Mathematics

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9 pages, 254 KiB

Open AccessArticle

A Mathematically Exact and Well-Determined System of Equations to Close Reynolds-Averaged Navier–Stokes Equations

by Sungmin Ryu

Mathematics 2023, 11(24), 4926; https://doi.org/10.3390/math11244926 - 11 Dec 2023

Viewed by 1609

Since Sir Osborne Reynolds presented the Reynolds-averaged Navier–Stokes (RANS) equations in 1895, the construction of complete closure for RANS equations has been regarded as extremely challenging. Taking into account that the Navier–Stokes equations are not coherent for instantaneous and mean flows, a body [...] Read more.

Since Sir Osborne Reynolds presented the Reynolds-averaged Navier–Stokes (RANS) equations in 1895, the construction of complete closure for RANS equations has been regarded as extremely challenging. Taking into account that the Navier–Stokes equations are not coherent for instantaneous and mean flows, a body of knowledge outside the scope of classical mechanics may be amenable to the closure problem. In this regard, the methodology of physics-to-geometry transformation, which is coherent for both flows, is applied to RANS equations to construct six additional equations. The proposed equations stand out from existing RANS closure models and turbulence quantity transport equations in two respects: they are mathematically exact and well-determined. Full article

(This article belongs to the Special Issue New Advances in Analytical and Numerical Techniques in Fluid Mechanics)

29 pages, 6971 KiB

Open AccessArticle

Exploring the Influence of Induced Magnetic Fields and Double-Diffusive Convection on Carreau Nanofluid Flow through Diverse Geometries: A Comparative Study Using Numerical and ANN Approaches

by Shaik Jakeer, Seethi Reddy Reddisekhar Reddy, Sathishkumar Veerappampalayam Easwaramoorthy, Hayath Thameem Basha and Jaehyuk Cho

Mathematics 2023, 11(17), 3687; https://doi.org/10.3390/math11173687 - 27 Aug 2023

Cited by 7 | Viewed by 1317

Abstract

This current investigation aims to explore the significance of induced magnetic fields and double-diffusive convection in the radiative flow of Carreau nanofluid through three distinct geometries. To simplify the fluid transport equations, appropriate self-similarity variables were employed, converting them into ordinary differential equations. [...] Read more.

This current investigation aims to explore the significance of induced magnetic fields and double-diffusive convection in the radiative flow of Carreau nanofluid through three distinct geometries. To simplify the fluid transport equations, appropriate self-similarity variables were employed, converting them into ordinary differential equations. These equations were subsequently solved using the Runge–Kutta–Fehlberg (RKF) method. Through graphical representations like graphs and tables, the study demonstrates how various dynamic factors influence the fluid’s transport characteristics. Additionally, the artificial neural network (ANN) approach is considered an alternative method to handle fluid flow issues, significantly reducing processing time. In this study, a novel intelligent numerical computing approach was adopted, implementing a Levenberg–Marquardt algorithm-based MLP feed-forward back-propagation ANN. Data collection was conducted to evaluate, validate, and guide the artificial neural network model. Throughout all the investigated geometries, both velocity and induced magnetic profiles exhibit a declining trend for higher values of the magnetic parameter. An increase in the Dufour number corresponds to a rise in the nanofluid temperature. The concentration of nanofluid increases with higher values of the Soret number. Similarly, the nanofluid velocity increases with higher velocity slip parameter values, while the fluid temperature exhibits opposite behavior, decreasing with increasing velocity slip parameter values. Full article

(This article belongs to the Special Issue New Advances in Analytical and Numerical Techniques in Fluid Mechanics)

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20 pages, 4058 KiB

Open AccessArticle

MHD Thermal and Solutal Stratified Stagnation Flow of Tangent Hyperbolic Fluid Induced by Stretching Cylinder with Dual Convection

by Sushila Choudhary, Prasun Choudhary, Nazek Alessa and Karuppusamy Loganathan

Mathematics 2023, 11(9), 2182; https://doi.org/10.3390/math11092182 - 5 May 2023

Cited by 11 | Viewed by 1887

Abstract

The magneto-hydrodynamic dual convection stagnation flow pattern behavior of a Tangent Hyperbolic (TH) fluid has been reported in this study. The radiation, Joule heating, and heat generation/absorption impacts have also been analyzed. The flow-narrating differential equations, which are constrained by a thermal and [...] Read more.

