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Axioms
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Recent Advancements in Computational Fluid Mechanics and Heat Transfer
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Recent Advancements in Computational Fluid Mechanics and Heat Transfer

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Physics".

Deadline for manuscript submissions: closed (30 November 2023) | Viewed by 13106

Special Issue Editor

Dr. Suresh Alapati

E-Mail Website
Guest Editor
Department of Mechatronics Engineering, Kyungsung University, 309, Suyeong-ro (Daeyeon-Dong), Nam-gu, Busan 48434, Republic of Korea
Interests: computational fluid dynamics; heat and mass transfer; multiphase and multicomponent flows; biofluid mechanics; fluid–structure interaction (FSI) problem; lattice Boltzmann method

Special Issue Information

Dear Colleagues,

The fluid mechanics and heat transfer field has gained significant importance in recent years because its applications are ubiquitous. Recent advancements in experimental techniques make it possible to predict fluid flow and heat transfer behavior in some applications. However, experimental methods cannot reveal all the physical mechanisms behind fluid flow in detail, and they are also cumbersome, time-consuming, and expensive. Therefore, it is necessary to develop theoretical and computational simulation techniques to understand the underlying physics of the fluid flow and heat transfer more clearly. Theoretical analysis often makes several assumptions and is restricted to simple situations. Thus, many scientists focus on developing computational methods to solve fluid flow and heat transfer problems. Numerical simulations are especially beneficial for obtaining detailed information that cannot be revealed from experiments and examining the effect of various physical parameters on fluid flow behavior.

This Special Issue focuses on numerical methods in fluid mechanics and heat transfer, emphasizing its recent advancements and their use in many industrial and academic applications. We welcome manuscripts on new modeling techniques and innovations that address the key issues and inherent difficulties in the simulation of fluid flow and heat transfer systems. Authors can submit manuscripts in, but not limited to, the following research areas:

  • Numerical methods and computational techniques in fluid flow, heat, and mass transfer;
  • Simulation of fluid flow and heat transfer involving complex boundaries;
  • Simulation of multiphase, multicomponent flows;
  • Computational methods for biofluid mechanics;
  • Numerical methods for nanofluids;
  • Numerical methods for solving fluid and flexible structure interaction (FSI) problems;
  • Numerical optimization techniques of thermofluid systems;
  • Artificial intelligence and machine learning techniques in fluid flow and heat transfer;
  • Theoretical approaches for micro- and nanofluidic problems;
  • Numerical strategies for solving fluid flow and heat transfer in porous media;
  • Solving fluid flow and heat transfer with open-source software;
  • Numerical methods for solving multiphysics problems such as MHD;
  • Parallel computing techniques, etc.

We invite manuscripts that focus on developing the following computational techniques for simulating fluid flow and heat transfer in the aforementioned applications: conventional methods such as the finite difference method (FDM), finite volume method (FVM), finite element method (FEM), and new, attractive computational methodologies such as the lattice Boltzmann method (LBM), smoothed particle hydrodynamics (SPH), molecular dynamics, dissipative particle dynamics, etc.

Dr. Suresh Alapati
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Axioms is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

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Published Papers (7 papers)

