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Advances in Computational Fluid Dynamics with Applications

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A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Dynamical Systems".

Deadline for manuscript submissions: closed (31 July 2023) | Viewed by 17799

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Special Issue Editors

Dr. Bagh Ali

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Guest Editor

Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an 710072, China
Interests: computational fluid dynamics; nanofluids; newtonian and non-newtonian fluids; heat and mass transfer; finite element analysis; hybrid nanofluids

Dr. Nehad Ali Shah

E-Mail Website
Guest Editor

Department of Mechanical Engineering, Sejong University, Seoul 05006, Republic of Korea
Interests: computational fluid dynamics; numerical simulation; numerical modeling; computational fluid mechanics

Special Issue Information

Dear Colleagues,

Modern fluid and thermodynamic modeling tools have become easier to use, generating advantages throughout the product development process. Computational fluid dynamics (CFD) employs applied mathematics, physics, and computer software to demonstrate how a gas or liquid flows, and how it impacts contact surfaces during flow. Computational fluid dynamics is based on the Navier–Stokes equations. The relationship between a flowing fluid’s velocity, pressure, temperature, and density is described by these equations.

Many people are familiar with computational fluid dynamics, which has been around since the early 20th century, as a tool for analyzing air flow around vehicles and aircraft. CFD has developed into a helpful tool in the data center for analyzing thermal properties and modeling airflow as server rooms’ cooling infrastructure has grown in complexity. The size, composition, and design of the data center must be known when using CFD software. It makes use of these data to generate a grid-based 3D mathematical model that can be rotated and examined from various perspectives. An administrator can determine where cool air is mixing or being wasted by using CFD modeling to locate hot areas.

In this Special Issue, computational fluid dynamics (CFD) research is the main topic, with a focus on current developments and numerous industrial and scholarly applications. Submissions are requested for papers on a variety of topics, including novel physical modeling and discoveries as well as the proper handling of challenges present in the numerical modeling of fluid flow systems. These include, but are not limited to, the following areas: (i) accurately and successfully simulating physical boundary conditions; (ii) conserving mass and energy; (iii) treating complicated physical phenomena realistically; (iv) extendibility to dealing with more multiphysics phenomena, such as magnetohydrodynamics (MHD), electrohydrodynamics (EHD), non-Newtonian flows, phase changes, nano-fluids, etc.

Dr. Bagh Ali
Dr. Nehad Ali Shah
Guest Editors

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Keywords

computational fluid dynamics
nanofluids flows
heat transfer
nanoparticle shape factors
nanoparticle aggregation
hybrid and ternary hybrid nanofluids
dynamic thermoelasticity
perturbations in continuous media (fluids)
finite element method

Published Papers (13 papers)

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Research

19 pages, 7922 KiB

Open AccessArticle

Numerical Analysis of Entropy Generation in a Double Stage Triangular Solar Still Using CNT-Nanofluid under Double-Diffusive Natural Convection

by Chemseddine Maatki

Mathematics 2023, 11(13), 2818; https://doi.org/10.3390/math11132818 - 23 Jun 2023

Cited by 1 | Viewed by 813

Abstract

The analysis of entropy generation provides valuable information for the design and optimization of thermal systems. Solar stills are used for water desalination and purification. Using renewable energies, they provide a sustainable solution for drinking water supply in remote areas and off-grid situations. This work focuses on the 3D numerical study of entropy generation in a two-stage solar still subjected to the natural double diffusion convection phenomenon in the presence of CNT nanoparticles. The effects of Rayleigh number, buoyancy ratio, and nanofluid concentration on thermal, solutal, and viscous irreversibilities and flow structure were studied. The results show that increasing the buoyancy ratio leads to an increase in thermal and solutal entropy generation. The results of this study also show that total entropy is minimal for positive volume force ratios, N, at a nanoparticle volume fraction of around 3%, and for negative N ratios, at a volume fraction of around 4%. Full article

(This article belongs to the Special Issue Advances in Computational Fluid Dynamics with Applications)