The magneto-hydrodynamic dual convection stagnation flow pattern behavior of a Tangent Hyperbolic (TH) fluid has been reported in this study. The radiation, Joule heating, and heat generation/absorption impacts have also been analyzed. The flow-narrating differential equations, which are constrained by a thermal and solutal stratified porous medium, are transmuted into a system of nonlinear differential equations. To provide a numerical solution to the flow problem, a computational model is created. Numerical solutions are obtained using the fifth-order exactness program (Bvp5c), and for validation of the results, a comparison is also made with the methodology of the Runge–Kutta fourth order. The physical implications are appraised and depicted using diagrams or tables against flow-controlling parameters, such as Hartmann number, porosity parameter, solutal stratification, the parameter of curvature, temperature stratification, local Weissenberg number, Schmidt number, etc. It has been observed that in the appearance of Joule heating phenomena, the fluid temperature is a lowering function of thermal stratification. The findings are compared to the existing literature and found to be consistent with earlier research. Full article

(This article belongs to the Special Issue New Advances in Analytical and Numerical Techniques in Fluid Mechanics)

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18 pages, 6129 KiB

Open AccessArticle

Effect of Thermal Radiation and Variable Viscosity on Bioconvective and Thermal Stability of Non-Newtonian Nanofluids under Bidirectional Porous Oscillating Regime

by Lioua Kolsi, Kamel Al-Khaled, Sami Ullah Khan and Nidhal Ben Khedher

Mathematics 2023, 11(7), 1600; https://doi.org/10.3390/math11071600 - 26 Mar 2023

Cited by 8 | Viewed by 1398

Abstract

The bioconvective flow of a Jeffrey fluid conveying tiny particles under the effect of an oscillating stretched bidirectional surface is considered in this paper. The effects of thermal radiation and a porous medium are also investigated. The Cattaneo–Christov diffusion theories are used to [...] Read more.

The bioconvective flow of a Jeffrey fluid conveying tiny particles under the effect of an oscillating stretched bidirectional surface is considered in this paper. The effects of thermal radiation and a porous medium are also investigated. The Cattaneo–Christov diffusion theories are used to analyze the heat and mass transfer phenomena. The activation energy effects are included in the concentration equation. The solved dimensionless equations system is established, based on non-dimensional variables. The analytical findings are evaluated using the homotopic analysis technique. The convergence of solutions is ensured. The results are validated by already available published findings and a good concordance is encountered. The fundamental physical aspect of flow parameters is graphically evaluated. The main results reveal that the velocity is reduced by increasing the permeability of the porous medium. An increase in the temperature occurs when the viscosity of the fluid is varied. The obtained results can be useful in thermal systems, energy production, heat transfer devices, solar systems, biofuels, fertilizers, etc. Full article

(This article belongs to the Special Issue New Advances in Analytical and Numerical Techniques in Fluid Mechanics)

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15 pages, 6964 KiB

Open AccessArticle

Darcy–Brinkman Double Diffusive Convection in an Anisotropic Porous Layer with Gravity Fluctuation and Throughflow

by Gangadharaiah Yeliyur Honnappa, Manjunatha Narayanappa, Ramalingam Udhayakumar, Barakah Almarri, Ahmed M. Elshenhab and Nagarathnamma Honnappa

Mathematics 2023, 11(6), 1287; https://doi.org/10.3390/math11061287 - 7 Mar 2023

Cited by 8 | Viewed by 1337

Abstract

The influence of the throughflow and gravity fluctuation on thermosolutal convection in an anisotropic porous bed with the Darcy–Brinkman effect is considered numerically. The critical Rayleigh numbers for the onset of stationary and oscillatory modes have been found via linear instability analysis. The [...] Read more.

The influence of the throughflow and gravity fluctuation on thermosolutal convection in an anisotropic porous bed with the Darcy–Brinkman effect is considered numerically. The critical Rayleigh numbers for the onset of stationary and oscillatory modes have been found via linear instability analysis. The impact of various gravitational functions in the presence of throughflow on stability is studied. The analysis has been carried out for decreasing and increasing gravity fluctuations. The convective problem has been numerically analyzed using a single-term Galerkin approach. The results show that the mechanical anisotropy parameter and Lewis number have a destabilizing effect, while the thermal anisotropy parameter, Darcy number, solutal Rayleigh number, throughflow parameter, and gravity parameter have a stabilizing effect on stationary and oscillatory convection. It is clear that the system changes in a way that makes it more stable for case (iii) gravity fluctuation and more unstable for case (iv) gravity fluctuation. Full article

(This article belongs to the Special Issue New Advances in Analytical and Numerical Techniques in Fluid Mechanics)

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19 pages, 1363 KiB

Open AccessArticle

Performance of Heat Transfer in Micropolar Fluid with Isothermal and Isoflux Boundary Conditions Using Supervised Neural Networks

by Muhammad Sulaiman, Naveed Ahmad Khan, Fahad Sameer Alshammari and Ghaylen Laouini

Mathematics 2023, 11(5), 1173; https://doi.org/10.3390/math11051173 - 27 Feb 2023

Cited by 21 | Viewed by 2264

Abstract

The current study delivers a numerical investigation on the performance of heat transfer and flow of micropolar fluid in porous Darcy structures with isothermal and isoflux walls (boundary conditions) of a stretching sheet. The dynamics and mechanism of such fluid flows are modelled [...] Read more.

