Search

In this research paper, the authors aim to establish a novel algorithm in the finite difference method (FDM). The novel idea is proposed in the mesh generation process, the process to generate random grids. The FDM over a randomly generated grid enables fast convergence and improves the accuracy of the solution for a given problem; it also enhances the quality of precision by minimizing the error. The FDM involves uniform grids, which are commonly used in solving the partial differential equation (PDE) and the fractional partial differential equation. However, it requires a higher number of iterations to reach convergence. In addition, there is still no definite principle for the discretization of the model to generate the mesh. The newly proposed method, which is the SM method, employed randomly generated grids for mesh generation. This method is compared with the uniform grid method to check the validity and potential in minimizing the computational time and error. The comparative study is conducted for the first time by generating meshes of different cell sizes, i.e., 10×10,20×20,30×30,40×4010\times 10,\hspace{.25em}20\times 20,\hspace{.25em}30\times 30,\hspace{.25em}40\times 40 using MATLAB and ANSYS programs. The two-dimensional PDEs are solved over uniform and random grids. A significant reduction in the computational time is also noticed. Thus, this method is recommended to be used in solving the PDEs.

Hybrid nanofluids provide several advantages over conventional fluids, including improved thermal characteristics, increased stability, customizable features, multifunctionality, and environmental advantages. Hybrid nanofluids are an appealing alternative for a variety of applications due to these benefits. This study aims to compute the non-similar solution of single-multi wall carbon nanotubes (SWCNTs-MWCNTs)-based hybrid nanofluid flow over an inclined extending surface. Heat transmission and flow are observed under the effects of quadratic convection, Darcy-Forchheimer quadratic drag forces, viscous dissipation, and non-linear thermal radiative heat flux. The velocity and thermal slip constraints are imposed at the inclined surface. For the model-based comparison, Xue, and Modified Hamilton Crosser thermal conductivity models for carbon nanotubes (CNTs) are adopted. The irreversibility of the system is also investigated using the second law of thermodynamics for the distinct CNTs-based thermal conductivity models. Non-similarity variables are adopted to convert nonlinear partial differential equations into dimensionless PDEs. Analytical modeling of non-similar systems is done by adopting non-similarity transformations up to second-level truncation, and the bvp4c technique is then used to compute the results numerically. The research found that at 75° of plate inclination, the Modified Hamilton Crosser model for CNTs outperforms the Xue model in terms of heat transfer rate. Further, entropy generation is significantly larger for the Xue model than for the Modified Hamilton Crosser model for CNTs against higher values of viscous dissipation and porosity parameters. It is also revealed that for opposing buoyancy force GR < 0, the temperature of the fluid escalates. This study possesses multiple applications including petroleum engineering, heat exchangers, environmental remediation, and biomedical applications. [ABSTRACT FROM AUTHOR]

Hybrid nanofluids generally exhibit better thermal efficiency than traditional nanofluids due to the synergistic effects of different types of nanoparticles. The combination of these nanoparticles can improve stability, thermal conductivity, and heat transfer performance. This study aims to investigate the effects of Hall current and ion slip on a three-dimensional, steady flow of hybrid nanofluid induced by a bidirectional extending surface while considering the presence of Zinc oxide (ZnO) and Gold (Au) nanoparticles dispersed in Kerosene oil and water to establish two different hybrid nanofluids. Additionally, a heat transfer analysis is conducted in the presence of Cattaneo-Christov (C-C) heat flux and variable heat source/sink. The characteristics of fluid flow are elaborated using the Tiwari and Das model, and a comparison between the two hybrid nanofluid models is presented in detail. The novelty of the envisioned model lies in the heat transfer comparison of two assumed hybrid nanofluid flows in the presence of Hall current and the ion slip over a bidirectional extended surface. The other assumed factors also boost the uniqueness of the model under consideration. To convert the flow model of partial differential equations into ordinary differential equations, relevant transformations are implemented, which are then numerically handled using the bvp4c scheme. The consequences of dimensionless quantities on flow and temperature distributions are highlighted using graphs, and the surface drag coefficients and surface heat transfer rates are also assessed and summarized. The study shows that ZnO-Au/water combination leads to higher heat transfer rates compared to ZnO-Au/Kerosene Oil. Additionally, the proposed model is validated in this research work. [ABSTRACT FROM AUTHOR]

