Search results

This paper aims to present dual solutions for the two-dimension copper oxide with silver (CuO–Ag) and zinc oxide with silver (ZnO–Ag) hybrid nanofluid flow past a permeable shrinking sheet in a dusty fluid with velocity slip.

The governing partial differential equations for the two dust particle phases are reduced to the pertinent ordinary differential equations using a similarity transformation. Closed-form analytical solutions for the reduced skin friction and reduced Nusselt number, as well as for the velocity and temperature profiles, were presented, both graphically and in tables, under specific non-dimensional physical parameters such as the suction parameter, Prandtl number, slip parameter and shrinking parameter, which are also presented in both figures and tables.

The results indicate that for the shrinking flow, the wall skin friction is higher in the dusty fluid when compared with the clear (viscous) fluid. In addition, the effect of the fluid–particle interaction parameter to the fluid phase can be seen more clearly in the shrinking flow. Furthermore, multiple (dual, upper and lower branch solutions) are found for the governing similarity equations and the upper branch solution expanded with higher values of the suction parameter. It can be confirmed that the lower branch solution is unstable.

In practice, the study of the stretching/shrinking flow is crucially important and useful. Both the problems of steady and unsteady flow of a dusty fluid have a wide range of possible applications in practice, such as in the centrifugal separation of particles, sedimentation and underground disposal of radioactive waste materials.

Even though the problem of dusty fluid has been broadly investigated, very limited results can be found for a shrinking sheet. Indeed, this paper has succeeded to obtain analytically dual solutions. The stability analysis can be performed by following many published papers on stretching/shrinking sheets. Finally, the critical values and plotting curves for obtaining single or dual solution are successfully presented.

The purpose of this paper is to address unsteady heat conduction in two subsets of ordinary bodies. One subset consists of a large plane wall, a long cylinder and a sphere in one dimension. The other subset consists of a short cylinder and a large rectangular bar in two dimensions. The prevalent assumptions in the two subsets are: constant initial temperature, uniform surface heat flux and thermo-physical properties invariant with temperature. The engineering applications of the unsteady heat conduction deal with the determination of temperature–time histories in the two subsets using electric resistance heating, radiative heating and fire pool heating.

To this end, a novel numerical procedure named the enhanced method of discretization in time (EMDT) transforms the linear one-dimensional unsteady, heat conduction equations with non-homogeneous boundary conditions into equivalent nonlinear “quasi–steady” heat conduction equations having the time variable embedded as a time parameter. The equivalent nonlinear “quasi–steady” heat conduction equations are solved with a finite difference method.

Based on the numerical computations, it is demonstrated that the approximate temperature–time histories in the simple subset of ordinary bodies (large plane wall, long cylinder and sphere) exhibit a perfect matching over the entire time domain 0 < t < ∞ when compared against the rigorous exact temperature–time histories expressed by classical infinite series. Furthermore, using the method of superposition of solutions in the convoluted subset (short cylinder and large rectangular crossbar), the same level of agreement in the approximate temperature–time histories in the simple subset of ordinary bodies is evident.

The performance of the proposed EMDT coupled with a finite difference method is exhaustively assessed in the solution of the unsteady, one-dimensional heat conduction equations with prescribed surface heat flux for: a subset of one-dimensional bodies (plane wall, long cylinder and spheres) and a subset of two-dimensional bodies (short cylinder and large rectangular bar).

The purpose of this study is to solve the Reynolds equation for finite journal bearings by using the physics-informed neural networks (PINNs) method. As a meshless method, it is unnecessary to use big data to train the neural networks, but to satisfy the Reynolds equation and the corresponding boundary conditions by using the known physics information.

Here, the boundary conditions are enforced through the loss function firstly, i.e. the soft constrain method. After this, an equation was constructed to build a surrogate model for satisfying the corresponding boundary conditions naturally, i.e. the hard constrain method.

For the soft one, in brief, the pressure results agree well with existing results, apart from the ones on the boundaries. While for the hard one, it can be noted that the discrepancies on the boundaries are reduced significantly.

The PINNs method is used to solve the Reynolds equation for finite journal bearings, and the error values on the boundaries for the results of the soft constrain method are improved by using the hard constrain method. Therefore, the hard constraint maybe also a good option when the pressure results on the boundaries are emphasized.

The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-02-2023-0045/

This study aims to investigate the dual solutions for axisymmetric flow and heat transfer due to a permeable radially shrinking disk in copper oxide (CuO) and silver (Ag) hybrid nanofluids with radiation effect.

