, the most promising strategy observed was number II for nanoparticles of 40 nm. Moreover, the mathematical models highlighted in this study were efficient in predicting behavior of colloidal solutions with sizes of 40 nm and 80 nm when in contact with different varieties of thiol PEG and may exempt new kinetic tests.

Optimal design of reinforced concrete beams for rectangular sections with straight haunches

Objective of this research is to present a mathematical model for optimal design of rectangular cross-section beams with straight haunches under the criterion of minimum cost considering the concrete cost and reinforcing steel cost, and taking into account the equations of the regulation (ACI 318S-14). This model presents the equations for a uniformly distributed load and a concentrated load located anywhere on the beam. Two examples are developed by the proposed model, one for uniformly distributed load and another for concentrated load showing the best solution for each case. The results show the following: a) The prismatic beams for uniformly distributed load have a total cost of the 8% greater, a total volume and a total weight of the 9% greater with respect to the non-prismatic beams; b) The prismatic beams for concentrated load have a total cost, a total volume and a total weight of the 6% greater with respect to the non-prismatic beams. The main conclusions are: For a smaller b width the optimal design for both models is presented. The non-prismatic beams are more economical, also these have less volume and less weight with respect to prismatic beams.

A Decision Support Model for Salary Structure Design

This article presents a simple mathematical model for salary structure design that enhances clarity and allows for reasonable trade-off between internal equity and external market competitiveness considerations in salary structure design. Practical use of the model is illustrated with an actual application in one organization.

Resilient hazardous-materials network design under uncertainty and perishability

The design of transportation networks for hazardous materials (hazmat) poses several elements of complexity, including vulnerability to disasters which may lead to significant loss of life and property. In this paper, we propose a new bi-objective mathematical model for hazmat transportation design considering resiliency and perishability. Minimization of cost and risk with built-in de-resiliency measures are considered as the two primary objective functions. To cope with uncertainties in the model, a new multi-stage stochastic programming approach is developed. In order to deal with the NP-hard nature of the problem and to solve the model in large instances, a new Pareto-based lower bound procedure is introduced. Further, illustrative numerical examples are solved and the efficiency of the proposed approach is verified. Lastly, a case study on hazmat transportation in Iranian context is presented to illustrate the methodology and develop managerial insights.

Application of Organic-Inorganic Hybrids in Chemical Analysis, Bio- and Environmental Monitoring

Organic-inorganic hybrids (OIH) are considered to be a powerful platform for applications in many research and industrial fields. This review highlights the application of OIH for chemical analysis, biosensors, and environmental monitoring. A methodology toward metrological traceability measurement and standardization of OIH and demonstration of the role of mathematical modeling in biosensor design are also presented. The importance of the development of novel types of OIH for biosensing applications is highlighted. Finally, current trends in nanometrology and nanobiosensors are presented.

Lightweight Design of Front Suspension Upright of Electric Formula Car Based on Topology Optimization Method

In order to obtain a lightweight front upright of an electric formula car’s suspension, the topology optimization method is used in the front upright structure design. The mathematical model of the lightweight optimization design is constructed, and the geometric model of the initial design of the front upright is subjected to the ultimate load condition. The structural optimization of a front upright resulted in the mass reduction of the upright by 60.43%. The optimized model was simulated and verified regarding the strength, stiffness, and safety factor under three different conditions, namely turning braking, emergency braking, and sharp turning. In the experiment, the uprights were machined and assembled and integrated into the racing suspension. The experimental results showed that the optimized front uprights met the requirements of performance.

Sizing verification of a 4kWp retrofitted grid-connected photovoltaic system: a case study in Shah Alam, Malaysia

Electricity are commonly generated from several types of energy resources such as fossil and nuclear energy. However, due to emission of carbon dioxide from both sources, renewable energy is introduced to provide a clean and secure sustainable energy. One of the potential renewable energy application is Photovoltaic (PV) system; namely grid-connected photovoltaic (GCPV) system and stand-alone photovoltaic (SAPV) system. In this study, a mathematical approach of SEDA’s GCPV sizing model is implemented to size a 4kWp of a retrofitted GCPV system by the method claimed to be the best practice mathematical design model under tropical climate Malaysia. The outcome of the sizing approach will then be evaluated with HelioScope software, one of commercial simulation tools available in current market. The final result obtained from both methods shows that the final PV array configuration is 1 x 12 (parallel x series) which is in agreement to the actual installed system.

