Article
Mathematics, Applied
Tran Dinh Ke, Lam Tran Phuong Thuy, Pham Thanh Tuan
Summary: We address the problem of identifying a source term in the Rayleigh-Stokes type equation with a nonlinear perturbation. The nonlinearity may exhibit superlinear growth and an additional measurement is provided at the final time and depends on the state. Our objective is to establish the unique solvability and stability of the solution. Additionally, we demonstrate that the obtained solution is differentiable and is the strong solution.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2022)
Article
Mathematics, Applied
Bo Yu
Summary: This paper proposes a high-order efficient numerical method for the generalized fractional Oldroyd-B fluid model and conducts numerical experiments to demonstrate its computational efficiency and accuracy, proving stability and convergence.
JOURNAL OF APPLIED MATHEMATICS AND COMPUTING
(2021)
Article
Mathematics, Applied
Weiping Bu, Huimin Yang, Yifa Tang
Summary: This paper proposes two fast and efficient numerical methods for a generalized Oldroyd-B fluid model with fractional derivatives. Fast evaluations of the Riemann-Liouville fractional derivatives are developed using convolution quadrature generated by the backward Euler and the second-order backward difference methods. Two fully discrete schemes are established for the considered problem by using these fast algorithms in time and employing the finite element method in space. The error estimates of these numerical schemes are discussed based on the property of the initial value and the right-hand function, without assuming the regularity of the exact solution. Numerical tests are presented to verify the effectiveness of the numerical schemes and confirm the theoretical results.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2023)
Article
Thermodynamics
Chen Yin, Zhiman Luan, Shaowei Wang
Summary: This paper investigates the linear stability analysis of Rayleigh-Marangoni-Benard convection with a deformable surface in a fluid overlying a highly porous layer. The study examines the oscillatory mode of both Rayleigh and Marangoni instabilities for non-Newtonian fluids, finding that a deformable upper surface destabilizes the system. The influence of various parameters on the stability of the system is discussed, including the depth ratio, Biot number, Galileo number, strain retardation time, stress relaxation time, and Marangoni number.
INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER
(2023)
Article
Engineering, Multidisciplinary
Aamir Ali, Javairia Akhtar, H. J. Anjum, M. Awais, Zahir Shah, Poom Kumam
Summary: Fluid motion can be caused by surface stretching, temperature or concentration differences. This study focuses on the 3D nanofluid flow due to expanding surface of Oldroyd-B fluid. The impact of various parameters on flow field is explored using nonlinear coupled ODE's and homotopy analysis method.
AIN SHAMS ENGINEERING JOURNAL
(2021)
Article
Mathematics, Applied
Jing Na Wang, Yong Zhou, Jia Wei He
Summary: In this paper, the fractional nonlinear Rayleigh-Stokes problem with final value condition is studied. The compactness of solution operators is obtained through finite dimensional approximation. The existence of solutions is established in weighted continuous function spaces, and regularization is achieved using the quasi-boundary value method due to ill posedness of the backward problem.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Materials Science, Multidisciplinary
Mahantesh S. Swamy, B. N. Hanumagowda, Umair Khan, K. Vidyashree, Ahmed M. Hassan, Abdulkafi Mohammed Saeed, Ranvijay Kumar
Summary: This study investigates the effect of internal heat source on thermal convection in an anisotropic horizontal porous layer saturated with viscoelastic liquids of the Oldroyd-B type. The anisotropy of the porous layer is considered by using a modified Darcy-Oldroyd model as the momentum equation. The energy equation is formulated to easily identify the influence of internal heat sources and anisotropy in thermal diffusivity on the stability criterion. Linear stability analysis is used to investigate the effects of anisotropy, viscoelasticity, and internal heat generation on the onset of thermal convection. Nonlinear stability analysis with the truncated Fourier series method is applied to study both steady and unsteady finite-amplitude convections and the effect of different governing parameters on the system's stability and convective heat transfer. The findings of this study have significant implications for various real-world applications, including oil reservoir modeling, crude oil extraction, crystal growth, pharmaceutical and medical industries, and geothermal energy utilization.
FRONTIERS IN MATERIALS
(2023)
Article
Engineering, Multidisciplinary
Talha Anwar, Poom Kumam, Asifa, Phatiphat Thounthong, Shah Muhammad, Faisal Zaid Duraihem
Summary: This article examines the influences of Newtonian heating and slip effects on unsteady magnetohydrodynamic flow of an Oldroyd-B fluid near a plate, considering the normal direction thermal radiation influence. Caputo-Fabrizio fractional derivative and numerical algorithms are applied to develop solutions, and the Nusselt number and skin friction coefficient relations are computed efficiently. The study compares the memory effects explanation between the Caputo-Fabrizio fractional model and classical models.