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17 pages, 3954 KiB

Open AccessArticle

Amplitude and Phase Angle of Oscillatory Heat Transfer and Current Density along a Nonconducting Cylinder with Reduced Gravity and Thermal Stratification Effects

by Zia Ullah, Nawishta Jabeen and Muhammad Usman Khan

Mathematics 2023, 11(9), 2134; https://doi.org/10.3390/math11092134 - 2 May 2023

Cited by 12 | Viewed by 1303

Abstract

Due to excessive heating, various physical mechanisms are less effective in engineering and modern technologies. The aligned electromagnetic field performs as insulation that absorbs the heat from the surroundings, which is an essential feature in contemporary technologies, to decrease high temperatures. The major goal of the present investigation is to use magnetism perpendicular to the surface to address this issue. Numerical simulations have been made of the MHD convective heat and amplitude problem of electrical fluid flow down a horizontally non-magnetized circular heated cylinder with reduced gravity and thermal stratification. The associated non-linear PDEs that control fluid motion can be conveniently represented using the finite-difference algorithm and primitive element substitution. The FORTRAN application was used to compute the quantitative outcomes, which are then displayed in diagrams and table formats. The physical features, including the phase angle, skin friction, transfer of heat, and electrical density for velocity description, the magnetic characteristics, and the temperature distribution, coupled by their gradients, have an impact on each of the variables in the flow simulation. In the domains of MRI resonant patterns, prosthetic heartvalves, interior heart cavities, and nanoburning devices, the existing magneto-hydrodynamics and thermodynamic scenario are significant. The main findings of the current work are that the dimensionless velocity of the fluid increases as the gravity factor

R_{g}

decreases. The prominent change in the phase angle of current density

α_{m}

and heat flux

α_{t}

is examined for each value of the buoyancy parameter at both

α = π / 6

and

π

angles. The transitory skin friction and heat transfer rate shows a prominent magnitude of oscillation at both

α = π / 6

and

π / 2

positions, but current density increases with a higher magnitude of oscillation. Full article

(This article belongs to the Special Issue Advances in Computational Fluid Dynamics with Applications)

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17 pages, 5263 KiB

Open AccessArticle

Role of Chemically Magnetized Nanofluid Flow for Energy Transition over a Porous Stretching Pipe with Heat Generation/Absorption and Its Stability

by Zeeshan, N. Ameer Ahammad, Nehad Ali Shah, Jae Dong Chung and Attaullah

Mathematics 2023, 11(8), 1844; https://doi.org/10.3390/math11081844 - 13 Apr 2023

Cited by 6 | Viewed by 1107

Abstract

The laminar movement in an expanding and contracting permeable pipe or surface has recently attracted the attention of many scholars owing to its application in engineering and biological processes. The objective of the current study is to examine the influence of chemical processes on magnetized nanofluid flow over extending or shrinking permeable pipes with a heat reservoir. The flow equations are renovated into first ODEs by introducing the new variable and then numerically solved by RK4 with a shooting procedure. The effect of emerging factors on the flow features is observed using graphs and elaborated in detail. From the analysis, the temperature is raised when the heat source is increased in both cases of wall expansion or contraction but declines in the case of heat sinks. In the case of a heat source, the temperature rises as the Hartmann and Prandtl numbers are enhanced, but in the case of a heat sink, the temperature falls. In the presence of heat sinks and injections, when the thermophoresis factor is increased, the concentration of nanoparticles is increased in both wall expansion and contractions. In both situations of wall extension or contraction, along with injection, the concentration of nanoparticles is a decreasing function of

N b

, while the concentration of nanoparticles is an increasing function in the case of a heat source. Additionally, for the confirmation of the RK4 code, the total average square residue error and average square residue error are also presented. For the stability analysis, the current work is compared with published work, and excellent agreement is established. The novelty of the present study is to investigate the effect of chemical reaction on magnetized nanofluid flow over extending and shrinking porous pipes with heat generation and absorption. Full article

(This article belongs to the Special Issue Advances in Computational Fluid Dynamics with Applications)

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25 pages, 7382 KiB

Open AccessArticle

Evolutionary Padé Approximation for Heat and Mass Transfer Analysis of Falkner–Skan Flow of a Bio-Convective Casson Fluid

by Ghada Ali Basendwah, Nauman Raza and Javaid Ali

Mathematics 2023, 11(7), 1688; https://doi.org/10.3390/math11071688 - 31 Mar 2023

