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The unsteady flow of fluids is crucial for real-world applications, efficiency and performance optimisation in various sectors, such as engineering, environmental impact research and developing technologies. Shape of nanoparticles in hybrid nanofluids is important for optimising energy applications and customising the performance of the nanofluid as it has effect on heat transport, material characteristics and stability. Considering the importance of unsteady flow and the shape factor of the nanoparticles, the present study aims to explore the solution of the unsteady flow problem of hybrid nanofluid over a stretching surface embedded within the porous medium. This study deals with the shape factor analysis by considering four shapes: brick, lamina, platelet and blade. The Legendre wavelet collocation technique is implemented to obtain the solution of the problem. It is revealed by creating a pie chart that the thermal conductivity is found to be maximum for lamina-shaped nanoparticles (i.e., 32%) while it is minimum for brick-shaped nanoparticles (i.e., 20%). The rate of heat transfer enhancement is also presented by the waterfall graph. The graph disclosed that on increasing the volume fraction of TiO(_2) from 1 to 10%, the rate of heat transfer is enhanced by 39.63%. The velocity profiles are inversely related to the temperature-dependent viscosity and velocity slip parameter.

The proper utilisation of the coating fluid is crucial for ensuring the effectiveness of the wire coating process. Its complexity and importance make it the central focus of the present study. Also, understanding wire coating processes is important for ensuring product performance, cost efficiency, regulatory compliance, customer satisfaction, innovation and environmental sustainability. By optimising the coating processes, manufacturers can produce high-quality wire products that meet market demands while minimising negative impacts on the environment and resources. The objective is to assess the quality and performance of the wire coating process by examining the fluid flow characteristics within the die. Therefore, a mathematical model is devised to study the rheological properties of Sisko fluid with a constant pressure gradient in an unsteady state. The governing equation with oscillating boundary constraints is converted into dimensionless form and solved numerically using the method of lines (MoL) technique. The findings are presented through 2D and 3D plots. Response surface methodology (RSM) is implemented to investigate the statistical significance and sensitivity of the parameters and to optimise the shear stress rate.

Hybrid nanomaterials have different applications and scientists have presented different methods to enhance the thermal efficiencies of cooling and heating systems, improving energy resources, thermal managements, extrusion processes, chemical reactions, etc. Current investigation reports a thermal study based on hybrid nanofluid model via fractional approach. The hybrid nanofluid contains molybdenum disulphide (MoS(_2)) and graphene oxide (GO) nanoparticles. Engine oil is used as a base liquid for which thermal properties need to be enhanced. Additionally, the impact of magnetic force is studied for electrically conducting hybrid nanofluid. Fractional computations are performed using Atanangana–Balenau (AB) fractional derivative, followed by the Laplace technique for integration assessment. The role of physical flow parameters is tested graphically. It is observed that the heat transfer phenomenon enhances due to nanoparticle volume fraction, the velocity profile declines due to Grashof number and skin friction coefficient increases due to fractional parameter and Grashof number.

Bolts are utilised extensively in machinery and often bear large loads. Reliable connection of bolts is related to the effective functioning of machinery. Therefore, it is of utmost importance to detect bolt looseness in time. However, the identification of bolt looseness is typically challenging due to the strong background noise. Compared with Gaussian white noise, only few researches were conducted on Poisson white noise. To detect the looseness of the bolt in the presence of strong Poisson white noise, we propose a novel method based on sub-harmonic resonance, time-domain averaging and adaptive stochastic resonance. The disadvantages of damaging characteristic frequencies that exist in a majority of approaches are overcome. In addition, the looseness is assessed by the quality factor derived from physical science. To verify the efficacy of the method, we propose numerical simulations and experimental validations. The results demonstrate that the proposed method has effectively detected bolt looseness under strong Poisson white noise. The detection of bolt looseness might benefit greatly by adopting the suggested approach.

Motivated by recent studies on non-local integrable models, we consider a non-local inhomogeneous linear differential equation model of Newtonian type:

where (lambda ) and (mu ) are real constants and f is continuous. Through decomposing functions into their even and odd parts, we transform the non-local model into a local model, and then with the classical ODE technique, solve the resulting local model under the even and odd constraints. The general solution involving two arbitrary constants is presented in nine cases of the coefficients.