ALEXANDRIA ENGINEERING JOURNAL
(2022)
Article
Mathematics, Applied
Omer Oruc
Summary: This paper presents an efficient numerical method for solving the two-dimensional fractional Rayleigh-Stokes problem for a heated generalized second grade fluid. The method is proven to be accurate and workable through numerical simulations.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2022)
Article
Chemistry, Multidisciplinary
Yingzi Jiang, Juan Zhang, Thabet Abdeljawad, Shafiq Ahmad, Muhammad Naveed Khan, Aysha Rehman, Abdulrazak H. Almaliki, Ahmed S. El-Shafay
Summary: The effect of Stefan blowing on the Cattaneo-Christov characteristics of the Blasius-Rayleigh-Stokes flow of self-motive Ag-MgO/water hybrid nanofluids with convective boundary conditions and a microorganism density is investigated in this study. The mathematical models are transformed into self-similarity equations and solved numerically to study the fluid flow, energy, and mass transfer features under different parameter values. The results show that the increase in certain parameters has a positive influence on the liquid velocity and boundary layer thickness.
Article
Engineering, Multidisciplinary
Moslem Uddin, Abdullah Murad
Summary: This paper mathematically analyzes the unsteady motion of a two-layer fluid induced by the oscillatory motion of a flat plate. The results obtained are new and complete, including the calculation of shear stresses at the boundaries. Physical insights into the flows of the particular problems are gained through illustrations.
ALEXANDRIA ENGINEERING JOURNAL
(2022)
Article
Computer Science, Interdisciplinary Applications
Bander Almutairi, Muhammad Kamran, Aamir Farooq, Hijaz Ahmad, Azeem Shahzad, Farman Ullah Khan, Ali Sikandar Khan, Bandar Almohsen
Summary: The study focuses on examining the flow formation of non-Newtonian fluids in a cylindrical annulus region using Taylor-Couette flow. The inner cylinder is subjected to imposed stresses while the outer cylinder remains inert. The velocity field and shear stresses of the fractional Oldroyd-B fluid are obtained using Hankel transform and Laplace transform. Graphical comparisons are made to evaluate the effects of different parameters on fluid motion.
INTERNATIONAL JOURNAL OF MODERN PHYSICS C
(2022)
Article
Mathematics, Applied
Ngoc Tran Bao, Luc Nguyen Hoang, Au Vo Van, Huy Tuan Nguyen, Yong Zhou
Summary: This paper explores an inverse problem for fractional Rayleigh-Stokes equations with non-linear source, where the fractional derivative in time is taken in the sense of Riemann-Liouville. The problem has various applications in non-Newtonian fluids, and the paper provides results on the existence and regularity of mild solutions.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Thermodynamics
Mukesh Kumar Awasthi
Summary: This paper examines the linear stability of the interface formed by a viscoelastic liquid and a viscous gas, considering the significant influence of heat and mass transfer at the interface. The effects of various physical parameters on the stability of the liquid/gas interface are investigated through theoretical and graphical analysis in the study.
INTERNATIONAL JOURNAL OF THERMAL SCIENCES
(2021)
Article
Mathematics, Applied
Yong Zhou, Jing Na Wang
Summary: The paper investigates the existence of solutions for the nonlinear Rayleigh-Stokes problem for a generalized second grade fluid with Riemann-Liouville fractional derivative. It demonstrates that the solution operator of the problem is compact and continuous in the uniform operator topology, and provides an existence result of mild solutions for the nonlinear problem.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Chemistry, Multidisciplinary
Ying Wang, Muhammad Waheed, Muhammad Kamran Jamil, Syed Mazhar Shah, Adnan Aslam, Hamideh Aram
Summary: This paper investigates the impact of the subdivision double-corona product of graphs on topological indices, specifically the first and second Zagreb indices, first reformulated Zagreb index, and forgotten topological index (F-index).
JOURNAL OF CHEMISTRY
(2022)
Article
Mathematics
Muhammad Kamran Jamil, Aisha Javed, Ebenezer Bonyah, Iqra Zaman
Summary: The paper investigates the upper and lower bounds of the zeroth-order general Randic index and the first general Zagreb index, and explores their relationships with connectivity, minimum degree, and independent number.
JOURNAL OF MATHEMATICS
(2022)
Article
Mathematics, Interdisciplinary Applications
Tulat Naeem, Muhammad Kamran Jamil, Khawaja Muhammad Fahd, Abdu AlAmeri
Summary: This research introduces the concept of the Wiener index WI under the structure of IFGs and investigates its relationship with the connectivity index CI. Furthermore, an application of the WI in transport network flow is proposed.
Article
Mathematics, Interdisciplinary Applications
Shehla Hameed, Muhammad Kamran Jamil, Muhammad Waheed, Muhammad Azeem, Senesie Swaray
Summary: Graph operations and topological descriptors play important roles in the study of complex networks, with topological descriptors being used to understand the characteristics of network graphs. This research extends the study on the first, second, first multiplicative, first reformulated Zagreb indices, and the forgotten index of subdivision double corona and subdivision double neighborhood corona products.