The partial differential equations that governed the problem will undergo a transformation into a set of similarity equations. Following this transformation, a numerical solution will be obtained using the boundary value problem solver, bvp4c, built in the MATLAB software. Later, analysis and discussion are conducted to specifically examine how various physical parameters affect both the flow characteristics and the thermal properties of the hybrid nanofluid.

Dual solutions are discovered to occur for the case of shrinking disk (λ < 0). Stronger suction triggers the critical values’ expansion and delays the boundary layer separation. Through stability analysis, it is determined that one of the solutions is stable, whereas the other solution exhibits instability, over time. Moreover, volume fraction upsurge enhances skin friction and heat transfer in hybrid nanofluid. The hybrid nanofluid’s heat transfer also heightened with the influence of radiation.

Flow over a shrinking disk has received limited research focus, in contrast to the extensively studied axisymmetric flow problem over a diverse set of geometries such as flat surfaces, curved surfaces and cylinder. Hence, this study highlights the axisymmetric flow due to a shrinking disk under radiation influence, using hybrid nanofluids containing CuO and Ag. Upon additional analysis, it is evidently shows that only one of the solutions exhibits stability, making it a physically dependable choice in practical applications. The authors are very confident that the findings of this study are novel, with several practical uses of hybrid nanofluids in modern industry.

The purpose of this paper is to study the new (3 + 1)-dimensional integrable fourth-order nonlinear equation which is used to model the shallow water waves.

By means of the Cole–Hopf transform, the bilinear form of the studied equation is extracted. Then the ansatz function method combined with the symbolic computation is implemented to construct the breather, multiwave and the interaction wave solutions. In addition, the subequation method tis also used to search for the diverse travelling wave solutions.

The breather, multiwave and the interaction wave solutions and other wave solutions like the singular periodic wave structure and dark wave structure are obtained. To the author’s knowledge, the solutions obtained are all new and have never been reported before.

The solutions obtained in this work have never appeared in other literature and can be regarded as an extension of the solutions for the new (3 + 1)-dimensional integrable fourth-order nonlinear equation.

This study describes the applicability of the a priori estimate method on a nonlocal nonlinear fractional differential equation for which the weak solution's existence and uniqueness are proved. The authors divide the proof into two sections for the linear associated problem; the authors derive the a priori bound and demonstrate the operator range density that is generated. The authors solve the nonlinear problem by introducing an iterative process depending on the preceding results.

The functional analysis method is the a priori estimate method or energy inequality method.

The results show the efficiency of a priori estimate method in the case of time-fractional order differential equations with nonlocal conditions. Our results also illustrate the existence and uniqueness of the continuous dependence of solutions on fractional order differential equations with nonlocal conditions.

The authors’ work can be considered a contribution to the development of the functional analysis method that is used to prove well-positioned problems with fractional order.

The authors confirm that this work is original and has not been published elsewhere, nor is it currently under consideration for publication elsewhere.

The objective of this paper is to analyze the relationship between innovation and the development of artificial intelligence (AI) and digital technologies in Europe. The use of digital technologies among European companies is studied through a composite index, while the relationship between innovation and AI is studied through a log-linear regression model. The results of the model have made possible to develop interesting indications for economic and industrial policy.

The use of digital technologies among European companies is studied through a composite index of AI and information technology (ICT) (using the Fair and Sustainable Welfare methodology) with the aim of measuring territorial gaps and to know which European countries are more or less inclined to its use, while the relationship between innovation and AI is studied through a log-linear regression model.

In the paper, two different methodologies were used to analyze the relationship between innovation and the development of digital technologies in Europe. The synthetic indicator made possible to develop a taxonomy between the different countries, the log-linear model made possible to identify and explain the determinants of innovation.

The description of the biunivocal relationship between innovation and AI is a topical and relevant issue that is treated in the paper in an original way using a synthetic indicator and a log-linear model.

本文旨在探討在歐洲、創新與人工智能和數字技術的發展之間的關係。研究人員透過一個綜合指數、去探討歐洲公司之間數字技術的使用狀況。至於創新與人工智能之間的關係, 則以對數線性回歸模型來進行研究。從模型所得的結果, 為我們提供了建議、去訂定適切的經濟和產業政策。

研究人員透過一個人工智能和資訊科技的綜合指數, 去探討歐洲企業之間數字技術的使用狀況 (研究人員使用了公平和可持續福利方法論), 其目標為測量領土差距, 以及確定哪些歐洲國家、大體上傾向於使用數字技術;至於創新與人工智能之間的關係, 則以對數性回歸模型來進行研究。

本文使用了兩個不同的方法、去探討在歐洲、創新與數字技術發展之間的關係。有關的合成指標, 使研究人員可製定一個不同國家間的分類法;而有關的對數線性模型, 則讓研究人員可確立並說明創新的決定因素。

本文使用了合成指標和對數線性模型、去探討創新與人工智能之間的一對一的關係, 這是時下受到關注和適宜的課題;就研究法而言, 本研究確是新穎獨創的。

The purpose of this study is to numerically model the rigid pavement resting on two-parameter soil and to examine its modal parameters.

