The technique of Levenberg–Marquardt back propagation with neural networks (TLMB-NN) was used in this research article to investigate the heat transfer of Maxwell base fluid flow of nanomaterials (HTM-BFN) with MHD over vertical moving surfaces. In this study, the effects of thermal energy, concentration, and Brownian motion are also employed. Moreover, the impacts of a heat-absorbing fluid with viscous dissipation and radiation have been explored. To simplify the governing equations from a stiff to a simple system of non-linear ODEs, we exploited the efficacy of suitable similarity transformation mechanism. Through applicability of state-of-the-art Adams numerical technique, a set of data for suggested (TLMB-NN) is generated for several situations (scenarios) by changing parameters, such as the Thermophoresis factor N_t, Hartmann number M, Eckert number E_c, concentration Grashoff parameter G_c, Prandtl number P_r, Lewis number Le, thermal Grashof number G_T, and Brownian motion factor N_b. The estimate solution of different instances has validated using the (TLMB-NN) training, testing, and validation method, and the recommended model was compared for excellence. Following that, regression analysis, mean square error, and histogram explorations are used to validate the suggested (TLMB-NN). The proposed technique is distinguished based on the proximity of the proposed and reference findings, with an accuracy level ranging from 10⁻⁹ to 10⁻¹⁰.

The numerical, analytical, theoretical and experimental study of thermal transport is an active field of research due to its enormous applications and use in numerous systems. This report covers the impacts of thermal transport on pseudo-plastic material past over a horizontal, heated and stretched porous sheet. Modeling of energy conservation is based upon a generalized heat flux model along with a heat generation/absorption factor. The modeled phenomenon is derived in the Cartesian coordinate system under the usual boundary-layer approach proposed by Prandtl, which removes the complexity of the problem. The modeled rheology is obtained in the form of coupled, nonlinear PDEs. These derived PDEs are converted into ODEs with the engagement of similarity transformation. Afterwards, converted ODEs containing some emerging parameters have been approximated numerically with a powerful and effective scheme, namely the finite element approach. The obtained results are compared with the published findings as a limiting case of current research, and an excellent agreement in the obtained solution was found, which guarantees the effectiveness of the used methodology. Furthermore, it is recommended that the finite element approach is a good method among other existing methods and can be effectively applied to nonlinear problems arising in the mathematical modeling of different phenomenon.

In this study, a novel data-driven control scheme is presented for MEMS gyroscopes (MEMS-Gs). The uncertainties are tackled by suggested type-3 fuzzy system with non-singleton fuzzification (NT3FS). Besides the dynamics uncertainties, the suggested NT3FS can also handle the input measurement errors. The rules of NT3FS are online tuned to better compensate the disturbances. By the input-output data set a data-driven scheme is designed, and a new LMI set is presented to ensure the stability. By several simulations and comparisons the superiority of the introduced control scheme is demonstrated.

The objective of this study is to explore the flow features and heat transfer properties of an MHD hybrid nanofluid between two parallel plates under the effects of joule heating and heat absorption/generation (MHD-HFRHT) by utilizing the computational strength of Levenberg–Marquardt Supervised Neural Networks (LM-SNNs). Similarity equations are utilized to reduce the governing PDEs into non-linear ODEs. A reference solution in the form of data sets for MHD-HFRHT flow is obtained by creating different scenarios by varying involved governing parameters such as the Hartman number, rotation parameter, Reynolds number, velocity slip parameter, thermal slip parameter and Prandtl number. These reference data sets for all scenarios are placed for training, validation and testing through LM-SNNs and the obtained results are then compared with reference output to validate the accuracy of the proposed solution methodology. AI-based computational strength with the applicability of LM-SNNs provides an accurate and reliable source for the analysis of the presented fluid-flow system, which has been tested and incorporated for the first time. The stability, performance and convergence of the proposed solution methodology are validated through the numerical and graphical results presented, based on mean square error, error histogram, regression plots and an error-correlation measurement. MSE values of up to the accuracy level of 1 × 10⁻¹¹ established the worth and reliability of the computational technique. Due to an increase in the Hartmann number, a resistance was observed, resulting in a reduction in the velocity profile. This occurs as the Hartmann number measures the relative implication of drag force that derives from magnetic induction of the velocity of the fluid flow system. However, the Reynolds number accelerates in the velocity profile due to the dominating impact of inertial force.

The main purpose of this research is to scrutinize the heat and mass transfer in the Casson hybrid nanofluid flow over an extending cylinder in the presence of a magnetic dipole and double stratification. The nanofluid contained chemically reactive hybrid nanoparticles (Ag, MgO) in the conventional fluids (water). The effects of viscous dissipation, radiation, and concentration stratification were taken into consideration. In the presence of gyrotactic microorganisms and the Non-Ficks Model, the flow was induced. Incorporating microorganisms into a hybrid nanofluid flow is thought to help stabilize the dispersed nanoparticles. For viscosity and thermal conductivity, experimental relations with related dependence on nanoparticle concentration were used. To acquire the nonlinear model from the boundary layer set of equations, suitable similarity transformations were employed. The built-in function bvp4c of Matlab software was utilized to solve the transformed equation numerically. The graphical results were obtained for temperature, velocity, concentration, and microorganism distribution for various parameters. The numerical amounts of drag friction, heat transport rate, and motile density number for different parameters are presented through tables. It is seen that the fluid velocity is augmented by the increase of the curvature parameter, while a decrease occurs in the fluid velocity with an increase in the magnetic and slips parameters. The comparison of the present study with previously available studies is discussed, which shows a good agreement with published results.

In this paper, the problem of frequency regulation in the multi-area power systems with demand response, energy storage system (ESS) and renewable energy generators is studied. Dissimilarly to most studies in this field, the dynamics of all units in all areas are considered to be unknown. Furthermore time-varying solar radiation, wind speed dynamics, multiple load changes, demand response (DR), and ESS are considered. A novel dynamic fractional-order model based on restricted Boltzmann machine (RBM) and deep learning contrastive divergence (CD) algorithm is presented for online identification. The controller is designed by the dynamic estimated model, error feedback controller and interval type-3 fuzzy logic compensator (IT3-FLC). The gains of error feedback controller and tuning rules of the estimated dynamic model are extracted through the fractional-order stability analysis by the linear matrix inequality (LMI) approach. The superiority of a schemed controller in contrast to the type-1 and type-2 FLCs is demonstrated in various conditions, such as time-varying wind speed, solar radiation, multiple load changes, and perturbed dynamics.