scholarly journals The Solutions of Non-Integer Order Burgers’ Fluid Flowing through a Round Channel with Semi Analytical Technique

Symmetry ◽  
2019 ◽  
Vol 11 (8) ◽  
pp. 962 ◽  
Author(s):  
M. Imran ◽  
D.L.C. Ching ◽  
Rabia Safdar ◽  
Ilyas Khan ◽  
M. Imran ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Fluid Flow ◽  
Laplace Transformation ◽  
Inverse Laplace Transform ◽  
Rotational Flow ◽  
Analytical Technique ◽  
Burgers Fluid ◽  
Stehfest’S Algorithm ◽  
The Impact ◽  
Round Channel

The solutions for velocity and stress are derived by using the methods of Laplace transformation and Modified Bessel’s equation for the rotational flow of Burgers’ fluid flowing through an unbounded round channel. Initially, supposed that the fluid is not moving with t = 0 and afterward fluid flow is because of the circular motion of the around channel with velocity Ω R t p with time positively grater than zero. At the point of complicated expressions of results, the inverse Laplace transform is alternately calculated by “Stehfest’s algorithm” and “MATHCAD” numerically. The numerically obtained solutions in the terms of the Modified Bessel’s equations of first and second kind, are satisfying all the imposed conditions of given mathematical model. The impact of the various physical and fractional parameters are also indeed and so presented by graphical demonstrations.

scholarly journals The impact of rheotaxis and flow on the aggregation of organisms

2021 ◽  
Vol 18 (183) ◽  
Author(s):  
K. J. Painter
Keyword(s):  
Mathematical Model ◽  
Fluid Flow ◽  
Population Distribution ◽  
Group Formation ◽  
Large Population ◽  
Aquatic Organisms ◽  
Environmental Flow ◽  
Systematic Analysis ◽  
The Impact ◽  
A Current

Dispersed populations often need to organize into groups. Chemical attractants provide one means of directing individuals into an aggregate, but whether these structures emerge can depend on various factors, such as there being a sufficiently large population or the response to the attractant being sufficiently sensitive. In an aquatic environment, fluid flow may heavily impact on population distribution and many aquatic organisms adopt a rheotaxis response when exposed to a current, orienting and swimming according to the flow field. Consequently, flow-induced transport could be substantially different for the population members and any aggregating signal they secrete. With the aim of investigating how flows and rheotaxis responses impact on an aquatic population’s ability to form and maintain an aggregated profile, we develop and analyse a mathematical model that incorporates these factors. Through a systematic analysis into the effect of introducing rheotactic behaviour under various forms of environmental flow, we demonstrate that each of flow and rheotaxis can act beneficially or detrimentally on the ability to form and maintain a cluster. Synthesizing these findings, we test a hypothesis that density-dependent rheotaxis may be optimal for group formation and maintenance, in which individuals increase their rheotactic effort as they approach an aggregated state.

scholarly journals Hydrodynamical Study of Creeping Maxwell Fluid Flow through a Porous Slit with Uniform Reabsorption and Wall Slip

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1852
Author(s):  
Hameed Ullah ◽  
Dianchen Lu ◽  
Abdul Majeed Siddiqui ◽  
Tahira Haroon ◽  
Khadija Maqbool
Keyword(s):  
Fluid Flow ◽  
Physical Phenomenon ◽  
Fluid Velocity ◽  
Axial Flow ◽  
Maximum Velocity ◽  
Maxwell Fluid ◽  
Two Dimensional ◽  
Mathematical Basis ◽  
Analytical Technique ◽  
The Impact

The present theoretical study investigates the influence of velocity slip characteristics on the plane steady two-dimensional incompressible creeping Maxwell fluid flow passing through a porous slit with uniform reabsorption. This two-dimensional flow phenomenon is governed by the mathematical model having nonlinear partial differential equations together with non-homogeneous boundary conditions. An analytical technique, namely the recursive approach, is used successfully to find the solutions of the problem. The explicit expressions for stream function, velocity components, pressure distribution, wall shear stress and normal stress difference have been derived. The axial flow rate, leakage flux and fractional reabsorption are also found out. The points of maximum velocity are identified. Non-dimensionalization is carried out and graphs are portrayed at different positions of the channel to show the impact of pertinent parameters: slip parameter, Maxwell fluid parameter and absorption parameter, on flow variables and found that the fluid velocity is affected significantly due to these parameters. This study provides a mathematical basis to understand the physical phenomenon for fluid flows through permeable boundaries which exists in different problems like gaseous diffusion, filtration and biological mechanisms.