This study is carried out using a one-dimensional beam element with three rotational and three translational degrees of freedom based on the finite element method. MATLAB programming is used to perform the free vibration analysis of the rigid pavement.

Cyclic frequency and their corresponding mode shapes were determined. It has been investigated how cyclic frequency changes as a result of variations in the thickness, span length of pavement, shear modulus, modulus of subgrade, different boundary conditions and element discretization. Thickness of the pavement and span length has greater effect on the cyclic frequency. Maximum increase of 29.7% is found on increasing the thickness, whereas the cyclic frequency decreases by 63.49% on increasing span length of pavement.

The pavement's free vibration is the sole subject of the current investigation. This study limits for the preliminary design phase of rigid pavements, where a complete three-dimensional finite element analysis is unnecessary. The current approach can be extended to future research using a different method, such as finite element grilling technique, mesh-free technique on reinforced concrete pavements or jointed concrete pavements.

The finite element approach adopted in this paper involves six degrees of freedom for each node. Furthermore, to the best of the authors’ knowledge, no prior study has done seven separate parametric investigations on the modal analysis of rigid pavement resting on two-parameter soil.

This paper aims to study a non-Newtonian micropolar fluid flow over a bidirectional flexible surface for multiple exact solutions of momentum boundary layer and thermal transport phenomenon subject to wall mass flux, second-order slip and thermal jump conditions.

The coupled equations are transformed into ordinary differential equations using similarity variables. Analytical and numerical techniques are used to solve the coupled equations for single, dual or multiple solutions.

The results show that the stretching flow, shrinking flow, the wall drag, thermal profile and temperature gradient manifest large changes when treated for special effects of the standard parameters. The role of critical numbers is definitive in locating the domains for the existence of exact solutions. The nondimensional parameters, such as mass transfer parameter, bidirectional moving parameter, plate deformation strength parameter, velocity slips, material parameter, thermal jump and Prandtl number, are considered, and their physical effects are presented graphically. The presence of governing parameters exhibits special effects on the flow, microrotation and temperature distributions, and various exact solutions are obtained for the special parametric cases.

The originality and value of this work lie in its exploration of non-Newtonian micropolar fluid flow over a bidirectional flexible surface, highlighting the multiple exact solutions for momentum boundary layers and thermal transport under various physical conditions. The study provides insights into the effects of key parameters on flow and thermal behavior, contributing to the understanding of complex fluid dynamics.

This study aims to improve the tribological properties of hydrodynamic journal bearing via surface texture, as well as the wear and antifriction mechanisms of textured bearing were represented. It provides a design direction for solving the tribological problem of rotor-bearing system.

In this paper, the variation of surface texture parameters (e.g. texture diameter, d; area density, sp; and depth, hp) were analyzed based on finite difference method. The optimal surface texture parameters were obtained by designing orthogonal experiments, and the relationship between friction and wear properties and microstructure was studied via combining electron probe microanalyzer, scanning electron microscope, X-ray diffractometer and friction and wear testing machine.

Dimensionless film pressure P increased as the d increased, whereas P first increased and then decreased as the sp and hp increased, and the maximum P was got as sp = 15% and hp = 25 µm, respectively. The friction coefficient of textured surface with suitable parameters was effectively reduced and the textured surface with the best antifriction effect was 5#. Orthogonal experimental design analysis showed that the influence order of factors on friction coefficient was as follows: sp > sp × d > d > d × hp > hp > sp × hp and the friction coefficient first decreased and then increased as the sp, d and hp increased. In addition, the friction and wear mechanism of textured bearing were three body friction and abrasive wear as the matrix structure and hard phase were a single β phase and Mn5Si3, respectively. While the antifriction mechanism of textured surface was able to store abrasive particles and secondary hydrodynamic lubrication was formed.

The sample with reasonable texture parameter design can effectively reduce friction and wear of hydrodynamic journal bearing without reducing the service life, which can provide a reference for improving the lubrication performance and mechanical efficiency of rotor-bearing system.