Cited by 1 | Viewed by 892

Abstract

This study presents numerical work to investigate the Falkner–Skan flow of a bio-convective Casson fluid over a wedge using an Evolutionary Padé Approximation (EPA) scheme. The governing partial differential equations and boundary conditions of a Falkner–Skan flow model are transformed to a system of ordinary differential equations involving ten dimensionless parameters by using similarity transformations. In the proposed EPA framework, an equivalent constrained optimization problem is formed. The solution of the resulting optimization problem is analogous to the solution of the dimensionless system of ordinary differential equations. The solutions produced in this work, with respect to various combinations of the physical parameters, are found to be in good agreement with those reported in the previously published literature. The effects of a non-dimensional physical-parameter wedge, Casson fluid, fluid phase effective heat capacity, Brownian motion, thermophoresis, radiation, and magnetic field on velocity profile, temperature profile, fluid concentration profile, and the density of motile microorganisms are discussed and presented graphically. It is observed that the fluid velocity rises with a rise in the Casson fluid viscosity force parameter, and an increase in the Prandtl number causes a decrease in the heat transfer rate. Another significant observation is that the temperature and fluid concentration fields are greatly increased by an increase in the thermophoresis parameter. An increase in the Péclet number suppresses the microorganism density. Moreover, the increased values of the Prandtl number increase the local Nusslet number, whereas the skin friction is increased when an increase in the Prandtl number occurs. Full article

(This article belongs to the Special Issue Advances in Computational Fluid Dynamics with Applications)

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26 pages, 4950 KiB

Open AccessArticle

Mixed Convection in a Horizontal Channel–Cavity Arrangement with Different Heat Source Locations

by Farhan Lafta Rashid, Asseel M. Rasheed Al-Gaheeshi, Mohammed Alhwayzee, Bagh Ali, Nehad Ali Shah and Jae Dong Chung

Mathematics 2023, 11(6), 1428; https://doi.org/10.3390/math11061428 - 15 Mar 2023

Cited by 4 | Viewed by 1308

Abstract

Several researchers are very interested in mixed convection heat transfer because of how widely it is used, particularly for solar thermal collectors, cooling electronic equipment, and chemical process instruments. Using COMSOL-Multiphysics, this article establishes laminar coupled mixed convection heat transfer characteristics across a horizontal channel–cavity architecture. Investigations are conducted into the effect of heat source location on isotherms, velocity distribution, pressure, temperature, average and local Nusselt numbers, and air density. The intake airflow Reynolds number is assumed constant on 2.8814. The enclosure with an isothermally heated right wall in the shape of a “<” as a heat source in three configurations (heat source in the base (1st case), in the upper step (2nd case), and the below step (3rd case). The obtained numerical results present that the higher heat transfer is performed in case two because the heat source is near the contact surface between the channel and the cavity. With the hot sources’ locations being altered, the velocity distribution seems to be unchanged. The increase in the positive y axis has no impact on the pressure distribution throughout the channel. Changing the position of the heated source does not seem to have any impact on the pressure distribution. Air density profiles start to diverge across cases around y = 0.035 m; the third example has a larger value than the second case, and the latter case has a larger value in the density distribution than the former. The contact between the enclosure and the channel (y = 0), where the greatest Nusselt number also occurs, exhibits the highest heat transfer. The maximal Nusselt number falls as y’s absolute value rises. Full article

(This article belongs to the Special Issue Advances in Computational Fluid Dynamics with Applications)

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20 pages, 6589 KiB

Open AccessArticle

Computational and Stability Analysis of MHD Time-Dependent Thermal Reaction Flow Impinging on a Vertical Porous Plate Enclosing Magnetic Prandtl Number and Thermal Radiation Effect

by Zeeshan, N. Ameer Ahammad, Nehad Ali Shah, Jae Dong Chung and Muhammad Shoaib Khan

Mathematics 2023, 11(6), 1376; https://doi.org/10.3390/math11061376 - 12 Mar 2023