scholarly journals The impact of rheotaxis and flow on the aggregation of organisms

2021 ◽  
Author(s):  
Kevin J Painter
Keyword(s):  
Mathematical Model ◽  
Fluid Flow ◽  
Population Distribution ◽  
Group Formation ◽  
Large Population ◽  
Aquatic Organisms ◽  
Environmental Flow ◽  
Systematic Analysis ◽  
The Impact ◽  
A Current

Dispersed populations often need to organise into groups. Chemical attractants provide one means of directing individuals into an aggregate, but whether these structures emerge can depend on various factors, such as there being a sufficiently large population or the response to the attractant being sufficiently sensitive. In an aquatic environment, fluid flow may heavily impact on population distribution and many aquatic organisms adopt a rheotaxis response when exposed to a current, orienting and swimming according to the flow field. Consequently, flow-induced transport could be substantially different for the population members and any aggregating signal they secrete. With the aim of investigating how flows and rheotaxis responses impact on an aquatic population's ability to form and maintain an aggregated profile, we develop and analyse a mathematical model that incorporates these factors. Through a systematic analysis into the effect of introducing rheotactic behaviour under various forms of environmental flow, we demonstrate that each of flow and rheotaxis can act beneficially or detrimentally on the ability to form and maintain a cluster. Synthesising these findings, we test a hypothesis that density-dependent rheotaxis may be optimal for group formation and maintenance, in which individuals increase their rheotactic effort as they approach an aggregated state.

The Impact of Light Polarisation on Light Field of Scenes with Multiple Reflections

2020 ◽  
pp. 108-115 ◽  
Author(s):  
Vladimir P. Budak ◽  
Anton V. Grimaylo
Keyword(s):  
Mathematical Model ◽  
Light Field ◽  
Global Illumination ◽  
Multiple Reflections ◽  
Software Environment ◽  
The Monte Carlo Method ◽  
Mueller Matrices ◽  
Volume Integration ◽  
The Impact

The article describes the role of polarisation in calculation of multiple reflections. A mathematical model of multiple reflections based on the Stokes vector for beam description and Mueller matrices for description of surface properties is presented. On the basis of this model, the global illumination equation is generalised for the polarisation case and is resolved into volume integration. This allows us to obtain an expression for the Monte Carlo method local estimates and to use them for evaluation of light distribution in the scene with consideration of polarisation. The obtained mathematical model was implemented in the software environment using the example of a scene with its surfaces having both diffuse and regular components of reflection. The results presented in the article show that the calculation difference may reach 30 % when polarisation is taken into consideration as compared to standard modelling.

Analyzing the Impact of Healthy Behavior on Weight Change with a Provable Mathematical Model (Preprint)

2020 ◽  
Author(s):  
Ayan Chatterjee ◽  
Ram Bajpai ◽  
Pankaj Khatiwada
Keyword(s):  
Physical Activity ◽  
Mathematical Model ◽  
Health Behavior ◽  
Weight Change ◽  
Simulated Data ◽  
Negative Behavior ◽  
Healthy Behavior ◽  
Healthy Habits ◽  
Lifestyle Diseases ◽  
The Impact

BACKGROUND Lifestyle diseases are the primary cause of death worldwide. The gradual growth of negative behavior in humans due to physical inactivity, unhealthy habit, and improper nutrition expedites lifestyle diseases. In this study, we develop a mathematical model to analyze the impact of regular physical activity, healthy habits, and a proper diet on weight change, targeting obesity as a case study. Followed by, we design an algorithm for the verification of the proposed mathematical model with simulated data of artificial participants. OBJECTIVE This study intends to analyze the effect of healthy behavior (physical activity, healthy habits, and proper dietary pattern) on weight change with a proposed mathematical model and its verification with an algorithm where personalized habits are designed to change dynamically based on the rule. METHODS We developed a weight-change mathematical model as a function of activity, habit, and nutrition with the first law of thermodynamics, basal metabolic rate (BMR), total daily energy expenditure (TDEE), and body-mass-index (BMI) to establish a relationship between health behavior and weight change. Followed by, we verified the model with simulated data. RESULTS The proposed provable mathematical model showed a strong relationship between health behavior and weight change. We verified the mathematical model with the proposed algorithm using simulated data following the necessary constraints. The adoption of BMR and TDEE calculation following Harris-Benedict’s equation has increased the model's accuracy under defined settings. CONCLUSIONS This study helped us understand the impact of healthy behavior on obesity and overweight with numeric implications and the importance of adopting a healthy lifestyle abstaining from negative behavior change.

