International Journal of Modern Physics B

This work contains simulation of solidification within a container with new structure. The assumption of neglecting velocity term for solidification formulation leads to the reduction of number equation for such 2D modeling to two equations and FEM was selected for this purpose. This model involves adaptive grid that incorporates the implicit approach for transient terms. The water that incorporates various sizes of nanopowders leads to creating new material and for predicting the properties, the formulation based on homogeneous mixing has been utilized. Adding nanoparticles leads to a reduction of the required time around 26.52% and 12.25% when $d_p=30$ and 50 nm while its effect for $d_p=40$ nm is 41.19%. As the size of the particles augments upto 40 nanometer, the required time declines around 19.96% while augmenting upto 50 nanometer leads to augment of time of around 49.2%.

This paper studies a chemical reactive Maxwell nanofluid flow in porous media with generalized Fourier and Fick laws in the presence of temperature-dependent thermal conductivity and robin conditions past a spinning cone. The characteristics of the fluid flow are examined using the Buongiorno nanofluid model. The equations that regulate the flow are highly nonlinear and are simplified using similarity transformations. Numerical solution is obtained by employing the bvp4c technique. The characteristics of various parameters on tangential and azimuthal velocities, heat, and mass transfers are depicted graphically. An opposing behavior on the tangential and azimuthal velocity fields is depicted in elevating the Deborah number. The solutal field upsurges on increasing the order of the reaction. The mass flux strengthens by augmenting the Schmidt number and solutal relaxation time. The validation of the proposed model in the limiting case is also given.

In this paper, the symmetry reduction method and Nucci’s reduction method are used to obtain exact solutions to the Triki–Biswas equation. Furthermore, the new conservation theorem is utilized for finding the conservation laws of the given model. The conservation laws are derived for each admitted symmetry of the Triki–Biswas equation and satisfy the divergence condition. The 3D, contour and 2D figures are finally plotted to show the dynamics of the obtained exact solutions.

The objective of this paper is to discuss the entropy generation in electromagnetohydrodynamic (EMHD) Darcy–Forchheimer nanomaterial flow. Porous space by Darcy–Forchheimer relation is characterized. Thermal expression comprises of radiation, heat generation, electric and magnetic fields and dissipation. Buongiorno model (thermophoresis and random motions) for nanomaterial is taken. Features of entropy generation are addressed. Furthermore, cubic autocatalysis isothermal chemical reactions are studied. Newton built in-shooting technique is implemented for the solution of nonlinear differential system invoking appropriate transformation. Influence for emerging parameters on velocity, concentration, entropy rate and thermal field is graphically addressed. Velocity has similar behaviors for magnetic and electric field variables. Larger approximation of Eckert number boosts up temperatures while reverse trend holds for Prandtl number. Concentration has reverse impact for random and thermophoresis parameters. Entropy generation follows a similar pattern for Brinkman number and porosity parameter.

Politics is a crucial aspect of society. It has a very high impact on the development of a community and its population. Thinking and acts of a few political persons/parties affect the whole population. In our work, a dynamical mathematical model is being considered to investigate the ideological pressure and change in a region where a group is being violent to achieve the desired political results. The estimation of model parameters is made, and the results of general elections of a specific region (Basque country) are used to paint the future political scenario of the region by the derived model. Analytical investigation for the system of nonlinear differential equations governing the social phenomenon is also done. The worth of the considered model is shown by stability analysis.

In this paper, an investigation into Williamson nanofluid stagnation point flow of nano-biofilm over a stretching/ shrinking sheet with chemical reaction is performed. Moreover, the impact of cylindrical-shaped nanoparticles, activation energy, and bioconvection has been considered. The fluid’s fluctuating transport properties (dynamic viscosity, heat conductivity, nanoparticle mass diffusivity) and microorganism diffusivity are evaluated. The nonlinear systems of partial differential equations are transformed into nonlinear differential equations via the implementation of similarity transformations. The shooting approach and RK-4 technique are used for this investigation. The impacts of various fluid transport characteristics and various factors on patterns of velocity, temperature, the concentration of nanoparticles, and motile density are described. The Brownian motion, heat source and thermophoresis parameters all lead to a more consistent temperature profile being observed. It is seen that concentration-dependent properties decrease the velocity profile while the temperature, concentration, and motile density profiles increase. Also, the physical quantities decrease with the rising values of concentration-dependent properties.

