Analytical solutions to the advection-diffusion equation with Atangana-Baleanu time-fractional derivative and a concentrated loading

Mirza, Itrat Abbas; Akram, Muhammad; Imtiaz, Waqas A.; Chung, Jae Dong

doi:10.1016/j.aej.2020.10.043

Cited by 12 publications

(11 citation statements)

References 35 publications

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“…The most general approach is to obtain velocity distribution by solving momentum equations to obtain velocity distribution and subsequently solving advection-diffusion equation in case of a steady flow problem. For a transient problem, a coupled analytical solution is needed to study the process [22].…”

Section: Advection With Fick's Diffusionmentioning

confidence: 99%

Modeling Approaches for Fluidic Mass Transport in Next Generation Micro and Nano Biomedical Sensors

2022

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This review discusses on current methodologies and trends in modeling fluidic mass transport phenomena in micro and nano scale biomedical devices. We have presented the governing equations for species transport in micro and nano scales and provided analytical as well as computational approaches that can aid in obtaining solutions for complex flow problems. We have also reviewed novel methodologies that modern research community utilized for simulating species transport in micro and nano biomedical sensing devices.

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Section: Advection With Fick's Diffusionmentioning

confidence: 99%

Modeling Approaches for Fluidic Mass Transport in Next Generation Micro and Nano Biomedical Sensors

2022

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“…Boundary conditions are located on the borders. Undisturbed ground temperature T UGT is a ground thermal property situated at a depth where the ground temperature is approximately invariable, depth value depends on climatic conditions and is different in various regions of the Earth [23,24].…”

Section: Overviewmentioning

confidence: 99%

A Framework Based on Finite Element Method (FEM) for Modelling and Assessing the Affection of the Local Thermal Weather Factors on the Performance of Anaerobic Lagoons for the Natural Treatment of Swine Wastewater

Brito-Espino

Martín

Báez

et al. 2021

Water

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Anaerobic lagoons are natural wastewater treatment systems suitable for swine farms in small communities due to its low operational and building costs, as well as for the environmental sustainability that these technologies enable. The local weather is one of the factors which greatly influences the efficiency of the organic matter degradation within anaerobic lagoons, since microbial growth is closely related to temperature. In this manuscript, we propose a mathematical model which involves the two-dimensional Stokes, advection–diffusion-reaction and heat transfer equations for an unstirred fluid flow. Furthermore, the Anaerobic Digestion Model No1 (ADM1), developed by the International Water Association (IWA), has been implemented in the model. The partial differential equations resulting from the model, which involve a large number of state variables that change according to the position and the time, are solved through the use of the Finite Element Method. The results of the simulations indicated that the methodology is capable of predicting reasonably well the steady-state of the concentrations for all processes that take place in the anaerobic digestion and for each one of the variables considered; cells, organic matter, nutrients, etc. In view of the results, it can be concluded that the model has significant potential for the design and the study of anaerobic cells’ behaviour within free flow systems.

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“…Currently, several various techniques are applied to solve fractional diffusion problems such as the Laplace, Mellin, and Fourier transforms. Mirza et al [5] solved the time-fractionalized advection-diffusion equation by exploiting the Atangana-Baleanu fractional derivative operator. Khan et al [6] performed a new modification of the Adomian decomposition method to solve the fractional convection-diffusion equation.…”

Section: Introductionmentioning

confidence: 99%

Distinctive Shape Functions of Fractional Differential Quadrature for Solving Two-Dimensional Space Fractional Diffusion Problems

Mustafa,

Ragb,

Salah

et al. 2023

Fractal Fract

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The aim of this study is to utilize a differential quadrature method with various kernels, such as Lagrange interpolation and discrete singular convolution, to tackle problems related to the Riesz fractional diffusion equation and the Riesz fractional advection–dispersion equation. The governing equation for convection and diffusion depends on both spatial and transient factors. By using the block marching technique, we transform these equations into an algebraic system using differential quadrature methods and the Caputo-type fractional operator. Next, we develop a MATLAB program that generates code capable of solving the fractional convection–diffusion equation in (1+2) dimensions for each shape function. Our goal is to ensure that our methods are reliable, accurate, efficient, and capable of convergence. To achieve this, we conduct two experiments, comparing the numerical and graphical results with both analytical and numerical solutions. Additionally, we evaluate the accuracy of our findings using the L∞ error. Our tests show that the differential quadrature method, which relies mainly on the discrete singular convolution shape function, is a highly effective numerical approach for fractional convective diffusion problems. It offers superior accuracy, faster convergence, and greater reliability than other techniques. Furthermore, we study the impact of fractional order derivatives, velocity, and positive diffusion parameters on the results.

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Analytical solutions to the advection-diffusion equation with Atangana-Baleanu time-fractional derivative and a concentrated loading

Cited by 12 publications

References 35 publications

Modeling Approaches for Fluidic Mass Transport in Next Generation Micro and Nano Biomedical Sensors

Modeling Approaches for Fluidic Mass Transport in Next Generation Micro and Nano Biomedical Sensors

A Framework Based on Finite Element Method (FEM) for Modelling and Assessing the Affection of the Local Thermal Weather Factors on the Performance of Anaerobic Lagoons for the Natural Treatment of Swine Wastewater

Distinctive Shape Functions of Fractional Differential Quadrature for Solving Two-Dimensional Space Fractional Diffusion Problems

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