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In this study, the numerical investigation of boundary layer flow over a moving plate in a nanofluid with viscous dissipation and constant wall temperature is considered. The governing non-linear partial differential equations are first transformed into a system of ordinary differential equations using a similarity transformation. The transformed equations are then solved numerically using the Keller-box method. Numerical solutions are obtained for the Nusselt number, Sherwood number and the skin friction coefficient as well as the concentration and temperature profiles. The features of the flow and heat transfer characteristics for various values of the Prandtl number, plate velocity parameter, Brownian motion and thermopherosis parameters, Eckert number and Lewis number are analyzed and discussed. It is found that the presence of viscous dissipation reduces the range of the plate velocity parameter for which the solution exists. The increase of both Brownian motion and thermophoresis parameters results to the decrease of the Nusselt number, while the Sherwood number increases with the increase of the thermophoresis parameter.

In this paper, the nonlinear primary resonances of an axially moving plate in aero-thermal environment concerning on manufacturing background of the hot rolling are studied. The equation of motion of the plate is established using the Burger’s nonlinear plate theory. The aerodynamic force is analytically derived based on the linear potential flow theory and the assumed mode method. The effect of the temperature change of the environment is taken into account in the structural modeling. The incremental harmonic balance method is applied for nonlinear vibration analysis of the system. The effects of the axially moving speed, the flow velocity and the temperature change on the nonlinear vibration properties of the plate are discussed. From the analysis, it can be seen that the plate exhibits hardening type of nonlinearity. The first-order generalized coordinate has a resonance peak, and the second to the fourth-order generalized coordinates have the resonance trough. With the axially moving speed, the flow velocity and the temperature change increase, the resonance frequency of the plate decreases. The amplitude of the resonance increases when the temperature change increases. The resonance amplitude increases with increasing excitation amplitude. This research can be helpful for the hot rolling process design in the manufacturing industry.

Hybrid nanofluid is considered a new type of nanofluid and is further used to increase the heat transfer efficiency. This paper explores the two-dimensional steady axisymmetric boundary layer which contains water (base fluid) and two different nanoparticles to form a hybrid nanofluid over a permeable moving plate. The plate is suspected to move to the free stream in the similar or opposite direction. Similarity transformation is introduced in order to convert the nonlinear partial differential equation of the governing equation into a system of ordinary differential equations (ODEs). Then, the ODEs are solved using bvp4c in MATLAB 2019a software. The mathematical hybrid nanofluid and boundary conditions under the effect of suction, S, and the concentration of nanoparticles, ϕ 1 (Al2O3) and ϕ 2 (TiO2) are taken into account. Numerical results are graphically described for the skin friction coefficient, C f , and local Nusselt number, N u x , as well as velocity and temperature profiles. The results showed that duality occurs when the plate and the free stream travel in the opposite direction. The range of dual solutions expand widely for S and closely reduce for ϕ . Thus, a stability analysis is performed. The first solution is stable and realizable compared to the second solution. The C f and N u x increase with the increment of S. It is also noted that the increase of ϕ 2 leads to an increase in C f and decrease in N u x .

Nanofluid dynamic properties have varied consequences in several contexts, including those of cooling, building environments, heat transfer structures, microwave flow cytometry, energy generation, hyperthermia therapies, and related activities. This work presents a numerical examination of the unsteady separated stagnation point flow of Al 2 O 3 / H 2 O nanofluid. The study examines the combined impact of buoyancy and heat source effects, as well as mass suction and slip conditions, on the behavior of the system. In this study, we establish a new mathematical model for nanofluids, which we use to derive similarity solutions in the form of a system of ordinary differential equations (ODEs). The bvp4c technique in MATLAB is used to find approximations to the solutions of certain reduced ODEs. A comprehensive analysis has been undertaken to investigate many physical parameters, revealing that the skin friction coefficient exhibits an upward trend with increasing nanoparticle volume percentage and an unsteadiness parameter for opposing flow. The pattern is also evident in the fluid’s heat transfer rate. In addition, the influence of the stagnation and unsteadiness parameters on the heat transfer performance is significant. The incorporation of the melting heat parameter results in a broader variety of temperature profiles, hence leading to a spontaneous decrease in the rate of heat transmission. Furthermore, the paper incorporates a validation process to substantiate the suggested model and reinforce the conclusions.

In this paper, the dynamic response of axially moving geometric nonlinear plates carrying moving mass is investigated. Based on von Kármán plate theory, the time-varying dynamic equation of the axially moving plate under moving loads is obtained by using the extended Hamiltonian principle and discretized into a set of finite-dimensional ordinary differential nonlinear equations by the assumed mode method. The equation incorporates the additional mass, damping, and stiffness matrix resulting from the inertia force, centrifugal force, and Coriolis force of the moving mass. Comparing the axially moving of plate, dynamic response results of linear and nonlinear results show the necessity of considering geometric nonlinearity in the model. The effects of system load parameters, including the mass of the moving load, the speed of the axially moving plate, and the plate’s aspect ratio on the vibration characteristics of the plate, are discussed. The dynamic responses of the axially moving plates under three different moving load trajectories are contrasted. Numerical results show that increasing the moving load mass and the speed of the axially moving plate leads to greater instability of the system, and the aspect ratio and different moving trajectories also have effects on the transverse vibration of the plate.