Power upgrading of WWR-S research reactor using plate-type fuel elements part I: Steady-state thermal-hydraulic analysis (forced convection cooling mode)

The design of a nuclear reactor core requires basic thermal-hydraulic information concerning the heat transfer regime at which onset of nucleate boiling (ONB) will occur, the pressure drop and flow rate through the reactor core, the temperature and power distributions in the reactor core, the departure from nucleate boiling (DNB), the condition for onset of flow instability (OFI), in addition to, the critical velocity beyond which the fuel elements will collapse. These values depend on coolant velocity, fuel element geometry, inlet temperature, flow direction and water column above the top of the reactor core. Enough safety margins to ONB, DNB and OFI must-emphasized. A heat transfer package is used for calculating convection heat transfer coefficient in single phase turbulent, transition and laminar regimes. The main objective of this paper is to study the possibility of power upgrading of WWR-S research reactor from 2 to 10 MWth. This study presents a one-dimensional mathematical model (axial direction) for steady-state thermal-hydraulic design and analysis of the upgraded WWR-S reactor in which two types of plate fuel elements are employed. FOR-CONV computer program is developed for the needs of the power upgrading of WWR-S reactor up to 10 MWth.

An IMC-PID controller with Particle Swarm Optimization algorithm for MSBR core power control

Internal Model Control (IMC) is a control strategy based on process mathematical model for controller design. The design idea of IMC is to parallelize the object model with the actual object, approximate the dynamic inversion of the model by the controller, and take the inverse of the minimum phase part of the model for a single variable system, and add it to the system. As the advantages of simple structure, intuitive design, no need for accurate object model, less on-line adjustment parameters in IMC design process, to explore the application of IMC in the field of nuclear reactor control, taking the core power control of Molten Salt Breeder Reactor (MSBR) as an example, a linear model of MSBR core system is established. The IMC technology was adopted and the IMC-PID controller with Particle Swarm Optimization (PSO) algorithm was designed to control the core power. The core power control of liquid molten salt reactor under step reactivity disturbance and load tracking is studied. The results show that the IMC-PID controller can control the core power well.

Design of Photobioreactors for Algal Biomass Growth

The present energy scenario of depleting sources of fossil fuel, increasing the cost of processed fuel and geopolitical policies have made it imperative that alternate energy sources and processes that reduce greenhouse gas emissions be identified. Biofuels from algae, in recent times, have emerged as a potential alternative to fossil fuels, as it can be easily produced, stored, and used as transportation fuels. Here, mathematical design models are developed for tubular, bubble column, and airlift photobioreactors to calculate their productivity for the growth of algal biomass. A modified Monod kinetic equation is used to estimate the specific growth rate of the biomass. The model equations are solved for tubular reactor systems and the estimated productivities are successfully validated against values available in published literature. It is found that the tubular reactor has productivity, around 2.1 g/L.day. The analysis is also done to identify the effect of light, nutrient, and carbon dioxide on overall productivity.

A sustainable mathematical model for design of net zero energy buildings

Energy is vital recourse for economic development of today's business. The services demanded of residential and commercial buildings require substantial energy use. Energy consumption in this sector has been growing in total, gradually. As a result the high emission of greenhouse gases is released and, hence, the saving energy with better building management have made a major priority of the energy and environment sectors throughout the world. In this direction, to reduce energy consumption and mitigate environmental impacts in buildings, net-zero energy buildings (NZEB) is a very effective solution. As a result, a multi-objective model is developed to identify the best combination of materials and construction options considering their related costs, energy efficiency, and environmental impacts of buildings, simultaneously. This sustainable model is presented to construct a building considering the construction costs and energy consumption of the design options. To design the NZEB, while minimizing costs and carbon emissions, use has been made of a combination of different types of active/heating and cooling systems and renewable equipment through such high-efficiency, effective, and updated technologies as the solar panel. Finally, the case study of a residential building with two scenarios is used to demonstrate the proposed framework. The results show that, for scenarios1 and 2 respectively using insulation thickness such as (wall, roof, and windows) and renewable equipment have the highest sustainable impact in NEBZ's performance.