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The purpose of this paper is to propose the knowledge of thermal transport of magneto hydrodynamic non-Newtonian fluid flow over a melting sheet in the presence of exponential heat source.

The group of PDE is mutated as dimension free with the assistance of similarity transformations and these are highly nonlinear and coupled. The authors solved the coupled ODE’s with the help of fourth-order Runge–Kutta based shooting technique. The impact of dimensionless sundry parameters on three usual distributions of the flow was analyzed and bestowed graphically. Along with them friction factor, heat and mass transfer rates have been assessed and represented with the aid of table.

Results exhibited that all the flow fields (velocity, concentration and temperature) are decreasing functions of melting parameter. Also the presence of cross-diffusion highly affects the heat and mass transfer performance.

Present paper deals with the heat and mass transfer characteristics of magnetohydrodynamics flow of non-Newtonian fluids past a melting surface. The effect of exponential heat source is also considered. Moreover this is a new work in the field of heat transfer in non-Newtonian fluid flows.

Whilst a modest number of investigations have been undertaken concerning nanofluids (NFs), the exploration of fluid flow under exponentially stretching velocities using NFs remains comparatively uncharted territory. This work presents a distinctive contribution through the comprehensive examination of heat and mass transfer phenomena in the NF ND–Cu/H₂O under the influence of an exponentially stretching velocity. Moreover, the investigation delves into the intriguing interplay of gyrotactic microorganisms and convective boundary conditions within the system.

Similarity transformations have been used on PDEs to convert them into dimensionless ODEs. The solution is derived by using the homotopy analysis method (HAM). The pictorial notations have been prepared for sundry flow parameters. Furthermore, some engineering quantities are calculated in terms of the density of motile microbes, Nusselt and Sherwood numbers and skin friction, which are presented in tabular form.

The mixed convection effect associated with the combined effect of the buoyancy ratio, bioconvection Rayleigh constant and the resistivity due to the magnetization property gives rise to attenuating the velocity distribution significantly in the case of hybrid nanoliquid. The parameters involved in the profile of motile microorganisms attenuate the profile significantly.

The current simulations have uncovered fascinating discoveries about how metallic NFs behave near a stretched surface. These insights give us valuable information about the characteristics of the boundary layer close to the surface under exponential stretching.

The novelty of the current investigation is the analysis of NF ND–Cu/H₂O along with an exponentially stretching velocity in a system with gyrotactic microorganisms. The investigation of fluid flow at an exponentially stretching velocity using NFs is still relatively unexplored.

Face contact has a strong impact on the service life of non-contacting gas face seals; the current research which mainly focuses on the face contact had appeared during the startup or shutdown operation. This paper aims to present a closed-form contact model of a gas face seal during the opened operation.

Referring to the axial rub-impact model of rotor dynamics, a closed-form contact model is developed under a nonparallel plane contact condition that corresponds to the local face contact of sealing rings arising from some disturbances during the opened operation. The closed-form contact model and a direct numerical contact model are performed on Gaussian surfaces to compare the contact behavior.

The closed-form contact model is in a good agreement with the direct numerical contact model. However, the closed-form contact model cannot involve the influence of grooves on the sealing ends. The error is eliminated in some other types of gas face seals such as coned gas face seals. Besides non-contacting face seals, the closed-form model can be applied to the axial rub impact of rotor dynamics.

A closed-form contact model of a gas face seal is established during the opened operation. The closed-form contact model is validated by a direct numerical contact model. The closed-form contact model also suits for axial rub-impact of rotor dynamics.

This paper aims to seek purely analytical results relying on the physical parameters including the temperature jump parameter.

The exponential fin profiles and heat transfer enhancement influenced by a temperature jump at the base are the main targets of this paper.

The introduced temperature slip at the base penetrates through the surface of the fin and reorganizes the distribution of temperature all over the surface. The overall impact of the temperature jump on the fin efficiency is such that it acts to lower the fin efficiency. However, the efficiency of the exponential fin is increasing for growing shape exponential fins as compared to the rectangular and decaying ones. Hence, exponential fins amenable to certain temperature jump has significance in technological cooling processes. Finally, the optimum dimensions regarding the base fin thickness and the fin length of the exponential profiles are assessed by means of optimizing the base heat transfer rate given a cross-sectional area.