An induced magnetic field is produced owing to an electric current flowing through the conductor. The induced magnetic field and the length of the conductor are in direct proportion. The current study examines the comparison of Yamada-Ota and Xue thermal conductivity models for a mixed convective hybrid nanoliquid flow through the permeable vertical channel influenced by an induced magnetic field. The projected model is supported by the combination of thermal radiation and heat generation and multiple slip conditions imposed on the walls. The Tiwari and Das model is adopted considering engine oil as a working liquid with immersed multiwalled and single-walled carbon nanotubes (CNTs) nanoparticles. The unique combination of strength, conductivity, and other properties make CNTs a promising material for an extensive variety of applications. These governing partial differential equations undergo conversion to ordinary differential equations via the similarity transformation and are then numerically processed with the bvp4c technique of the MATLAB program. The outcomes are deliberated logically via illustrations and tables. It is perceived that fluid velocity is compromised by strengthening the induced magnetic field. Nevertheless, an opposing trend is witnessed for the enhanced values of the Prandtl number. [ABSTRACT FROM AUTHOR]

In varied practical situations, the assumption of constant values are considered for approximations or simplifications to make computations more adaptable. Nevertheless, when there is a requirement for precision, accuracy, and exact results, the consideration of variable characteristics becomes essential. Considering the same, the article's uniqueness lies in studying variable thermal conductivity, variable viscosity, and variable mass diffusivity as governing factors. This study analyzes the movement of a three-dimensional Maxwell nanofluid across a rotating deformable disk deliberating the Hall current and Ion slip impact. In addition, the analysis seeks to boost the stability of the nanofluid flow by incorporating the impact of bio-convection. The velocity slip and convective constraints are enforced at the boundary. The Von Karman transformations are engaged, and accordingly, a numerical solution is computed. Graphical illustrations are used to highlight the significant effects of the problem. The findings revealed that the fluid velocity decreases in both the azimuthal and radial directions for different estimations of the variable viscosity and Deborah number. Additionally, the fluid velocities in the azimuthal and radial directions exhibit opposite trends for Hall current and Ion slip. The endorsement of the presented results is also provided in this study. [ABSTRACT FROM AUTHOR]

Heat transfer improves significantly when the working fluid has high thermal conductivity. Heat transfer can be found in fields such as food processing, solar through collectors, and drug delivery. Considering this notable fact, this work is focused on investigating the bio-convection-enhanced heat transfer in the existence of convective boundary conditions in the flow of hybrid nanofluid across a stretching surface. Buongiorno fluid model with hybrid nanoparticles has been employed along the swimming microorganisms to investigate the mixture base working fluid. The developed nonlinear flow governing equations have been tackled numerically with the help of the bvp4c. The effects of relevant parameters on the flow dynamic have been portrayed in a graphical representation. The velocity profile decreases by raising the levels of buoyancy ratio and mixed convection in the range of. It has been discovered that when bioconvection levels rise, motile microbe migration abruptly slows, which results in a decrease in fluid acceleration. The concentration of fluid flow declined for the Lewis number, but the opposite trend has been observed for the elastic parameter, thermophoresis parameter, and buoyancy ratio. With rising values of Brownian motion and thermophoretic diffusion, the surface drag and Nusselt number decrease significantly. Whereas, the opposite trend has been observed when the values of the thermal Biot number, Prandtl number and buoyancy ratio are enhanced. Additionally, data from this study have been validated by comparison with those that have previously been published, and an appropriate rate of agreement has been observed. Graphic Abstract [ABSTRACT FROM AUTHOR]