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Research

15 pages, 8476 KiB  
Article
Simulation of an Elastic Rod Whirling Instabilities by Using the Lattice Boltzmann Method Combined with an Immersed Boundary Method
by Suresh Alapati, Wooseong Che, Sunkara Srinivasa Rao and Giang T. T. Phan
Axioms 2023, 12(11), 1011; https://doi.org/10.3390/axioms12111011 - 26 Oct 2023
Viewed by 1361
Abstract
Mathematical modeling and analysis of biologically inspired systems has been a fascinating research topic in recent years. In this work, we present the results obtained from the simulation of an elastic rod (that mimics a flagellum axoneme) rotational motion in a viscous fluid [...] Read more.
Mathematical modeling and analysis of biologically inspired systems has been a fascinating research topic in recent years. In this work, we present the results obtained from the simulation of an elastic rod (that mimics a flagellum axoneme) rotational motion in a viscous fluid by using the lattice Boltzmann method (LBM) combined with an immersed boundary method (IBM). A finite element model consists of a set of beam and truss elements used to discretize the flagellum axoneme while the fluid flow is solved by the well-known LBM. The hydrodynamic coupling to maintain the no-slip boundary condition between the fluid and the elastic rod is conducted with the IBM. The rod is actuated with a torque applied at its base cross-section that acts as a driving motor of the axoneme. We simulated the rotational dynamics of the rod for three different rotational frequencies (low, medium, and high) of the motor. To compare with previous publication results, we chose the sperm number Sp=L(4πμω)/(EI)1/4 as the validation parameter. We found that at the low rotational frequency, f = 1.5 Hz, the rod performs stable twirling motion after attaining an equilibrium state (the rod undergoes rigid rotation about its axis). At the medium frequency, f = 2.65 Hz, the rod undergoes whirling motion, where the tip of the rod rotates about the central rotational axis of the driving motor. When the frequency increases further, i.e., when it reaches the critical value, fc ≈ 2.7 Hz, the whirling motion becomes over-whirling, where the tip of the filament falls back to the base and performs a steady crank-shafting motion. All three rotational dynamics, twirling, whirling, and over-whirling, and the critical value of rotational frequency are in good agreement with the previously published results. We also observed that our present simulation technique is computationally more efficient than previous works. Full article
(This article belongs to the Special Issue Recent Advancements in Computational Fluid Mechanics and Heat Transfer)
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31 pages, 1016 KiB  
Article
Barotropic-Baroclinic Coherent-Structure Rossby Waves in Two-Layer Cylindrical Fluids
by Jing Xu, Yong Fang, Jingxuan Geng and Huanhe Dong
Axioms 2023, 12(9), 856; https://doi.org/10.3390/axioms12090856 - 4 Sep 2023
Cited by 1 | Viewed by 935
Abstract
In this paper, the propagation of Rossby waves under barotropic-baroclinic interaction in polar co-ordinates is studied. By starting from the two-layer quasi-geotropic potential vorticity equation (of equal depth) with the β effect, the coupled KdV equations describing barotropic-baroclinic waves are derived using multi-scale [...] Read more.
In this paper, the propagation of Rossby waves under barotropic-baroclinic interaction in polar co-ordinates is studied. By starting from the two-layer quasi-geotropic potential vorticity equation (of equal depth) with the β effect, the coupled KdV equations describing barotropic-baroclinic waves are derived using multi-scale analysis and the perturbation expansion method. Furthermore, in order to more accurately describe the propagation characteristics of barotropic-baroclinic waves, fifth-order coupled KdV-mKdV equations were obtained for the first time. On this basis, the Lie symmetry and conservation laws of the fifth-order coupled KdV-mKdV equations are analyzed in terms of their properties. Then, the elliptic function expansion method is applied to find the soliton solutions of the fifth-order coupled KdV-mKdV equations. Based on the solutions, we further simulate the evolution of Rossby wave amplitudes and investigate the influence of the high-order terms—time and wave number—on the propagation of barotropic waves and baroclinic waves. The results show that the appearance of the higher-order effect makes the amplitude of the wave lower, the width of the wave larger, and the whole wave flatter, which is obviously closer to actual Rossby wave propagation. The time and wave number will also influence wave amplitude and wave width. Full article
(This article belongs to the Special Issue Recent Advancements in Computational Fluid Mechanics and Heat Transfer)
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22 pages, 3735 KiB  
Article
Design of Finite Difference Method and Neural Network Approach for Casson Nanofluid Flow: A Computational Study
by Muhammad Shoaib Arif, Kamaleldin Abodayeh and Yasir Nawaz
Axioms 2023, 12(6), 527; https://doi.org/10.3390/axioms12060527 - 27 May 2023
Cited by 8 | Viewed by 1363
Abstract
To boost productivity, commercial strategies, and social advancement, neural network techniques are gaining popularity among engineering and technical research groups. This work proposes a numerical scheme to solve linear and non-linear ordinary differential equations (ODEs). The scheme’s primary benefit included its third-order accuracy [...] Read more.