The flow and heat transfer characteristics of both single-wall and multi-wall carbon nanotubes (CNTs) with water and kerosene as base fluid on a moving plate with slip effect are studied numerically. By employing similarity transformation, governing equations are transformed into a set of nonlinear ordinary equations. These equations are solved numerically using the bvp4c solver in Matlab which is a very efficient finite difference method. The influence of numerous parameters such as nanoparticle volume fraction, velocity ratio parameter and first order slip parameter on velocity, temperature, skin friction and heat transfer rate are further explored and discussed in the form of graphical and tabular forms. The results reveal that dual solutions exist when the plate and free stream move in the opposite direction and slip parameter was found to widen the range of the possible solutions. However, skin friction coefficients decrease, whereas the heat transfer increases in the presence of slip parameter. Single-wall carbon nanotubes (SWCNTs) give higher skin friction and heat transfer compared to multi-wall carbon nanotubes (MWCNTs) due to the fact that they have higher density and thermal conductivity. A stability analysis is carried out to determine the stability of the solutions obtained.

Purpose This study aims to investigate the micropolar fluid flow through a moving flat plate containing CoFe2O4-TiO2 hybrid nanoparticles with the substantial influence of thermophoresis particle deposition and viscous dissipation. Design/methodology/approach The partial differential equations are converted to the similarity equations of a particular form through the similarity variables. Numerical outcomes are computed by applying the built-in program bvp4c in MATLAB. The process of flow, heat and mass transfers phenomena are examined for several physical aspects such as the hybrid nanoparticles, micropolar parameter, the thermophoresis particle deposition and the viscous dissipation. Findings The friction factor, heat and mass transfer rates are higher with an increment of 1.4%, 2.2% and 1.4%, respectively, in the presence of the hybrid nanoparticles (with 2% volume fraction). However, they are declined because of the rise of the micropolar parameter. The imposition of viscous dissipation reduces the heat transfer rate, significantly. Meanwhile, thermophoresis particle deposition boosts the mass transfer. Multiple solutions are developed for a certain range of physical parameters. Lastly, the first solution is shown to be stable and reliable physically. Originality/value As far as the authors have concerned, no work on thermophoresis particle deposition of hybrid nanoparticles on micropolar flow through a moving flat plate with viscous dissipation effect has been reported in the literature. Most importantly, this current study reported the stability analysis of the non-unique solutions and, therefore, fills the gap of the study and contributes to new outcomes in this particular problem.

An analysis of the interaction mechanisms between a Shaped Charge Jet (SCJ) and a single Moving Plate (MP) is proposed in this article using both experimental and numerical approaches. First, an experimental set-up is presented. Four collision tests have been performed: two tests in Backward Moving Plate (BMP) configuration, where the plate moves in opposition to jet, and two tests in Forward Moving Plate (FMP) configuration, where the plate moves alongside the jet. Based on the virtual origin approximation, a methodology (the Virtual Origin Method, VOM) is developed to extract quantities from the X-ray images, which serve as comparative data. γSPH simulations are carried out to complete the analysis, as they well capture the disturbance dynamics observed in the experiments. Based on these complementary experimental and numerical results, a new physical description is proposed through a detailed analysis of the interaction. It is shown that the SCJ/MP interaction is driven at first order by the contact geometry. Thus, BMP and FMP configurations do not generate the same disturbances because their local flow geometries are different. In the collision point frame of reference, the BMP flows in the same direction as the jet, causing its overall deflection. On the contrary, the FMP flow opposes that of the jet leading to an alternative creation of fragments and ligaments. An in-depth study, using the VOM shows that deflection angles, fragment-ligament creation frequencies, and deflection velocities evolve as the interaction progresses through slower jet elements.

In this study, analytical and numerical methods are applied to investigate the dynamic response of an axially moving plate subjected to parametric and forced excitation. Based on the classical thin plate theory, the governing equation of the plate coupled with fluid is established and further discretized through the Galerkin method. These equations are solved using the method of multiple scales to obtain amplitude-frequency curves and phase-frequency curves. The stability of steady-state response is examined using Lyapunov’s stability theory. In addition, numerical analysis is employed to validate the results of analytical solutions based on the Runge–Kutta method. The multi-value and stability of periodic solutions are verified through stable periodic orbits. Detailed parametric studies show that proper selection of system parameters enables the system to stay in primary resonance or simultaneous resonance, and the state of the system can switch among different periodic motions, contributing to the optimization of fluid–structure interaction system.

The present article mainly focuses on the transient thermal dispersal within a moving plate using the non-Fourier heat flux model. Furthermore, the innovative, sophisticated artificial neural network strategy with the Levenberg-Marquardt backpropagated scheme (ANNS-LMBS) is proposed for determining the transient temperature in the convective-radiative plate. Using dimensionless terms, the energy model for transient heat exchange is simplified into a non-dimensional form. The arising partial differential equation (PDE) is then numerically tackled using the finite difference method (FDM). A data set for the various scenarios of the thermal parameters influencing the thermal variation through the plate has been generated using the FDM. In addition, the effect of the dimensionless physical variables on the thermal profile of a moving plate has been examined and discussed in detail. Increments in the convection-conduction and radiation-conduction parameters are figured to yield a reduction in the transient thermal dispersion. An upsurge in the Peclet number caused the improvement of thermal dispersal in the plate.