Cited by 7 | Viewed by 1208

Abstract

The aim of the present study is to investigate magnetohydrodynamic (MHD) time-dependent flow past a vertical slanted plate enclosing heat and mass transmission (HMT), induced magnetic field (IMF), thermal radiation (TR), and viscous and magnetic dissipation characteristics on a chemical reaction fluid flow. A boundary layer estimate is taken to develop a movement that exactly captures the time-dependent equations for continuity, momentum, magnetic induction, energy, concentration, generalized Ohm’s law, and Maxwell’s model. Partial differential equations designate the path occupied by the magnetized fluid as it passes through the porous matrix. In addition, a heat source is included in the model in order to monitor the flow nature in the current study. Because of the nonlinearity in the governing equations, the mathematical models are computed numerically by RK4 method. Further, tables and graphs are depicted to elucidate the physical influence of important factors on the flow characteristics. The novelty of the present work is investigating the irregular heat source and chemical reaction over the porous rotating channel. It is perceived that high thermal radiation occurs with increases in temperature and concentration. It is witnessed that the IMF effect is diminished for large values of magnetic Prandtl number (MPN). It is also analyzed that with increasing the heat source factor, the velocity of the fluid enhances. For stability analysis, the existing effort is compared with the published work and good agreement is found. Moreover, the residue error estimation confirms our solution. Full article

(This article belongs to the Special Issue Advances in Computational Fluid Dynamics with Applications)

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13 pages, 5251 KiB

Open AccessArticle

Solar Radiation and Thermal Convection of Hybrid Nanofluids for the Optimization of Solar Collector

by Safyan Mukhtar and Taza Gul

Mathematics 2023, 11(5), 1175; https://doi.org/10.3390/math11051175 - 27 Feb 2023

Cited by 12 | Viewed by 1293

Abstract

This study aims to show the role of the stagnation point flow in solar optimization in the presence of a Riga plate. This requirement is conceivable in the case of solar energy management with a suitable solar collector covering and visual thermal optimization. Solar energy radiation and thermal convection of glycol (C₃H₈O₂)-based aluminum oxide (Al₂O₃) and copper (Cu) nanoparticles were used for a solar collector, and were studied in terms of the stagnation point flow theoretically. Stagnation refers to the state of a solar thermal system in which the flux varies in the collection loop to control the extra heating. The CVFEM code was used to analyze the flow in the case of represented stagnation using the FEA-Tools multiple physics software that manages partial derivative equations (PDEs). The streamlined patterns and energy contours for different cases were studied in detail. The transformation equations were treated with the numerical method (RK-4 technique) and showed strong agreement of the physical results corresponding to the initial conditions and boundaries. The results showed that hybrid nanofluids have the advanced capability to enhance the thermal performance of the base solvent and provide uniform distribution to the solar panel. The solar optimization and uniform thermal expansion results are displayed graphically. Full article

(This article belongs to the Special Issue Advances in Computational Fluid Dynamics with Applications)

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21 pages, 8610 KiB

Open AccessArticle

Role of Nanofluid and Hybrid Nanofluid for Enhancing Thermal Conductivity towards Exponentially Stretching Curve with Modified Fourier Law Inspired by Melting Heat Effect

by Zeeshan, N. Ameer Ahammad, Nehad Ali Shah and Jae Dong Chung

Mathematics 2023, 11(5), 1170; https://doi.org/10.3390/math11051170 - 27 Feb 2023

Cited by 14 | Viewed by 1247

Abstract

The intensive of this study is to examine the melting heat and second-order slip (SoS) effect at the boundary in nanofluid and hybrid nanofluid (HN) ethylene–glycol (EG) based fluid through a curved surface using the Modified Fourier Law (MFL) and dust particles. Considering similarity transformation, the PDEs are converted to ODEs and then solved numerically by using the finite element method (FEM). The effects of solid volume fraction (SVF), melting heat factor, curvature factor, first and second-order slip factor, fluid particle concentration factor, and mass concentration factor on the velocity field, dust phase velocity (DPV), temperature field, dust phase temperature (DPT), and the Ski Friction (SF) are investigated through graphs and tables. The thermophysical properties of nanofluid and HN are depicted in tables. The novelty of the present work is to investigate the dusty- and dusty-hybrid nanoliquids over the curved surface with a melting heat effect and MFL which has not yet been studied. In the limiting case, the present work is compared with the published work and a good correlation is found. The confirmation of the mathematical model error estimations has been computed. Full article

(This article belongs to the Special Issue Advances in Computational Fluid Dynamics with Applications)