The current study delivers a numerical investigation on the performance of heat transfer and flow of micropolar fluid in porous Darcy structures with isothermal and isoflux walls (boundary conditions) of a stretching sheet. The dynamics and mechanism of such fluid flows are modelled by nonlinear partial differential equations that are reduced to a system of nonlinear ordinary differential equations by utilizing the porosity of medium and similarity functions. Generally, the explicit or analytical solutions for such nonlinear problems are hard to calculate. Therefore, we have designed a computer or artificial intelligence-based numerical technique. The reliability of neural networks using the machine learning (ML) approach is used with a local optimization technique to investigate the behaviours of different material parameters such as the Prandtl number, micropolar parameters, Reynolds number, heat index parameter, injection/suction parameter on the temperature profile, fluid speed, and spin/rotational behaviour of the microstructures. The approximate solutions determined by the efficient machine learning approach are compared with the classical Runge–Kutta fourth-order method and generalized finite difference approximation on a quasi-uniform mesh. The accuracy of the errors lies around 10⁻⁸ to 10⁻¹⁰ between the traditional analytical solutions and machine learning strategy. ML-based techniques solve different problems without discretization or computational work, and are not subject to the continuity or differentiability of the governing model. Moreover, the results are illustrated briefly to help implement microfluids in drug administering, elegans immobilization, and pH controlling processes. Full article

(This article belongs to the Special Issue New Advances in Analytical and Numerical Techniques in Fluid Mechanics)

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21 pages, 9344 KiB

Open AccessArticle

Insights into the 3D Slip Dynamics of Jeffrey Fluid Due to a Rotating Disk with Exponential Space-Dependent Heat Generation: A Case Involving a Non-Fourier Heat Flux Model

by Ali Saleh Alshomrani

Mathematics 2023, 11(5), 1096; https://doi.org/10.3390/math11051096 - 22 Feb 2023

Cited by 1 | Viewed by 1369

Abstract

The dynamics of non-Newtonian Jeffrey fluid in conjunction with a spinning disk surface can be problematic in heating systems, polymer technology, microelectronics, advanced technology, and substantive disciplines. Therefore, the significance of the Hall current and Coriolis forces in terms of the dynamics of [...] Read more.

The dynamics of non-Newtonian Jeffrey fluid in conjunction with a spinning disk surface can be problematic in heating systems, polymer technology, microelectronics, advanced technology, and substantive disciplines. Therefore, the significance of the Hall current and Coriolis forces in terms of the dynamics of Jeffrey fluid flowing across a gyrating disk subject to non-Fourier heat flux was investigated in this study. A temperature-related heat source (TRHS) and exponential-related heat source (ERHS) were incorporated into the model to improve the thermal characteristics. Thermal radiation and multiple slip effects were employed in the flow system. The connected non-linear PDEs governing the transport were transmuted into non-linear ODEs and solved using the Runge–Kutta shooting technique (RKST). The results of the RKST were substantiated in previous studies and found to have adequate reliability. The numerical values of the coefficient of friction and the Nusselt number were simulated. The non-Fourier heat flux was found to have a higher rate of heat transfer (HTR) than with traditional Fourier heat flux. Furthermore, both TRHS and ERHS phenomena support the progression of HTR. The swelling effects of the Hall current influence the velocities, whilst the temperature of the Jeffrey fluid shows the opposite tendency. Furthermore, asymptotic variances were detected for larger Hall parameter values. Full article

(This article belongs to the Special Issue New Advances in Analytical and Numerical Techniques in Fluid Mechanics)

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21 pages, 2850 KiB

Open AccessArticle

Modified Finite Element Study for Heat and Mass Transfer of Electrical MHD Non-Newtonian Boundary Layer Nanofluid Flow

by Muhammad Shoaib Arif, Wasfi Shatanawi and Yasir Nawaz

Mathematics 2023, 11(4), 1064; https://doi.org/10.3390/math11041064 - 20 Feb 2023

Cited by 6 | Viewed by 1988

Abstract

Research into the effects of different parameters on flow phenomena is necessary due to the wide range of potential applications of non-Newtonian boundary layer nanofluid flow, including but not limited to production industries, polymer processing, compression, power generation, lubrication systems, food manufacturing, and [...] Read more.

Research into the effects of different parameters on flow phenomena is necessary due to the wide range of potential applications of non-Newtonian boundary layer nanofluid flow, including but not limited to production industries, polymer processing, compression, power generation, lubrication systems, food manufacturing, and air conditioning. Because of this impetus, we investigated non-Newtonian fluid flow regimes from the perspectives of both heat and mass transfer aspects. In this study, heat transfer of electrical MHD non-Newtonian flow of Casson nanofluid over the flat plate is investigated under the effects of variable thermal conductivity and mass diffusivity. Emerging problems occur as nonlinear partial differential equations (NPDEs) in opposition to the conservation laws of mass, momentum, heat, and species transportation. The shown problem can be recast as a set of ordinary differential equations by making the necessary changes. A modified finite element method is adopted to solve the obtained set of ODEs. The numerical method is based on Galerkin weighted residual approach, and Gauss–Legendre numerical integration is adopted in the modified finite element method application procedure. To clarify the obtained results, another numerical technique is employed to solve the reduced ODEs. With the help of error tables and the flowing behavior of complicated physical parameters on estimated solutions, this study graphically and tabulatively explains the convergence of analytic solutions. Comparing some of the obtained results with those given in past research is also done. From the obtained results, it is observed that the velocity profile escalates by improving the electric parameter. Our intention is for this paper to serve as a guide for academics in the future who will be tasked with addressing pressing issues in the field of industrial and engineering enclosures. Full article