The invention of novel light-harvesting materials is one of the primary reasons behind the acceleration of current scientific advancement and technological innovation in the solar sector. Organometal halide perovskite (OHP) has recently attracted a great deal of interest because of the high-energy conversion efficiency that has reached within a few years of its discovery and development. Modern machine learning (ML) technology is quickly advancing in a variety of fields, providing blueprints for the discovery and rational design of new and improved material properties. In this paper, we apply ML to optimize the material composition of OHPs, propose design methods and forecast their performance. Our ML model is built using 285 datasets that were taken from about 700 experimental articles. We have developed two different ML models to predict the bandgap and performance parameters of solar cell. In the first model, we employed three ML algorithms to investigate the relationship between bandgap and perovskite material composition. We estimated the performance characteristics using projected and actual bandgap. Second, ML models are used to predict the performance parameters employing the bandgap of perovskite and energy difference between electron transport layer (ETL) and hole transport layer (HTL) with perovskite as an input parameter. Simulation results suggest that the artificial neural network (ANN) technique, which predicts the bandgap by taking into consideration how cations and halide ions interact with one another, demonstrates a better degree of accuracy (with a Pearson coefficient of 0.91 and root mean square error of 0.059). The constructed ML model closely fits the theoretical prediction made by Shockley and Queisser, and that is almost hard for a person to discover from an aggregation of datasets.

This paper analyzes the analytical and numerical solutions’ structure of the combined mKdV equation and KdV equation (mKdV+KdV equation) using the Khater II (Khat. II) method and three accurate B-spline numerical schemes. ExCBS, SBS and TQBS numerical schemes are the numerical systems used. The handled model describes many distinct phenomena such as wave propagation of bounded particles with a harmonic force in a one-dimensional nonlinear lattice, propagation of ion-acoustic waves of small amplitude without Landau damping in plasma physics, and propagation of thermal pulse through a single sodium fluoride crystal in solid physics. Numerous examples show the relationship between quick and slow soliton, which generates phase shift. This phase shift is shown in a contour map to show the modest and colossal energy density along the path of fast and slow colliding solitons. Calculating the difference between analytical and numerical solutions shows whether they match spline-connected and distribution graphs.

Ferrofluids are made through the suspension of magnetic nanoparticles which are commonly used for the treatment of hyperthermia, malignant tumor treatment, magnetic cell separation, etc. These nanoparticles provide satisfactory results for the heat transport phenomena. Motivated by the applications of these nanoparticles, this study is performed for water-based nanofluid with a different type of magnetic nanoparticles for renewable energy and the development of the advanced cooling process of the radiator. Further, this study also talks about the impact of magnetized nanoparticles on natural convection flow occupied in a square cavity. The nanosized magnetic particles are mixed up in water to make a more convective flow. In this computational study, the momentum equation is updated with magnetohydrodynamics terms. The mathematical problem is achieved in the form of nonlinear complex partial differential equations which are simulated by using the renowned Galerkin finite element technique. The numerical code is validated with the previous study on the natural convection flow of viscous fluid in a square cavity and the verification procedure verified the good accuracy of the applied developed numerical code. The impact of the Hartmann number, Rayleigh number and the volume friction coefficient is discussed through contours and graphs. It is observed that nanofluids have more capacity to store energy as compared to regular fluids due to superior thermal transport properties. Moreover, the cobalt oxide (Co₃${\text{O}}_4)$ nanoparticles provide a greater heat transfer rate due to greater thermal conductivity as compared to other nanoparticles cobalt ferrite (CoFe₂${\text{O}}_4)$, magnetite (Fe₃${\text{O}}_4)$ and manganese–zinc–ferrite (Mn–Zn–Fe₂${\text{O}}_4)$. The heat transfer rate is increased by 30% for cobalt oxide, 18% for magnetite, 15% for manganese–zinc–ferrite and 12% for cobalt ferrite, respectively. Hence, the cobalt oxide nanoparticles which have a greater heat transfer rate can contribute to solar energy engineering and the advanced cooling process of the radiator.

The coupled-Higgs equation, which depicts a system of preserved scalar nucleons cooperating with unbiased scalar mesons, is investigated using the ${\varphi }^6$-model expansion approach in this paper. We want to look at the various particles that are created when scalar nucleons collide with unbiased scalar mesons. The modulus of the elliptic function $m\to 0$ and $m\to 1$ is used to obtain the trigonometric and hyperbolic functions. Under the stated limited constraints, all found solutions are used to validate the partial differential equation. We displayed 3D surfaces and 2D visuals of selected solutions produced with the assistance of a computer program to shed more light on the dynamic behavior of the acquired solutions.