This manuscript contains the modeling and analysis of an unsteady Carreau fluid with a magnetohydrodynamical effect over a stretching sheet. The governing momentum and energy equations admit a self-similarity solution. The system of ordinary differential equations has been solved analytically by the homotopy analysis method (HAM) and numerically by BVP4C (Matlab routine). An analysis of results shows that obtained analytical and numerical solutions are in excellent agreement with existing results in the literature. Furthermore, the effect of various fluid parameters on the velocity and temperature profiles are studied graphically. It is observed that velocity increases in the stretching sheet for power law index n and the Weissenberg number $We$, whereas it decreases for magnetic parameter $M^2$. Tabular analysis on skin friction and heat transfer rate is also presented against pertinent fluid parameters.

In this research work, the nonlinear coupled Konno–Oono (CKO) system is under examination to explore the dynamical soliton wave structure in the magnetic field through two distinct approaches with qualitative analysis. The magnetic potential represents an essential tool in constructing diverse functions in the fluency of the magnetic field. Based on the nature and physical context of certain magnetic fields, the CKO nonlinear evolution system was raised to modify the magnetic effects. Such impacts on the dynamics for the CKO system depend on the magnetic potential. The current study aims to expand the use of the sine–cosine and tan–cotan methods to process the CKO equations analytically. The two techniques show the applicability, simplicity, and low complexity based on the traveling-wave procedure. Assorted bright, dark, and mixed closed-form soliton solutions have been derived. The 3D solitons with different structures have been depicted. The interaction of displacements inside the magnetic field is also shown. For more generality, and because of the new findings in real-life applications of fractional calculus, the time-fractional CKO model in different versions is discussed, and its effects are illustrated. Finally, we analyze the stability explorations for the corresponding nonlinear ordinary system out of its sensitivity, bifurcation, and chaotic behaviors.

The present study develops a deep learning method for predicting the boiling heat transfer coefficient (HTC) of nanoporous coated surfaces. Nanoporous coated surfaces have been used extensively over the years to improve the performance of the boiling process. Despite the large amount of experimental data on pool boiling of coated nanoporous surfaces, precise mathematical-empirical approaches have not been developed to estimate the HTC. The proposed method is able to cope with the complex nature of the boiling of nanoporous surfaces with different working fluids with completely different thermophysical properties. The proposed deep learning method is applicable to a wide variety of substrates and coating materials manufactured by various manufacturing processes. The analysis of the correlation matrix confirms that the pore diameter, the thermal conductivity of the substrate, the heat flow, and the thermophysical properties of the working fluids are the most important independent variable parameters estimation under consideration. Several deep neural networks are designed and evaluated to find the optimized model with respect to its prediction accuracy using experimental data (1042 points). The best model could assess the HTC with an R² = 0.998 and (mean absolute error) MAE% = 1.94.

A precise microclimate control for dynamic climate changes in greenhouses allows the industry and researchers to develop a simple, robust, reliable, and intelligent model. Accordingly, the objective of this investigation was to develop a method that can accurately define the most suitable environment in the greenhouse for an optimal yield of roses. Herein, an optimal and highly accurate BO-DNN surrogate model was developed (based on 300 experimental data points) for a quick and reliable classification of the rose yield environment considering some of the most influential variables including soil humidity, temperature and humidity of air, CO₂ concentration, and light intensity (lux) into its architecture. Initially, two BO techniques (GP and GBRT) are used for the tuning process of the hyper-parameters (such as learning rate, batch size, number of dense nodes, number of dense neurons, number of input nodes, activation function, etc.). After that, an optimal and simple combination of the hyper-parameters was selected to develop a DNN algorithm based on 300 data points, which was further used to classify the rose yield environment (the rose yield environments were classified into four classes such as soil without water, correct environment, too hot, and very cold environments). The very high accuracy of the proposed surrogate model (0.98) originated from the introduction of the most vital soil and meteorological parameters as the inputs of the model. The proposed method can help in identifying intelligent greenhouse environments for efficient crop yields.