(This article belongs to the Special Issue New Advances in Analytical and Numerical Techniques in Fluid Mechanics)

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27 pages, 14004 KiB

Open AccessArticle

Numerical Study of a Phase Change Material Energy Storage Tank Working with Carbon Nanotube–Water Nanofluid under Ha’il City Climatic Conditions

by Lioua Kolsi, Ahmed Kadhim Hussein, Walid Hassen, Lotfi Ben Said, Badreddine Ayadi, Wajdi Rajhi, Taher Labidi, Ali Shawabkeh and Katta Ramesh

Mathematics 2023, 11(4), 1057; https://doi.org/10.3390/math11041057 - 20 Feb 2023

Cited by 16 | Viewed by 2133

Abstract

A numerical investigation of a phase change material (PCM) energy storage tank working with carbon nanotube (CNT)–water nanofluid is performed. The study was conducted under actual climatic conditions of the Ha’il region (Saudi Arabia). Two configurations related to the absence or presence of [...] Read more.

A numerical investigation of a phase change material (PCM) energy storage tank working with carbon nanotube (CNT)–water nanofluid is performed. The study was conducted under actual climatic conditions of the Ha’il region (Saudi Arabia). Two configurations related to the absence or presence of conductive baffles are studied. The tank is filled by encapsulated paraffin wax as the PCM, and CNT–water nanofluid flows through the capsules. The main goal is to increase the temperature of the PCM to 70 °C in order to store the thermal energy, which can then be used during the night and cloudy weather. Numerical computations are made using the finite element method (FEM) based on actual measured weather conditions. Climate conditions were collected from a weather station located on the roof of the engineering college’s building at the University of Ha’il. The collected data served as input to the numerical model, and the simulations were performed for three months (December, March, and July). The solid CNT volume fraction range was (0 ≤ ϕ ≤ 0.05) and the nanofluid volume flow rate ranged was (0.5 L/min ≤ V ≤ 3 L/min). For both considered cases (with and without baffles), it was found that the use of CNT–nanofluid led to a reduction in the charging time and enhanced its performance. An increase in the volumetric flow rate was found to accelerate the melting process. The best performances of the storage tank occurred during July due to the highest solar irradiation. Furthermore, it was found that the use of baffles had no beneficial effects on the melting process. Full article

(This article belongs to the Special Issue New Advances in Analytical and Numerical Techniques in Fluid Mechanics)

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20 pages, 5863 KiB

Open AccessArticle

Numerical Investigation of Internal Flow Properties around Horizontal Layered Trees by Using the Reynolds Stress Model

by FAKHAR Muhammad Abbas, Norio Tanaka and Amina

Mathematics 2023, 11(3), 712; https://doi.org/10.3390/math11030712 - 31 Jan 2023

Viewed by 1665

Abstract

The aim of this article is to numerically explore the effects of a horizontal double layer of trees (HDLT) across the whole width of the channel on the flow structures under a steady flow rate and subcritical conditions. The numerical domain was established [...] Read more.

The aim of this article is to numerically explore the effects of a horizontal double layer of trees (HDLT) across the whole width of the channel on the flow structures under a steady flow rate and subcritical conditions. The numerical domain was established in ANSYS Workbench, and post-processing (i.e., meshing + boundary conditions) along with simulation was carried out by utilizing the computational fluid dynamics tool FLUENT. The three-dimensional (3D) Reynolds stress model and Reynolds-averaged Navier–Stokes equations were used to analyze the flow properties. The numerical model was first validated and then used for simulation purposes. Two varying configurations of HDLT were selected, represented as Arrangement 1 (tall emerged trees (T_t) + short submerged trees (S_t)) and Arrangement 2 (short submerged trees (S_t) + tall emerged trees (T_t)), along with different flow heights. The model accurately captured the simulated results, as evidenced by the vertical distributions of the velocity profiles and Reynolds stresses at specific locations. The strong inflection in velocity and Reynolds stress profiles was observed at the interface of S_t, contributing to turbulence and giving rise to vertical transportation of momentum between flow layers. While these profiles were almost constant from the beds to the tops of trees at those locations lying in taller trees (T_t), there was an approximate 31–65% increase in streamwise velocities at locations 1–6 in cases 1–2, along with a 54–77% increase at locations 7–10 in cases 3–4, in the unvegetated zone (Z > 0.035 m) compared to the vegetated zone (Z < 0.035 m). The magnitude of turbulence kinetic energy and the eddy dissipation rate were significantly larger inside the short submerged and tall emerged trees as compared to the unvegetated region, i.e., upstream and downstream regions. Similarly, the production of turbulence kinetic energy was approximately 50% and 70% greater inside the tree region (Z < 0.035 m) as compared to above the shorter trees during cases 1–2 and 3–4, respectively. Full article

(This article belongs to the Special Issue New Advances in Analytical and Numerical Techniques in Fluid Mechanics)