Fluid mechanics has been linked to a wide range of disciplines, such as atmospheric science, oceanography and astrophysics. In this paper, we focus our attention on a ((3+1))-dimensional variable-coefficient Kadomtsev-Petviashvili-like equation in a fluid. Through the Hirota method, we derive a bilinear form. We obtain an auto-Bäcklund transformation based on the truncated Painlev(acute{textrm{e}}) expansion and a bilinear Bäcklund transformation based on the bilinear form. With the variable coefficients (alpha (t)), (beta (t)), (gamma (y,t)), (delta (t)) and (mu (t)) taken as certain constraints, one- and two-kink solutions are shown. Based on the one-kink solutions, we take (gamma (y,t)) as the linear and trigonometric functions of y, and then give the ring-type and periodic-type one-kink waves, where t and y are the independent variables. According to the two-kink solutions, we obtain the parabolic-type, linear-type and periodic-type kink waves.

This paper aims to propose a material-independent novel locally-active memristor (LAM) model, which is applied to the fourth-order autonomous chaotic oscillation circuit to investigate the phenomena and mechanisms of chaos and hyperchaos. Under different parameter configurations, the LAM-based system can exhibit rich dynamic behaviours and multistability, such as multi-equilibrium points, period, chaos and hyperchaos attractors. The phase diagram, bifurcation diagram, Lyapunov exponential spectrum, basins of attraction and dynamics map are used to analyse the complex dynamics of the system. In addition, we find many types of coexisting attractors, including periodic attractors with multiple different periods, hyperchaotic attractors with multiple different scrolls, a double-scroll chaotic attractor with a shock wave orbit and so on. This work fills the gap by theoretical analysis and numerical simulation. And proves that the local activity and non-volatility of memristors are two important reasons for the generation of complex and coexisting attractors.

The current work is concerned with some novel solutions of the new extended (3 + 1)-dimensional Boiti–Leon–Manna–Pempinelli equation (BLMPE) that plays a key role in the incompressible fluid. The N-soliton solutions (NSSs) are extracted by virtue of the Hirota form which is developed using the Cole–Hopf transform. Based on the NSSs, we elaborate the resonance conditions of the soliton molecules and derive the soliton molecules of the 2-solitons, 3-solitons and 4-solitons on the (x, y)-, (x, z)- and (y, z)-planes. Additionally, we also explore some novel hybrid interaction solutions including the interaction between the soliton molecule and solitons and the interaction between the breather solution and the solitons. Correspondingly, the dynamic properties of the solutions are depicted graphically. The derived solutions in this study are all new and can enlarge the exact solutions of the new extended (3 + 1)-dimensional BLMPE. Besides, they can enable us to understand nonlinear dynamic behaviours better.

The spherical tokamak (ST) operates in a steady state with a high fusion gain. The 0-dimensional power balance model, including radiation losses to determine Q value as an inductive fusion gain, and the current balance model for determining (Q_{textrm{CD}}) as a non-inductive fusion gain, is used to investigate the viability of D–(^{3})He fuel for a steady-state operation. The spherical tokamak’s geometry, including the magnetic field (B_{t}) and (beta _{textrm{th}}) as a ratio of its kinetic pressure to the magnetic pressure, is used to analyse the impact of the confinement enhancement factor (H_{y2}) and the impurity density fraction (f_{textrm{I}}) on (Q_{textrm{CD}}). By comparing the obtained values with the device data, plasma characteristics, such as the safety factor (q_{textrm{I}}) and Greenwald density limit (N_{textrm{G}}) are examined to determine the optimum density limit and safety factor for an assurance about (Qapprox Q_{textrm{CD}}) as the aim of steady-state operation. A comparison with ARIES-III performance is also made. The overall plant power balance equation is included. Furthermore, the desirable plant thermal efficiency value (eta _{textrm{th}}) and normalised beta value (beta _{N}) for producing net electric power (P_{textrm{NET}}>) 1 GW for the ST are achieved. Therefore, ST’s capability of having a lower aspect ratio A and higher elongation (kappa _{s}) than ARIES-III in generating more significant fusion power with lower (H_{y2}) and higher energy confinement time (tau _{E}) is approved.