To boost productivity, commercial strategies, and social advancement, neural network techniques are gaining popularity among engineering and technical research groups. This work proposes a numerical scheme to solve linear and non-linear ordinary differential equations (ODEs). The scheme’s primary benefit included its third-order accuracy in two stages, whereas most examples in the literature do not provide third-order accuracy in two stages. The scheme was explicit and correct to the third order. The stability region and consistency analysis of the scheme for linear ODE are provided in this paper. Moreover, a mathematical model of heat and mass transfer for the non-Newtonian Casson nanofluid flow is given under the effects of the induced magnetic field, which was explored quantitatively using the method of Levenberg–Marquardt back propagation artificial neural networks. The governing equations were reduced to ODEs using suitable similarity transformations and later solved by the proposed scheme with a third-order accuracy. Additionally, a neural network approach for input and output/predicted values is given. In addition, inputs for velocity, temperature, and concentration profiles were mapped to the outputs using a neural network. The results are displayed in different types of graphs. Absolute error, regression studies, mean square error, and error histogram analyses are presented to validate the suggested neural networks’ performance. The neural network technique is currently used on three of these four targets. Two hundred points were utilized, with 140 samples used for training, 30 samples used for validation, and 30 samples used for testing. These findings demonstrate the efficacy of artificial neural networks in forecasting and optimizing complex systems. Full article
(This article belongs to the Special Issue Recent Advancements in Computational Fluid Mechanics and Heat Transfer)
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23 pages, 9421 KiB  
Article
Numerical Investigation by Cut-Cell Approach for Turbulent Flow through an Expanded Wall Channel
by Ramzy M. Abumandour, Adel M. El-Reafay, Khaled M. Salem and Ahmed S. Dawood
Axioms 2023, 12(5), 442; https://doi.org/10.3390/axioms12050442 - 29 Apr 2023
Cited by 1 | Viewed by 1421
Abstract
The expanded wall channel backward-facing step (BFS) and axisymmetric diffuser plays an important role in the society of fluid dynamics. Using a cut-cell technique is an established new method to treat the inclined wall of an axisymmetric diffuser. Cut-cell handle to reach the [...] Read more.
The expanded wall channel backward-facing step (BFS) and axisymmetric diffuser plays an important role in the society of fluid dynamics. Using a cut-cell technique is an established new method to treat the inclined wall of an axisymmetric diffuser. Cut-cell handle to reach the shape of the inclined wall, an axisymmetric diffuser and complex geometry. It helps treat the boundary condition at the wall in an accurate physical way. The turbulent flow through the geometries is solved by using Reynolds averaged Navier-Stokes equations (RANS) with the standard k-ε model. A self-built FOTRAN code based on the finite volume method with the Semi-Implicit Method for Pressure Linked Equations (SIMPLE) algorithm for pressure velocity coupling is established and examined with published experimental data for two different geometries backward-facing step (BFS) and axisymmetric diffuser. The results of the new technique reflect good agreement between the numerical results and the experimental data. A parametric study of the impact of area ratios (2, 2.5, 3, 3.5) in a backward-facing step on pressure, velocity, and turbulent kinetic energy. The angles (7°, 10°, 14°) and area ratios (2, 2.5, 3, 3.5) effect of an axisymmetric diffuser on the streamlines, local skin friction, pressure, velocity, turbulent kinetic energy, and separation zone. Full article
(This article belongs to the Special Issue Recent Advancements in Computational Fluid Mechanics and Heat Transfer)
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18 pages, 1936 KiB  
Article
An Analytical Solution to the One-Dimensional Unsteady Temperature Field near the Newtonian Cooling Boundary
by Honglei Ren, Yuezan Tao, Ting Wei, Bo Kang, Yucheng Li and Fei Lin
Axioms 2023, 12(1), 61; https://doi.org/10.3390/axioms12010061 - 5 Jan 2023
Cited by 2 | Viewed by 2796
Abstract
One-dimensional heat-conduction models in a semi-infinite domain, although forced convection obeys Newton’s law of cooling, are challenging to solve using standard integral transformation methods when the boundary condition φ(t) is an exponential decay function. In this study, a general theoretical [...] Read more.
One-dimensional heat-conduction models in a semi-infinite domain, although forced convection obeys Newton’s law of cooling, are challenging to solve using standard integral transformation methods when the boundary condition φ(t) is an exponential decay function. In this study, a general theoretical solution was established using Fourier transform, but φ(t) was not directly present in the transformation processes, and φ(t) was substituted into the general theoretical solution to obtain the corresponding analytical solution. Additionally, the specific solutions and corresponding mathematical meanings were discussed. Moreover, numerical verification and sensitivity analysis were applied to the proposed model. The results showed that T(x,t) was directly proportional to the thermal diffusivity (a) and was inversely proportional to calculation distance (x) and the coefficient of cooling ratio (λ). The analytical solution was more sensitive to the thermal diffusivity than other factors, and the highest relative error between numerical and analytical solutions was roughly 4% under the condition of 2a and λ. Furthermore, T(x,t) grew nonlinearly as the material’s thermal diffusivity or cooling ratio coefficient changed. Finally, the analytical solution was applied for parameter calculation and verification in a case study, providing the reference basis for numerical calculation under specific complex boundaries, especially for the study of related problems in the fields of fluid dynamics and peridynamics with the heat-conduction equation. Full article