scholarly journals Nanofluid flow containing carbon nanotubes with quartic autocatalytic chemical reaction and Thompson and Troian slip at the boundary

2020 ◽  
Vol 10 (1) ◽  
Author(s):  
Muhammad Ramzan ◽  
Jae Dong Chung ◽  
Seifedine Kadry ◽  
Yu-Ming Chu ◽  
Muhammad Akhtar
Keyword(s):  
Mathematical Model ◽  
Carbon Nanotubes ◽  
Drag Force ◽  
Chemical Reaction ◽  
Slip Velocity ◽  
Volume Fraction ◽  
Surface Drag ◽  
Nanofluid Flow ◽  
Velocity Parameter ◽  
The Impact

Abstract A mathematical model is envisioned to discourse the impact of Thompson and Troian slip boundary in the carbon nanotubes suspended nanofluid flow near a stagnation point along an expanding/contracting surface. The water is considered as a base fluid and both types of carbon nanotubes i.e., single-wall (SWCNTs) and multi-wall (MWCNTs) are considered. The flow is taken in a Dacry-Forchheimer porous media amalgamated with quartic autocatalysis chemical reaction. Additional impacts added to the novelty of the mathematical model are the heat generation/absorption and buoyancy effect. The dimensionless variables led the envisaged mathematical model to a physical problem. The numerical solution is then found by engaging MATLAB built-in bvp4c function for non-dimensional velocity, temperature, and homogeneous-heterogeneous reactions. The validation of the proposed mathematical model is ascertained by comparing it with a published article in limiting case. An excellent consensus is accomplished in this regard. The behavior of numerous dimensionless flow variables including solid volume fraction, inertia coefficient, velocity ratio parameter, porosity parameter, slip velocity parameter, magnetic parameter, Schmidt number, and strength of homogeneous/heterogeneous reaction parameters are portrayed via graphical illustrations. Computational iterations for surface drag force are tabulated to analyze the impacts at the stretched surface. It is witnessed that the slip velocity parameter enhances the fluid stream velocity and diminishes the surface drag force. Furthermore, the concentration of the nanofluid flow is augmented for higher estimates of quartic autocatalysis chemical.

scholarly journals Modelling the impact of delaying vaccination against SARS-CoV-2 assuming unlimited vaccine supply

2021 ◽  
Vol 18 (1) ◽  
Author(s):  
Marcos Amaku ◽  
Dimas Tadeu Covas ◽  
Francisco Antonio Bezerra Coutinho ◽  
Raymundo Soares Azevedo ◽  
Eduardo Massad
Keyword(s):  
Mathematical Model ◽  
Vaccination Campaign ◽  
Vaccination Rate ◽  
Sao Paulo ◽  
The State ◽  
São Paulo ◽  
Health Authorities ◽  
The World ◽  
The Moment ◽  
The Impact

Abstract Background At the moment we have more than 177 million cases and 3.8 million deaths (as of June 2021) around the world and vaccination represents the only hope to control the pandemic. Imperfections in planning vaccine acquisition and difficulties in implementing distribution among the population, however, have hampered the control of the virus so far. Methods We propose a new mathematical model to estimate the impact of vaccination delay against the 2019 coronavirus disease (COVID-19) on the number of cases and deaths due to the disease in Brazil. We apply the model to Brazil as a whole and to the State of Sao Paulo, the most affected by COVID-19 in Brazil. We simulated the model for the populations of the State of Sao Paulo and Brazil as a whole, varying the scenarios related to vaccine efficacy and compliance from the populations. Results The model projects that, in the absence of vaccination, almost 170 thousand deaths and more than 350 thousand deaths will occur by the end of 2021 for Sao Paulo and Brazil, respectively. If in contrast, Sao Paulo and Brazil had enough vaccine supply and so started a vaccination campaign in January with the maximum vaccination rate, compliance and efficacy, they could have averted more than 112 thousand deaths and 127 thousand deaths, respectively. In addition, for each month of delay the number of deaths increases monotonically in a logarithmic fashion, for both the State of Sao Paulo and Brazil as a whole. Conclusions Our model shows that the current delay in the vaccination schedules that is observed in many countries has serious consequences in terms of mortality by the disease and should serve as an alert to health authorities to speed the process up such that the highest number of people to be immunized is reached in the shortest period of time.