Exact solutions are provided for optimum exponential type fins subjected to a temperature jump. The optimum dimensions regarding the base fin thickness and the fin length of the exponential profiles are assessed.

This paper aims to examine the influence of radiative nanoparticles on incompressible electrically conducting upper convected Maxwell fluid (rate type fluid) flow over a convectively heated exponential stretching sheet with suction/injection in the presence of heat source taking chemical reaction into account. Also, a comparison of the flow behavior of Newtonian and Maxwell fluid containing nanoparticles under the effect of different thermophysical parameters is elaborated. Velocity, temperature and nanoparticle volume fractions are assumed to have exponential distribution at boundary. Buongiorno model is considered for nanofluid transport.

The equations, which govern the flow, are reduced to ordinary differential equations using suitable transformation. The transformed equations are solved using a robust homotopy analysis method. The convergence of the homotopy series solution is explicitly discussed. The present results are compared with the results reported in the literature and are found to be in good agreement.

It is observed from the present study that larger relaxation time leads to slower recovery, which results in a decrease in velocity, whereas temperature and nanoparticle volume fraction is increased. Maxwell nanofluid has lower velocity with higher temperature and nanoparticle volume fraction when compared with Newtonian counterpart. Also, the presence of magnetic field leads to decrease the velocity of the nanofluid and enhances the skin coefficient friction. The existence of thermal radiation and heat source enhance the temperature. Further, the presence of chemical reaction leads to decrease in nanoparticle volume fraction. Higher value of Deborah number results in lower the rate of heat and mass transfer.

The novelty of present work lies in understanding the impact of fluid elasticity and radiative nanoparticles on the flow over convectively heated exponentially boundary surface in the presence of a magnetic field using homotopy analysis method. The current results may help in designing electronic and industrial applicants. The present outputs have not been considered elsewhere.

In this communication, a theoretical simulation is aimed to characterize the Darcy–Forchheimer flow of a magneto-couple stress fluid over an inclined exponentially stretching sheet. Stokes’ couple stress model is deployed to simulate non-Newtonian microstructural characteristics. Two different kinds of thermal boundary conditions, namely, the prescribed exponential order surface temperature (PEST) and prescribed exponential order heat flux, are considered in the heat transfer analysis. Joule heating (Ohmic dissipation), viscous dissipation and heat source/sink impacts are also included in the energy equation because these phenomena arise frequently in magnetic materials processing.

The governing partial differential equations are transformed into nonlinear ordinary differential equations (ODEs) by adopting suitable similar transformations. The resulting system of nonlinear ODEs is tackled numerically by using the Runge–Kutta fourth (RK4)-order numerical integration scheme based on the shooting technique. The impacts of sundry parameters on stream function, velocity and temperature profiles are viewed with the help of graphical illustrations. For engineering interests, the physical implication of the said parameters on skin friction coefficient, Nussult number and surface temperature are discussed numerically through tables.

As a key outcome, it is noted that the augmented Chandrasekhar number, porosity parameter and Forchhemeir parameter diminish the stream function as well as the velocity profile. The behavior of the Darcian drag force is similar to the magnetic field on fluid flow. Temperature profiles are generally upsurged with the greater magnetic field, couple stress parameter and porosity parameter, and are consistently higher for the PEST case.

The findings obtained from this analysis can be applied in magnetic material processing, metallurgy, casting, filtration of liquid metals, gas-cleaning filtration, cooling of metallic sheets, petroleum industries, geothermal operations, boundary layer resistors in aerodynamics, etc.

From the literature review, it has been found that the Darcy–Forchheimer flow of a magneto-couple stress fluid over an inclined exponentially stretching surface with heat flux conditions is still scarce. The numerical data of the present results are validated with the already existing studies under limited cases and inferred to have good concord.