Article
Mathematics
Muhammad Azeem, Muhammad Kamran Jamil, Aisha Javed, Ali Ahmad
Summary: The concept of M-polynomials plays an important role in determining the algebraic form of a system or network. In this study, we focus on the abstract form of Y-shaped junctions and develop vertex-degree-based M-polynomial formulas. By introducing topological index-based concepts, we verify the existing results in the literature.
JOURNAL OF MATHEMATICS
(2022)
Article
Multidisciplinary Sciences
Constantin Fetecau, Dumitru Vieru
Summary: The governing equations for the fluid velocity and shear stress in isothermal MHD unidirectional motions of incompressible second-grade fluids through porous medium have identical forms, allowing for exact steady-state solutions with shear stress on the boundary. Closed-form expressions for fluid velocity, shear stress, and Darcy's resistance are provided, with results verified through solutions for motions over an infinite flat plate presented in different forms. The fluid behavior in motions between infinite parallel plates is symmetric with respect to the median plane due to boundary conditions.
Article
Computer Science, Information Systems
Sidra Bukhari, Muhammad Kamran Jamil, Muhammad Azeem, Senesie Swaray
Summary: This article discusses the design of p-type networks using CVNET and nano studio, and the study of resolvability parameters of patched networks such as metric dimension and edge metric dimension.
Article
Chemistry, Physical
Constantin Fetecau, Abdul Rauf, Tahir Mushtaq
Summary: The motion problems of Burgers fluids between parallel plates were investigated analytically and numerically, considering magnetic and porous effects and a differential expression of shear stress on the lower plate. Closed-form expressions were determined for the non-dimensional steady state velocity and shear stress fields, as well as the corresponding Darcy's resistances. These are the first exact solutions for hydromagnetic motions of Burgers fluids through porous media with a differential expression of shear stress on the boundary.
ZEITSCHRIFT FUR NATURFORSCHUNG SECTION A-A JOURNAL OF PHYSICAL SCIENCES
(2023)
Article
Multidisciplinary Sciences
Constantin Fetecau, Itrat Abbas Mirza, Dumitru Vieru
Summary: Mass, energy, and momentum transfer processes between fluid-saturated porous media and adjacent free flow are investigated in this paper. The flow dynamics are strongly influenced by the mechanisms at the interface and conditions on the outer surface. Analytical solutions for the dimensionless velocity fields are determined using Bessel functions, Laplace transform, and appropriate interface and boundary conditions. The dependence of the velocity fields and permeability on the characteristics of the porous layer is discussed numerically and graphically.
Article
Mathematics
Muhammad Azeem, Muhammad Kamran Jamil, Yilun Shang
Summary: The act of locating the exact position of nodes in a network is called network localization. In this study, the localization of a generalized hexagonal cellular network was conducted, and the exact locating number for this network was determined and proven. Furthermore, the generalized version of the locating set and locating number was also discussed.
Article
Chemistry, Physical
Sidra Bukhari, Muhammad Kamran Jamil, Muhammad Azeem
Summary: The article discusses the importance of vanadium in the industry and its role as a catalyst and stabilizer in steel production. It also explores the concept of resolvability parameters in graph theory and applies it to the study of vanadium carbide networks, highlighting its potential impact on research and industrial applications.
Article
Chemistry, Physical
Muhammad Tanzeel Ali Kanwal, Muhammad Azeem, Muhammad Kamran Jamil
Summary: This article explores the boundary contribution of partition dimension parameters in chemical complexes, demonstrating the impact of vertex numbers on resolving partition sets. Graph theory allows for easier design and management of complex networks.
Article
Multidisciplinary Sciences
Yong Tang, Muhammad Labba, Muhammad Kamran Jamil, Muhammad Azeem, Xiujun Zhang
Summary: Humanity has always benefited from quantification of natural occurrences in mathematics and other pure scientific fields. Graph theory has been particularly helpful in applied sciences, such as chemistry. By creating a graph representation of a chemical network or structure, graph theory contributes to understanding the valency of atoms and uncertainty in a system. This research develops new edge-weighted entropies that correspond to valency-based topological indices and applies them to clay mineral tetrahedral sheets.
Article
Multidisciplinary Sciences
Constantin Fetecau, Shehraz Akhtar, Costica Morosanu
Summary: Closed-form expressions have been obtained to characterize the non-dimensional velocity and corresponding non-trivial shear stress in the context of two magnetohydrodynamic (MHD) motions exhibited by incompressible generalized Burgers' fluids. The obtained solutions represent the first exact analytical solutions for MHD motions of such fluids under the condition of shear stress prescribed along the boundary. The establishment of these solutions relies upon the utilization of a perfect symmetry existing between the governing equations of fluid velocity and shear stress.
Article
Multidisciplinary Sciences
Muhammad Imran, Rashad Ismail, Muhammad Azeem, Muhammad Kamran Jamil, Esmail Hassan Abdullatif Al-Sabri
Summary: Euclidean geometry is used to establish the parameters and invariants of the Sombor graph, and the recently developed Sombor indices for various nanotube Y-junctions are examined in this article.