The present article focuses on the new meticulous model based on the postulate of memory-dependent derivatives to analyze the thermo-mechanical interactions inside the nano-beam-based machined resonators. Also, the size effect on dynamic responses of thermoelastic vibrations of homogeneous and isotropic nano-beam is considered. The fundamental expressions are formulated in the frame of non-local generalized thermoelasticity with paired relaxation times by operating the results of Euler-Bernoulli beam theory, non-local effect, and memory-dependent derivative. The proposed model is applied to study the nano-beam-based machined resonator subjected to the ramp-type heating and exponentially decaying time-dependent load. Closed-form solutions of the physical fields are examined by applying the Laplace transform mathematical mechanism. However, the coherence of the new thermal conductivity framework, a collation has been bestowed among the results obtained in the presence or absence of the memory-dependent derivative; also, the size effect is analyzed on the significant parameters of nano-beam such as deflection, temperature, displacement as well as bending moment. Moreover, the prominent influence of the distinct affecting parameters such as constituents of memory-dependent derivative (kernel function and time delay) and ramping time parameter with an applied load on the physical fields have been investigated with the help of quantitative results. [ABSTRACT FROM AUTHOR]

Nanofluids with immersed metallic nanoparticles possess a higher thermal conductivity. The extent of this enhancement is largely dependent on the amount of the volume fraction, composition, nanoparticles' shape, and size. The current study emphasizes nanofluid (gold-ethylene glycol) flow with different shapes past a horizontal infinite permeable conduit. The porous walls exhibit the fluid to move in or out of the channel as the walls expand or contract. The flow problem is modeled in a Cartesian coordinate system by employing the Tiwari-Das nanofluid model. Heat transfer is enhanced with the inclusion of Cattaneo–Christov combined with heat generation/absorption effect and temperature-dependent thermal conductivity. The Hamilton–Crosser model is adopted here for the cylindrical and platelet shapes nanoparticles. By invoking appropriate transformation, the equations are transmuted into ordinary differential equations and are solved numerically by employing the bvp4c approach. The influence of the key parameters is illustrated graphically. A protuberant decline is observed in the cylindrical shape nanoparticles in the thermal field on augmenting the thermal relaxation parameter. The drag force coefficient elevates on incrementing the volume fraction of nanoparticles. A significant correlation is noticed in the findings of the comparison with the existing literature. [ABSTRACT FROM AUTHOR]

In this investigation, we utilize advanced versions of the Extended Direct Algebraic Method (EDAM), namely the modified EDAM (mEDAM) and r+mEDAM, to explore families of optical soliton solutions in the Fractional Perturbed Radhakrishnan–Kundu–Lakshmanan Model (FPRKLM). Our study stands out due to its in-depth investigation and the identification of multiple localized and stable soliton families, illuminating their complex behavior. We offer visual validation via carefully designed 3D graphics that capture the complex behaviors of these solitons. The implications of our research extend to fiber optics, communication systems, and nonlinear optics, with the potential for driving developments in optical devices and information processing technologies. This study conveys an important contribution to the field of nonlinear optics, paving the way for future advancements and a greater comprehension of optical solitons and their applications. [ABSTRACT FROM AUTHOR]

This research uses a novel analytical method known as the modified Extended Direct Algebraic Method (mEDAM) to explore families of soliton solutions for the complex structured Coupled Fractional Biswas–Arshed Model (CFBAM) in Birefringent Fibers. The Direct Algebraic Method (DAM) is extended by the mEDAM's methodology to compute more analytical solutions that would otherwise be difficult to acquire. We use this method to derive several families of soliton solutions and examine their characteristics. We also look at how different model parameters, such as amplitude, width, and propagation speed, affect the dynamics of soliton. Our use of 2D and 3D graphics to illustrate the soliton solutions also makes it possible to see the soliton dynamics more clearly. The outcomes also demonstrate that the method suggested has proven successful in producing soliton solutions for intricate structures such as the CFBAM. [ABSTRACT FROM AUTHOR]