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16 pages, 3281 KiB

Open AccessArticle

Numerical Study of Thermo-Electric Conversion for TEG Mounted Wavy Walled Triangular Vented Cavity Considering Nanofluid with Different-Shaped Nanoparticles

by Fatih Selimefendigil, Mohamed Omri, Walid Aich, Hatem Besbes, Nidhal Ben Khedher, Badr M. Alshammari and Lioua Kolsi

Mathematics 2023, 11(2), 483; https://doi.org/10.3390/math11020483 - 16 Jan 2023

Cited by 2 | Viewed by 1766

Abstract

The effects of the combined utilization of wavy wall and different nanoparticle shapes in heat transfer fluid for a thermoelectric generator (TEG) mounted vented cavity are numerically analyzed. A triangular wave form of the cavity is used, while spherical and cylindrical-shaped alumina nanoparticles [...] Read more.

The effects of the combined utilization of wavy wall and different nanoparticle shapes in heat transfer fluid for a thermoelectric generator (TEG) mounted vented cavity are numerically analyzed. A triangular wave form of the cavity is used, while spherical and cylindrical-shaped alumina nanoparticles are used in water up to a loading amount of 0.03 as solid volume fraction. The impacts of wave amplitude on flow and output power features are significant compared to those of the wave number. The increment in the generated power is in the range of 74.48–92.4% when the wave amplitude is varied. The nanoparticle shape and loading amount are effective in the rise of the TEG power, while by using cylindrical-shaped nanoparticles, higher powers are produced as compared to spherical ones. The rise in the TEG power by the highest loading amount is achieved as 50.7% with cylindrical-shaped particles, while it is only 4% with spherical-shaped ones. Up to a 194% rise of TEG power is attained by using the triangular wavy form of the wall and including cylindrical-shaped nanoparticles as compared to a flat-walled cavity using only pure fluid. Full article

(This article belongs to the Special Issue New Advances in Analytical and Numerical Techniques in Fluid Mechanics)

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21 pages, 4205 KiB

Open AccessArticle

A Comparative Numerical Study of Heat and Mass Transfer Individualities in Casson Stagnation Point Fluid Flow Past a Flat and Cylindrical Surfaces

by Khalil Ur Rehman, Wasfi Shatanawi and Saba Yaseen

Mathematics 2023, 11(2), 470; https://doi.org/10.3390/math11020470 - 16 Jan 2023

Cited by 17 | Viewed by 2154

Abstract

There is a consensus among researchers that the simultaneous involvement of heat and mass transfer in fluid flow owns numerous daily life applications like energy systems, automobiles, cooling of electronic devices, power generation by the stream, electric power, and diagnosing and characterizing diseases, [...] Read more.

There is a consensus among researchers that the simultaneous involvement of heat and mass transfer in fluid flow owns numerous daily life applications like energy systems, automobiles, cooling of electronic devices, power generation by the stream, electric power, and diagnosing and characterizing diseases, to mention just a few. Owing to such motivation, we considered both heat and mass transfer aspects in non-Newtonian fluid flow regimes. The Casson fluid is considered as a non-Newtonian fluid. For better novelty the flow is considered at both flat and cylindrical surfaces along with stagnation point, magnetic field, mixed convection, heat generation, viscous dissipation, thermal radiations, and temperature-dependent thermal conductivity. The ultimate differential equations are nonlinear, and hence difficult to solve analytically. Therefore, a numerical scheme, namely the shooting method with the Runge–Kutta algorithm, is adopted to report an acceptable solution for flow field description. The outcomes are shared comparatively for flat and cylindrical surfaces. We have seen that compared to a flat surface, the cylindrical surface has a larger Nusselt number magnitude. Full article

(This article belongs to the Special Issue New Advances in Analytical and Numerical Techniques in Fluid Mechanics)

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16 pages, 7832 KiB

Open AccessArticle

Numerical Investigation of a Rotating Magnetic Field Influence on Free Convective CNT/Water Nanofluid Flow within a Corrugated Enclosure

by Khalid B. Saleem, Mohamed Omri, Walid Aich, Badr M. Alshammari, Hatem Rmili and Lioua Kolsi

Mathematics 2023, 11(1), 18; https://doi.org/10.3390/math11010018 - 21 Dec 2022

Cited by 4 | Viewed by 1614

Abstract

This paper emphasizes the effect of applying a rotating magnetic field on the natural convective flow of CNT/Water nanofluid inside a corrugated square cavity differentially heated through its sidewalls, while the upper and lower boundaries are supposed to be perfectly insulated. The aim [...] Read more.