Modeling and Experiments of Laser Cladding With Droplet Injection

2005 ◽  
Vol 127 (9) ◽  
pp. 978-986 ◽  
Author(s):  
J. Choi ◽  
L. Han ◽  
Y. Hua
Keyword(s):  
Fluid Flow ◽  
Laser Cladding ◽  
Dynamic Motion ◽  
Cladding Layer ◽  
Melt Pool ◽  
Material Deposition ◽  
Modeling And Experiments ◽  
Solid Liquid Interface ◽  
Solid Liquid ◽  
The Impact

Laser aided Directed Material Deposition (DMD) is an additive manufacturing process based on laser cladding. A full understanding of laser cladding is essential in order to achieve a steady state and robust DMD process. A two dimensional mathematical model of laser cladding with droplet injection was developed to understand the influence of fluid flow on the mixing, dilution depth, and deposition dimension, while incorporating melting, solidification, and evaporation phenomena. The fluid flow in the melt pool that is driven by thermal capillary convection and an energy balance at the liquid–vapor and the solid–liquid interface was investigated and the impact of the droplets on the melt pool shape and ripple was also studied. Dynamic motion, development of melt pool and the formation of cladding layer were simulated. The simulated results for average surface roughness were compared with the experimental data and showed a comparable trend.

scholarly journals Innovations in anaerobic digestion: a model-based study

2021 ◽  
Vol 14 (1) ◽  
Author(s):  
Karol Postawa ◽  
Jerzy Szczygieł ◽  
Marek Kułażyński
Keyword(s):  
Mathematical Model ◽  
Anaerobic Digestion ◽  
Production Efficiency ◽  
Biogas Production ◽  
Biogas Plant ◽  
Methane Content ◽  
Pig Manure ◽  
Pig Slurry ◽  
Production Chain ◽  
The Impact

Abstract Background Increasing the efficiency of the biogas production process is possible by modifying the technological installations of the biogas plant. In this study, specific solutions based on a mathematical model that lead to favorable results were proposed. Three configurations were considered: classical anaerobic digestion (AD) and its two modifications, two-phase AD (TPAD) and autogenerative high-pressure digestion (AHPD). The model has been validated based on measurements from a biogas plant located in Poland. Afterward, the TPAD and AHPD concepts were numerically tested for the same volume and feeding conditions. Results The TPAD system increased the overall biogas production from 9.06 to 9.59%, depending on the feedstock composition, while the content of methane was slightly lower in the whole production chain. On the other hand, the AHPD provided the best purity of the produced fuel, in which a methane content value of 82.13% was reached. At the same time, the overpressure leads to a decrease of around 7.5% in the volumetric production efficiency. The study indicated that the dilution of maize silage with pig manure, instead of water, can have significant benefits in the selected configurations. The content of pig slurry strengthens the impact of the selected process modifications—in the first case, by increasing the production efficiency, and in the second, by improving the methane content in the biogas. Conclusions The proposed mathematical model of the AD process proved to be a valuable tool for the description and design of biogas plant. The analysis shows that the overall impact of the presented process modifications is mutually opposite. The feedstock composition has a moderate and unsteady impact on the production profile, in the tested modifications. The dilution with pig manure, instead of water, leads to a slightly better efficiency in the classical configuration. For the TPAD process, the trend is very similar, but the AHPD biogas plant indicates a reverse tendency. Overall, the recommendation from this article is to use the AHPD concept if the composition of the biogas is the most important. In the case in which the performance is the most important factor, it is favorable to use the TPAD configuration.

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