The present research investigates symmetric soliton solutions for the Fractional Coupled Konno–Onno System (FCKOS) by using two improved versions of an Extended Direct Algebraic Method (EDAM) i.e., modified EDAM (mEDAM) and r+mEDAM. By obtaining precise analytical solutions, this research explores the characteristics and behaviours of symmetric solitons in FCKOS. Further, the amplitude, shape and propagation behaviour of some solitons are visualized by means of a 3D graph. This investigation fosters a more thorough comprehension of non-linear wave phenomena in considered systems and offers helpful insights towards soliton behavior in it. The outcomes reveal that the recommended techniques are successful in constructing symmetric soliton solutions for complex models like the FCKOS. [ABSTRACT FROM AUTHOR]

The flow of air containing small particles past a pointed area of an aircraft, bullet and bonnet of vehicles exhibits the flow over paraboloid surface of revolution. Therefore, the study of Al2O3-H2O nanofluid over upper paraboloid horizontal surface of revolution (UPHSR) is organized. The concerned model develops via thermal conductivity dealing with the particles shape factor and similarity transforms. Afterward, numerical analysis is performed and the influences of pertinent parameters on the velocity and temperature (η) in Al2O3-H2O are examined. The deep inspection of the results in the view of physics behind them revealed that Al2O3-H2O drops for the stringer magnetic field. Further, nonlinear thermal radiations and internal heat generation made Al2O3-H2O a better heat conductor which increased its applications in a broad zone. [ABSTRACT FROM AUTHOR]

Numerous methods have been introduced in the literature for numerical solution of two-dimensional hyperbolic telegraph equations. Improved techniques using explicit group methods derived from the standard and skewed (rotated) finite difference operators have been developed over the last few years in solving the linear systems that arise from the discretization of the several types of partial differential equations. The preconditioning strategies play a vital role in accelerating the convergence rates of these group iterative methods. In this paper, we present a preliminary study of the formulation of new preconditioned scheme based on explicit group relaxation methods for the difference solution of the telegraph equations. The efficient and robustness of these new formulations over the existing explicit group schemes demonstrated through numerical experiments. [ABSTRACT FROM AUTHOR]

The construction of a specific splitting-type preconditioner in block formulation applied to a class of group relaxation iterative methods derived from the centred and rotated skewed finite difference approximations has been shown to improve the convergence rates of these methods. In this paper, we present some theoretical convergence analysis on this preconditioner specifically applied to the linear systems resulted from these group iterative schemes in solving an elliptic boundary value problem. We will theoretically show the relationship between the spectral radiuses of the iteration matrices of the preconditioned methods which affects the rate of convergence of these methods. We will also show that the spectral radius of the preconditioned matrices is smaller than that of their unpreconditioned counterparts if the relaxation parameter is in a certain optimum range. Numerical experiments will also be presented to confirm the agreement between the theoretical and the experimental results. [ABSTRACT FROM AUTHOR]

Abstract The present analysis aims to compute the non-similar solution of a chemically reactive Prandtl nanofluid across an elongated surface in a permeable medium, with a uniform magnetic field applied perpendicular to the surface. The Buongiorno model is used to study the random motion and thermophoresis of the nanoliquid by considering factors such as viscous dissipation, Joule heating, and multiple slips. By using appropriate transformations and a non-similarity approach, the governing flow equations are scaled down to the second level and numerically analyzed using the MATLAB bvp4c algorithm. The profound effects of the dimensionless parameters are illustrated graphically for the velocity, temperature, and solutal profiles. The impact of drag force, thermal, and solutal transmission at the interface of the deformable sheet are inspected in tabulated form. The results of this study revealed that higher Prandtl and elastic parameters lead to an increase in fluid velocity but a rise in thermal slip parameter results in the opposite behavior. An increase in Hartmann number and porosity parameters upsurges drag force, whereas an increase in the slip parameter reduces it. The research is validated by comparing it to previous studies, and a strong correlation is observed. It is examined that the percentage (%) error with both comparative papers is between −0.0017181 and 0.0006.377 which is almost negligible. Thus, confirming the reliability and precision of the formulated problem. [ABSTRACT FROM AUTHOR]