This paper emphasizes the effect of applying a rotating magnetic field on the natural convective flow of CNT/Water nanofluid inside a corrugated square cavity differentially heated through its sidewalls, while the upper and lower boundaries are supposed to be perfectly insulated. The aim of this study is to highlight the impact of a large variety of parameters, namely Hartman number, frequency of rotation, Rayleigh number, nanoparticles volume fraction, and corrugation aspect ratio on the flow behaviour and thermal transport characteristics. The governing non-linear coupled differential equations are solved by using the finite element technique. Outcomes indicated that the thermal energy exchange is improved with the Rayleigh number increment and nanoparticles loading, while it is weakened with the rising of Ha, ascribed to the Lorentz force opposition to buoyancy. Moreover, enlarging the corrugation aspect ratio causes the apparition of stagnant fluid zones and the rate of heat transfer is reduced as a result. Full article

(This article belongs to the Special Issue New Advances in Analytical and Numerical Techniques in Fluid Mechanics)

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20 pages, 3130 KiB

Open AccessArticle

Investigation of Mixed Convection in Spinning Nanofluid over Rotating Cone Using Artificial Neural Networks and BVP-4C Technique

by Ali Hassan, Qusain Haider, Najah Alsubaie, Fahad M. Alharbi, Abdullah Alhushaybari and Ahmed M. Galal

Mathematics 2022, 10(24), 4833; https://doi.org/10.3390/math10244833 - 19 Dec 2022

Cited by 4 | Viewed by 1816

Abstract

The significance of back-propagated intelligent neural networks (BINs) to investigate the transmission of heat in spinning nanofluid over a rotating system is analyzed in this study. The buoyancy effect is incorporated along with the constant thermophysical properties of nanofluids. Levenberg–Marquardt intelligent networks (ANNLMBs) [...] Read more.

The significance of back-propagated intelligent neural networks (BINs) to investigate the transmission of heat in spinning nanofluid over a rotating system is analyzed in this study. The buoyancy effect is incorporated along with the constant thermophysical properties of nanofluids. Levenberg–Marquardt intelligent networks (ANNLMBs) are employed to study heat transmission by using a trained artificial neural network. The system of highly non-linear flow governing partial differential equations (PDEs) is transformed into ordinary differential equations (ODEs) which is taken as a system model. This achieved system model is utilized to generate data set using the “Adams” method for distinct scenarios of heat transmission investigation in a spinning nanofluid over a rotating system for the implementation of the proposed ANNLMB. Additionally, with the help of training, testing, and validation, the approximate solution of heat transmission in a spinning nanofluid in a rotating system is obtained using a BNN-based solver. The generated reference data achieved employing the proposed artificial neural network based on a Levenberg–Marquardt intelligent network is distributed in the following manner: training at 82%, testing at 9%, and validation at 9%. Furthermore, MSE, histograms, and regression analyses are performed to depict and discuss the impact of the varying influence of key parameters, such as unsteadiness “s” in spinning flow, Prandtl number effect “pr”, the rotational ratio of nanofluid and cone

α_{1}

and buoyancy effect

γ_{1}

on velocities

F^{'} G

and temperature

Θ

profiles. The mean square error confirms the accuracy of the achieved results. Prandtl number and unsteadiness decrease the temperature profile and thermal boundary layer of the rotating nanofluid. Full article

(This article belongs to the Special Issue New Advances in Analytical and Numerical Techniques in Fluid Mechanics)

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16 pages, 2619 KiB

Open AccessArticle

Linear and Energy-Stable Method with Enhanced Consistency for the Incompressible Cahn–Hilliard–Navier–Stokes Two-Phase Flow Model

by Qiming Huang and Junxiang Yang

Mathematics 2022, 10(24), 4711; https://doi.org/10.3390/math10244711 - 12 Dec 2022

Cited by 1 | Viewed by 1889

Abstract

The Cahn–Hilliard–Navier–Stokes model is extensively used for simulating two-phase incompressible fluid flows. With the absence of exterior force, this model satisfies the energy dissipation law. The present work focuses on developing a linear, decoupled, and energy dissipation-preserving time-marching scheme for the hydrodynamics coupled [...] Read more.

The Cahn–Hilliard–Navier–Stokes model is extensively used for simulating two-phase incompressible fluid flows. With the absence of exterior force, this model satisfies the energy dissipation law. The present work focuses on developing a linear, decoupled, and energy dissipation-preserving time-marching scheme for the hydrodynamics coupled Cahn–Hilliard model. An efficient time-dependent auxiliary variable approach is first introduced to design equivalent equations. Based on equivalent forms, a BDF2-type linear scheme is constructed. In each time step, the unique solvability and the energy dissipation law can be analytically estimated. To enhance the energy stability and the consistency, we correct the modified energy by a practical relaxation technique. Using the finite difference method in space, the fully discrete scheme is described, and the numerical solutions can be separately implemented. Numerical results indicate that the proposed scheme has desired accuracy, consistency, and energy stability. Moreover, the flow-coupled phase separation, the falling droplet, and the dripping droplet are well simulated. Full article

(This article belongs to the Special Issue New Advances in Analytical and Numerical Techniques in Fluid Mechanics)

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26 pages, 9935 KiB

Open AccessArticle

Analytical Modeling of Multistage Hydraulically Fractured Horizontal Wells Producing in Multilayered Reservoirs with Inter-Layer Pure-Planar Crossflow Using Source/Sink Function Method

by Chang Su, Wanju Yuan and Gang Zhao

Mathematics 2022, 10(24), 4680; https://doi.org/10.3390/math10244680 - 9 Dec 2022

Cited by 1 | Viewed by 1709

Abstract

This study presents a comprehensive analytical modeling technology to model transient behaviors of multilayered reservoirs with inter-layer pure-planar crossflow induced by multi-stage hydraulically fractured horizontal well (MHFHW). The objective of this study is to develop an analytical model for multilayered reservoirs in conjunction [...] Read more.