Trajectory tracking is an important issue to underactuated unmanned surface vehicles (USVs). However, parametric uncertainties and environmental disturbances bring great challenges to the precise trajectory tracking control of USVs. This paper aims to propose a robust trajectory tracking control algorithm with exponential stability for underactuated USVs with parametric uncertainties and unknown environmental disturbances.

In this method, the backstepping method and sliding mode control method are combined to ensure that the underactuated USV can track and maintain the desired trajectory. In addition, a modified switching-gain adaptation algorithm is adopted to enhance the robustness and reduce chattering. Besides, the global exponential stability of the closed-loop system is proved by Lyapunov’s direct method.

The proposed method in this paper offers a robust trajectory tracking solution to underactuated USVs and it is verified by simulations and experiments. Compared with the traditional proportion-integral-derivative method and several state-of-the-art algorithms, the proposed method has superior performance in simulation and experimental results.

This paper proposes a robust trajectory tracking control algorithm with exponential stability for underactuated USVs. The proposed method achieves exponential stability with better robustness and transient performance.

This paper aims to present a sliding mode control method based on disturbance observer (DO) for improving the reaching law of permanent magnet synchronous motor (PMSM).

Aiming at the insufficiency of the traditional exponential reaching law used in sliding mode variable structure control, an exponential reaching law related to the speed error is proposed. The improved exponential reaching law can adaptively adjust the size of the constant velocity term in the reaching law according to the size of the speed error, so as to adaptively adjust the speed of the system approaching the sliding mode surface to overcome the control deviation and improve the dynamic and steady state performance. To improve the anti-interference ability of the system, a DO is proposed to observe the external disturbance of the system, and the observed value is used to compensate the system. The stability of the system is analyzed by Lyapunov theorem. The effectiveness of this method is proved by simulation and experiment.

Simulation and experiment show that the proposed method has the advantages of fast response and strong anti-interference ability.

The proposed method cannot observe the disturbance caused by the change of internal parameters of the system.

A sliding mode control method for PMSM is proposed, which has good control performance. The proposed method can effectively suppress chattering, ensure fast response speed and have strong anti-interference ability. The effectiveness of the algorithm is verified by simulation and experiment.

The purpose of this study is to study the impacts of exponential space-dependent heat source (ESHS) and thermal radiation in Marangoni convective flow of Cross fluid. The passively controlled model is developed to exhibit the nanoparticles’ concentration on the surface.

The resulting problem under consideration is tackled by using the shooting approach.

Temperature field augments with enhancement of the thermophoretic, exponential-based space heat source (ESHS) and radiation parameters, whereas it decays with the increase of the Marangoni ratio parameter.

To the best of the authors’ knowledge, no such analysis has yet been reported.

This paper aims to improve upon the performance of magnetic fluid‐based squeeze film between transversely rough curved annular plates by embarking on a comparative study of the geometrical structure of the curved annular plates.

The objectives are met by mathematically modeling a magnetic fluid‐based squeeze film between transversely rough curved annular plates. The standard method is to solve the associated Reynolds' equation with appropriate boundary conditions by describing the random roughness through a stochastic random variable with non‐zero mean, variance and skewness. Results for bearing performance characteristics such as pressure distribution and load‐carrying capacity are numerically computed. In order to analyze the quantitative effect of the roughness, different geometrical structures of surfaces have been considered and the results are compared.

Certainly, the performance of the bearing with the magnetic fluid lubricant is comparatively better than the conventional lubricant. The findings indicate that although the effect of roughness is adverse in general, the adverse effect introduced by roughness and aspect ratio can be compensated for, to a considerable extent, by the positive effect of magnetization parameter in the case of negatively skewed roughness by choosing the curvature parameters properly.

From the industry point of view, this investigation will be definitely useful for improving the performance of the squeeze film based on magnetic fluid between transversely rough curved annular plates by minimizing the effect of roughness. Furthermore, it offers an additional degree of freedom from a design point of view in the form of the geometrical structure of the surfaces.

The paper presents significant information as it compares shapes and offers suggestions for the best improved performance from a bearing's longevity point of view. This study presents an approach for the enhanced performance of the magnetic fluid‐based squeeze film between transversely rough curved annular plates.