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16 pages, 968 KiB

Open AccessArticle

Significance of Tiny Particles of Dust and TiO₂ Subject to Lorentz Force: The Case of Non-Newtonian Dusty Rotating Fluid

by Bagh Ali, N. Ameer Ahammad, Windarto, Abayomi S. Oke, Nehad Ali Shah and Jae Dong Chung

Mathematics 2023, 11(4), 877; https://doi.org/10.3390/math11040877 - 9 Feb 2023

Cited by 3 | Viewed by 1129

Abstract

This work examined the thermodynamics of the MHD rotating dusty Maxwell water-based nanofluid with suspended dust particles. This study examines the importance of increasing the volume fraction of tiny particles of TiO₂ and dust on fluid dynamics. With appropriate similarity transformations, the governing PDEs for both fluid and dusty-phase models are transformed into non-linear linked non-dimensional ODEs. To acquire graphical consequences, the bvp4c technique is implemented in MATLAB scripts. The primary and secondary velocities’ magnitude in both phases decreases with an increase in the dust particle volume concentration, Lorentz force, rotating, and Maxwell fluid parameters. The growing strength of tiny particles of dust and TiO₂ is responsible for the upshot of temperature in both dust and nanofluid phases. A visual representation of the Nusselt number and skin friction coefficients are is provided. Full article

(This article belongs to the Special Issue Advances in Computational Fluid Dynamics with Applications)

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22 pages, 4961 KiB

Open AccessArticle

Analysis of Error and Stability of Nanofluid over Horizontal Channel with Heat/Mass Transfer and Nonlinear Thermal Conductivity

by Zeeshan, N. Ameer Ahammad, Nehad Ali Shah, Jae Dong Chung, Attaullah and Haroon Ur Rasheed

Mathematics 2023, 11(3), 690; https://doi.org/10.3390/math11030690 - 29 Jan 2023

Cited by 24 | Viewed by 1679

Abstract

The current investigation aims to analyze the nanofluid flow between two infinite rotating horizontal channels. The lower plate is porous and stretchable. The impact of physical parameters such as Hall current, thermal characteristics, heat source/sink, chemical reaction on velocity, temperature, and concentration profiles are discussed through graphs. The governing equations are transformed to ordinary differential equations using suitable transformations and then solved numerically using the RK4 approach along with the shooting technique. For varying values of the Schmidt number (SN) and the chemical reaction factor (CRF), the concentration profile declines, but decreases for the activation energy. It is observed that the velocity profile declines with the increasing values of the suction factor. The velocity profile increases when the values of the rotation factors are increased. The temperature field exhibits a rising behavior with increasing values of the thermophoresis factor, Brownian motion, and the thermal radiation factor. It is also observed that the heat transfer rate is significant at the lower wall with the increasing values of the Prandtl number (PN). For the numerical solution, the error estimation and the residue error are calculated for the stability and confirmation of the mathematical model. The novelty of the present work is to investigate the irregular heat source and chemical reaction over the porous rotating channel. A growing performance is revealed by the temperature field, with the increase in the Brownian motion (BM), thermophoresis factor (TF), thermal conductivity factor (TCF), and the radiation factor (RF). Full article

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19 pages, 1653 KiB

Open AccessArticle

Analytical Investigation of Some Time-Fractional Black–Scholes Models by the Aboodh Residual Power Series Method

by Muhammad Imran Liaqat, Ali Akgül and Hanaa Abu-Zinadah

Mathematics 2023, 11(2), 276; https://doi.org/10.3390/math11020276 - 5 Jan 2023

Cited by 10 | Viewed by 1382

Abstract

In this study, we use a new approach, known as the Aboodh residual power series method (ARPSM), in order to obtain the analytical results of the Black–Scholes differential equations (BSDEs), which are prime for judgment of European call and put options on a non-dividend-paying stock, especially when they consist of time-fractional derivatives. The fractional derivative is considered in the Caputo sense. This approach is a combination of the Aboodh transform and the residual power series method (RPSM). The suggested approach is based on a new version of Taylor’s series that generates a convergent series as a solution. The advantage of our strategy is that we can use the Aboodh transform operator to transform the fractional differential equation into an algebraic equation, which decreases the amount of computation required to obtain the solution in a subsequent algebraic step. The primary aspect of the proposed approach is how easily it computes the coefficients of terms in a series solution using the simple limit at infinity concept. In the RPSM, unknown coefficients in series solutions must be determined using the fractional derivative, and other well-known approximate analytical approaches like variational iteration, Adomian decomposition, and homotopy perturbation require the integration operators, which is challenging in the fractional case. Moreover, this approach solves problems without the need for He’s polynomials and Adomian polynomials, so the small size of computation is the strength of this approach, which is an advantage over various series solution methods. The efficiency of the suggested approach is verified by results in graphs and numerical data. The recurrence errors at various levels of the fractional derivative are utilized to demonstrate the convergence evidence for the approximative solution to the exact solution. The comparison study is established in terms of the absolute errors of the approximate and exact solutions. We come to the conclusion that our approach is simple to apply and accurate based on the findings. Full article