This study presents a comprehensive analytical modeling technology to model transient behaviors of multilayered reservoirs with inter-layer pure-planar crossflow induced by multi-stage hydraulically fractured horizontal well (MHFHW). The objective of this study is to develop an analytical model for multilayered reservoirs in conjunction with complex MHFHW and to achieve not only accurate and efficient computation, but also well-organized solutions expressed in a systematically integrated manner. The consideration of inter-layer crossflow across adjacent layers sets up the foundation for successful modeling of multilayered reservoirs. Source/sink function method (SSFM) is applied to describe fluid flow. Unsteady-state pressure or production rate solutions of MHFHW with the advantages of fast computation, accurate, and stable solutions are achieved. Comparative and consistent outcomes generated by this work and widely applied industry software have largely enhanced our technical confidence. More importantly, innovatively defined modified dimensionless terms that integrate systematic well-reservoir geometry information, as well as rock/fluid properties of each layer, have been newly applied to regulate the new modified dimensionless rate decline curve. This new technique sheds light on the reservoir characterization practice for complicated reservoir systems. Theoretical results in terms of transient pressure and rate were generated by the proposed multilayered model (SSFM-ML) for five scenarios of general concern, under various reservoir and well parameters, which were examined and discussed to demonstrate technical robustness. Not only does this study give solutions to the targeted multiple layered reservoirs, but it also provides insights into modeling three-dimensional fluid flow in heterogeneous reservoir with complex well configurations. It is recommended that future research should be conducted for more complicated two- and three-dimensional reservoirs, using the similar strategy of developing new type curves through adopting other new forms of modified dimensionless rate and time terms. Full article

(This article belongs to the Special Issue New Advances in Analytical and Numerical Techniques in Fluid Mechanics)

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20 pages, 723 KiB

Open AccessArticle

Note on the Numerical Solutions of Unsteady Flow and Heat Transfer of Jeffrey Fluid Past Stretching Sheet with Soret and Dufour Effects

by Hossam A. Nabwey, Muhammad Mushtaq, Muhammad Nadeem, Muhammad Ashraf, Ahmed M. Rashad, Sumayyah I. Alshber and Miad A. Hawsah

Mathematics 2022, 10(24), 4634; https://doi.org/10.3390/math10244634 - 7 Dec 2022

Cited by 5 | Viewed by 1898

Abstract

A numerical investigation of unsteady boundary layer flow with heat and mass transfer of non-Newtonian fluid model, namely, Jeffrey fluid subject, to the significance of Soret and Dufour effects is carried out by using the local nonsimilarity method and homotopy analysis method. An [...] Read more.

A numerical investigation of unsteady boundary layer flow with heat and mass transfer of non-Newtonian fluid model, namely, Jeffrey fluid subject, to the significance of Soret and Dufour effects is carried out by using the local nonsimilarity method and homotopy analysis method. An excellent agreement in the numerical results obtained by both methods is observed and we establish a new mathematical approach to obtain the solutions of unsteady-state flow with heat and mass transfer phenomenons. Similarity transformation is applied to governing boundary layer partial differential equations to obtain the set of self-similar, nondimensional partial differential equations. Graphical results for different emerging parameters are discussed. The dimensionless quantities of interest skin friction coefficient, Sherwood number, and Nusselt number are discussed through tabulated results. The main novelty of the current work is that the average residual error of the

m t h

-order approximation of the OHAM scheme for steady-state solution is decreased for higher-order approximation. Further, a rapid development of the boundary layer thickness with the increasing values of dimensionless time

τ

is observed. It is noted that for large values of

τ

, the steady state in the flow pattern is gained. It is worth mentioning that the magnitude of Sherwood number is increased with the increasing values of Schmidt number

S c

and Dufour number

D_{f}

. The magnitude of local Nisselt number is increased for the increasing values of Soret number,

S r

. Full article

(This article belongs to the Special Issue New Advances in Analytical and Numerical Techniques in Fluid Mechanics)

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18 pages, 2971 KiB

Open AccessArticle

Energy Transfer through a Magnetized Williamson Hybrid Nanofluid Flowing around a Spherical Surface: Numerical Simulation

by Oruba Ahmad Saleh Alzu’bi, Firas A. Alwawi, Mohammed Z. Swalmeh, Ibrahim Mohammed Sulaiman, Abdulkareem Saleh Hamarsheh and Mohd Asrul Hery Ibrahim

Mathematics 2022, 10(20), 3823; https://doi.org/10.3390/math10203823 - 16 Oct 2022

Cited by 8 | Viewed by 1320

Abstract

A computational simulation of Williamson fluid flowing around a spherical shape in the case of natural convection is carried out. The Lorentz force and constant wall temperature are taken into consideration. In addition, upgrader heat transfer catalysts consisting of multi-walled carbon tubes, molybdenum [...] Read more.