(This article belongs to the Special Issue Recent Advancements in Computational Fluid Mechanics and Heat Transfer)
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16 pages, 1859 KiB  
Article
Generalized Mathematical Model of Brinkman Fluid with Viscoelastic Properties: Case over a Sphere Embedded in Porous Media
by Siti Farah Haryatie Mohd Kanafiah, Abdul Rahman Mohd Kasim and Syazwani Mohd Zokri
Axioms 2022, 11(11), 609; https://doi.org/10.3390/axioms11110609 - 1 Nov 2022
Cited by 2 | Viewed by 1785
Abstract
The process of heat transfer that involves non-Newtonian fluids in porous regions has attracted considerable attention due to its practical application. A mathematical model is proposed for monitoring fluid flow properties and heat transmission in order to optimize the final output. Thus, this [...] Read more.
The process of heat transfer that involves non-Newtonian fluids in porous regions has attracted considerable attention due to its practical application. A mathematical model is proposed for monitoring fluid flow properties and heat transmission in order to optimize the final output. Thus, this attempt aims to demonstrate the behavior of fluid flow in porous regions, using the Brinkman viscoelastic model for combined convective transport over a sphere embedded in porous medium. The governing partial differential equations (PDEs) of the proposed model are transformed into a set of less complex equations by applying the non-dimensional variables and non-similarity transformation, before they are numerically solved via the Keller-Box method (KBM) with the help of MATLAB software. In order to validate the model for the present issue, numerical values from current and earlier reports are compared in a particular case. The studied parameters such as combined convection, Brinkman and viscoelastic are analyzed to obtain the velocity and temperature distribution. Graphs are used to illustrate the variation in local skin friction and the Nusselt number. The results of this study showcase that when the viscoelastic and Brinkman parameters are enlarged, the fluid velocity drops and the temperature increases, while the combined convection parameter reacts in an opposite manner. Additionally, as the Brinkman and combined convection parameters are increased, the physical magnitudes of skin friction and Nusselt number are increased across the sphere. Of all the parameters reported in this study, the viscoelastic parameter could delay the separation of boundary layers, while the Brinkman and combined convection parameters show no effect on the flow separation. The results obtained can be used as a foundation for other complex boundary layer issues, particularly in the engineering field. The findings also can help researchers to gain a better understanding of heat transfer analysis and fluid flow properties. Full article
(This article belongs to the Special Issue Recent Advancements in Computational Fluid Mechanics and Heat Transfer)
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20 pages, 442 KiB  
Article
A Priori Estimates for the Solution of an Initial Boundary Value Problem of Fluid Flow through Fractured Porous Media
by Nurlana Alimbekova, Abdumauvlen Berdyshev and Dossan Baigereyev
Axioms 2022, 11(8), 408; https://doi.org/10.3390/axioms11080408 - 17 Aug 2022
Cited by 1 | Viewed by 1421
Abstract
The paper studies a model of fluid flow in a fractured porous medium in which fractures are distributed uniformly over the volume. This model includes a nonlinear equation containing several terms with fractional derivatives in the sense of Caputo of order belonging to [...] Read more.
The paper studies a model of fluid flow in a fractured porous medium in which fractures are distributed uniformly over the volume. This model includes a nonlinear equation containing several terms with fractional derivatives in the sense of Caputo of order belonging to the interval 1,2. The relevance of studying this problem is determined by its practical significance in the oil industry, since most of the world’s oil reserves are in these types of reservoirs. The uniqueness of the solution to the problem in a differential form and its dependence on the initial data and the right-hand side of the equation is proved. A numerical method is proposed based on the use of the finite difference approximation for integer and fractional time derivatives and the finite element method in the spatial direction. A change of variables is introduced to reduce the order of the fractional derivatives. Furthermore, the fractional derivative is approximated by using the L1-method. The stability and convergence of the proposed numerical method are rigorously proved. The theoretical order of convergence is confirmed by the results of numerical tests for a problem of fluid flow in fractured porous media with a known exact solution. Full article
(This article belongs to the Special Issue Recent Advancements in Computational Fluid Mechanics and Heat Transfer)
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