(This article belongs to the Special Issue Advances in Computational Fluid Dynamics with Applications)

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17 pages, 6784 KiB

Open AccessArticle

A Nonlinear Structure of a Chemical Reaction Model and Numerical Modeling with the New Aspect of Existence and Uniqueness

by Tahira Sumbal Shaikh, Ali Akgül, Muhammad Aziz-ur Rehman, Nauman Ahmed, Muhammad Sajid Iqbal, Naveed Shahid, Muhammad Rafiq and Manuel De la Sen

Mathematics 2023, 11(1), 37; https://doi.org/10.3390/math11010037 - 22 Dec 2022

Cited by 2 | Viewed by 1568

Abstract

In this article, a nonlinear autocatalytic chemical reaction glycolysis model with the appearance of advection and diffusion is proposed. The occurrence and unicity of the solutions in Banach spaces are investigated. The solutions to these types of models are obtained by the optimization of the closed and convex subsets of the function space. Explicit estimates of the solutions for the admissible auxiliary data are formulated. An elegant numerical scheme is designed for an autocatalytic chemical reaction model, that is, the glycolysis model. The fundamental traits of the prescribed numerical method, for instance, the positivity, consistency, stability, etc., are also verified. The authenticity of the proposed scheme is ensured by comparing it with two extensively used numerical techniques. A numerical example is presented to observe the graphical behavior of the continuous system by constructing the numerical algorithm. The comparison depicts that the projected numerical design is more productive as compared to the other two schemes, as it holds all the important properties of the continuous model. Full article

(This article belongs to the Special Issue Advances in Computational Fluid Dynamics with Applications)

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23 pages, 5965 KiB

Open AccessArticle

Significance of Multi-Hybrid Morphology Nanoparticles on the Dynamics of Water Fluid Subject to Thermal and Viscous Joule Performance

by Meznah M. Alanazi, Awatif A. Hendi, Qadeer Raza, M. Zubair Akbar Qureshi, Fatima Shafiq Hira, Bagh Ali, Nehad Ali Shah and Jae Dong Chung

Mathematics 2022, 10(22), 4259; https://doi.org/10.3390/math10224259 - 14 Nov 2022

Cited by 5 | Viewed by 1303

Abstract

Three-dimensional flow via swirling porous disks and an annular sector is carried out using fully developed hybrid nanofluids. Here, a single-phase simulation based on thermophysical characteristics using various nanoparticle sizes and shapes is taken into account. A regression function connected with the permeable Reynolds number for injection and suction was created. We used the well-known and accurate “shooting approach” to apply to the governing, nonlinear, ordinary differential equation systems to obtain numerical results. Additionally, parametric research was employed to control the impact of embedded flow factors on concentration, velocity, and temperature. While the physical features of the bottom and upper disks, such as the skin friction coefficient and Nusselt number, are provided in a table, their characterization of the flow of several regulatory flow parameters, such as fluid velocity and temperature, is depicted graphically. The experimental range of nanoparticle fractions of 1% to 4% is considered with the Nusselt number having notable effects at

φ

= 4%. Both walls demonstrate the effects of an increase in injection factor, shear stress, and tensile stress. As the Eckert number rises at the lower wall, the rate of heat transfer dramatically increases, and the opposite is true for the upper wall. The rate of heat transmission is significantly impacted by the addition of different base fluids containing various kinds of nanoparticles. The aforementioned research created a solid foundation for the development of electronic computers with an emphasis on nanotechnology and biomedical devices. Full article

(This article belongs to the Special Issue Advances in Computational Fluid Dynamics with Applications)

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