A computational simulation of Williamson fluid flowing around a spherical shape in the case of natural convection is carried out. The Lorentz force and constant wall temperature are taken into consideration. In addition, upgrader heat transfer catalysts consisting of multi-walled carbon tubes, molybdenum disulfide, graphene oxide, and molybdenum disulfide are employed. The Keller box approach is used to solve the mathematical model governing the flow of hybrid Williamson fluid. To validate our findings, the key parameters in the constructed model are set to zero. Next, the extent of the agreement between our results and published results is observed. Numerical and graphical results that simulate the impressions of key parameters on physical quantities related to energy transmission are obtained, discussed, and analyzed. According to the results of this study, increasing the value of the Weissenberg number causes an increase in both the fluid temperature and drag force, while it also leads to a decrease in both the velocity of the fluid and the rate of energy transmission. Increasing the magnetic field intensity leads to a reduction in the rate of heat transfer, drag force, and fluid velocity while it has an appositive effect on temperature profiles. Full article

(This article belongs to the Special Issue New Advances in Analytical and Numerical Techniques in Fluid Mechanics)

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13 pages, 736 KiB

Open AccessArticle

Estimation of Heat Diffusion in Human Tissue at Adverse Temperatures Using the Cylindrical Form of Bioheat Equation

by Javid Gani Dar, Mir Aijaz, Ibrahim M. Almanjahie and Arundhati Warke

Mathematics 2022, 10(20), 3820; https://doi.org/10.3390/math10203820 - 16 Oct 2022

Cited by 1 | Viewed by 1882

Abstract

Background: The assessment of the evolution or fall of the temperature distribution of all biological tissues, and particularly human in vivo tissues at adverse temperatures, is crucial because excess cold or heat can impair the human body and its physiological processes. However, [...] Read more.

Background: The assessment of the evolution or fall of the temperature distribution of all biological tissues, and particularly human in vivo tissues at adverse temperatures, is crucial because excess cold or heat can impair the human body and its physiological processes. However, this estimation through experimental investigations is challenging due to the ability of the human body to bear a wide range of unfavourable temperatures. Thus, it becomes imperative to frame a mathematical model and its solution for the measurement of the temperature distribution in the selected tissue. Method: The three-dimensional cylindrical bioheat equation, with initial and boundary conditions, was used to formulate a mathematical model. The model was solved using the variables-separable method. Results: The model was solved analytically, and MATLAB software was used for numerical calculations and a graphical representation. The model was applied to display the temperature distributions in human skin and in the head. Conclusions: The paper helps predict the distribution of heat and corresponding burn or cold injuries in human tissue well in advance of applying any thermal treatment such as targeted tumour hyperthermia or cryosurgery. Full article

(This article belongs to the Special Issue New Advances in Analytical and Numerical Techniques in Fluid Mechanics)

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19 pages, 6209 KiB

Open AccessArticle

Comparative Study on Rosseland’s Heat Flux on Three-Dimensional MHD Stagnation-Point Multiple Slip Flow of Ternary Hybrid Nanofluid over a Stretchable Rotating Disk

by Gaurav Gupta and Puneet Rana

Mathematics 2022, 10(18), 3342; https://doi.org/10.3390/math10183342 - 15 Sep 2022

Cited by 24 | Viewed by 2052

Abstract

This article investigates the three-dimensional magneto stagnation-point flow of ternary hybrid nanofluid caused by a radially extended infinite gyrating disk with multiple slip effects. The main concern is to analyze the characteristics of heat transport when linear thermal radiation (LTR), quadratic thermal radiation [...] Read more.

This article investigates the three-dimensional magneto stagnation-point flow of ternary hybrid nanofluid caused by a radially extended infinite gyrating disk with multiple slip effects. The main concern is to analyze the characteristics of heat transport when linear thermal radiation (LTR), quadratic thermal radiation (QTR), and full nonlinear thermal radiation (FNTR) are significant. Ternary fluid is a composition of water, spherical-shaped silver, cylindrical-shaped aluminum oxide, and platelet-shaped aluminum nanoparticles. Non-uniform heat source effects are taken into account. The governing equations are constructed using a single-phase nanofluid model using boundary layer theory and von Karman variables. The consequent nonlinear problem is solved with an efficient finite element method and the results are verified with the available data. The Nusselt number and friction factors are computed for both clean fluid and ternary nanofluid subjected to three different forms of Rosseland’s thermal radiation. Our results demonstrate that the rate of heat transport (Nusselt number) is higher in the FNTR case than in QTR and LTR, and it is even higher for ternary nanofluid compared to clean fluid. Further, the heat transport rate gets reduced for a higher heat source parameter. The rotation of the disk escalates the shear stress along both the radial and axial directions. The multiple slip boundary conditions lead to condensed boundary layers over a disk surface. Full article

(This article belongs to the Special Issue New Advances in Analytical and Numerical Techniques in Fluid Mechanics)

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