Free convection flow of non-Newtonian fluids over flat, heated surfaces is an important natural phenomenon that also occurs in human-made engineering processes under various physical and mechanical situations. In the current study, the free convection magnetohydrodynamic flow of Jeffrey fluid with heat and mass transfer over an infinite vertical plate is examined. Mathematical modeling is performed using Fourier’s and Fick’s laws, and heat and momentum equations have been obtained. The non-dimensional partial differential equations for energy, mass, and velocity fields are determined using the Laplace transform method in a symmetric manner. Later on, the Laplace transform method is employed to evaluate the results for the temperature, concentration, and velocity fields with the support of Mathcad software. The governing equations, as well as the initial and boundary conditions, satisfy these results. The impacts of fractional and physical characteristics have been shown by graphical illustrations. The obtained fractionalized results are generalized by a more decaying nature. By taking the fractional parameter $\beta ,\gamma \to 1$, the classical results with the ordinary derivatives are also recovered, making this a good direction for symmetry analysis. The present work also has applications with engineering relevance, such as heating and cooling processes in nuclear reactors, the petrochemical sector, and hydraulic apparatus where the heat transfers through a flat surface. Moreover, the magnetized fluid is also applicable for controlling flow velocity fluctuations.

Pulsatory movements appear in a variety of fascinating applications involving periodic flow propagation and control. Pulsing encourages mixing and, as a result, mass and heat exchange with the boundaries. Pulsing also helps to decrease surface fouling by allowing solid particles to migrate. An exact solution of the Navier–Stokes equations for the transport of an incompressible viscous fluid in a channel with arbitrary pressure distribution is described in this study. The flow is defined by two primary parameters: the pulsation parameter, which is determined by the periodic pressure gradient, and the kinetic Reynolds number, which is determined by the pulsation frequency. The purpose of employing hybrid nanofluid (HNF) is to increase the base fluid’s thermal conductivity. We regard Ag and Au as nanoparticles (NPs) and blood as a base fluid for this phenomenon. Broadening this reveals that the consideration of nanoparticles has impressively extended the warm movement at the parcels of both turbulent and laminar frameworks. Attention is paid to the slope of speed, temperature, and voltage. The geometric model is therefore described using a symmetry technique. We developed the governing equation for this problem’s analytical solutions. The velocity and temperature fields solution is given in the form of the Bessel and modified Bessel functions. Graph results show the mathematical benefits of the current limits: for instance, Hartmann number $M$, solid volume part of nanoparticles $\varphi$, Reynolds number $R{e}_{\beta }$, Prandtl number $Pr$, intermittent slob limit, etc. The strain angles introduced in the stress contrast, frictional force, velocity profile, and temperature profile were obtained, and the characteristics of the vortex were investigated. Resources at various boundaries of the perceptual flow are examined. As with the final essence, the smoothest results are analyzed and recorded. It has also been discovered that the velocity may be regulated by the external magnetic field, which affects the temperature profiles and hence the heat transfer, which can be enhanced or lowered by mastering the magnetic field.

The correlation between two disparate variables conquers a significant habitation in statistics. The concept of correlation coefficient (CC) is one of the well-known indicators, but it is not used in interval-valued intuitionistic fuzzy hypersoft set (IVIFHSS) information. It is a generalization of interval-valued intuitionistic fuzzy soft sets and a refined extension of intuitionistic fuzzy hypersoft sets. However, using the CC and weighted correlation coefficient (WCC) has not yet been explored for IVIFHSS information. The core objective of this research is to present the correlation coefficient (CC) and weighted correlation coefficient (WCC) for interval-valued intuitionistic fuzzy hypersoft sets (IVIFHSS) and their mandatory properties. A prioritization technique for order preference by similarity to the ideal solution (TOPSIS) is developed based on proposed correlation measures. To ensure the symmetry of the developed scheme, we consider mathematical clarifications of correlation contractions. Based on assessments, it conceded vibrant multi-attribute decision-making (MADM) methodology with the most substantial significance. In addition, a statistical illustration is designated to regulate the operative usage of a decision-making configuration in thermal energy storage techniques. The productivity of the advocated algorithm is more reliable than existing replicas to control the favorable configurations of the premeditated study.

The new Laplace variational iterative method is used in this research for solving the (2+1)-D and (3+1)-D Burgers equations. This technique relies on the modified variational iteration method and the Laplace transform. To apply this approach, the differential problem is first transformed into an algebraic form using the Laplace transform, and then the algebraic equations are iteratively solved using the modified variational iterative approach. By utilizing this technique, the Burgers equations can be solved both numerically and analytically. The study demonstrates the effectiveness of the new Laplace variational iterative approach through three specific examples.

Viscoelastic liquid sheet of couple-stress type streaming with relative motion into an inviscid gas through porous molium is studied theoretically and quantitatively in this project. To derive the differential equations that describe liquids, gases, and the electric field, we linearized the governing equations of motion and continuity, Maxwell’s equations in quasi-static approximation, and the appropriate boundary conditions at the two interfaces. Then we used the normal mode method. It was demonstrated analytically that the solutions to these differential equations can be found for both symmetric and antisymmetric disturbances, respectively. We could not obtain an explicit form of the growth rates since we could not solve the dispersion relations for both situations because they were obtained in highly complex forms. The Mathematica program is used to solve the dimensionless forms of the dispersion relations numerically using Gaster’s theorem. Various influences on the stability analysis of the considered system have been studied in detail, and it is determined that the system in the presence of a porous material is more unstable than it would be otherwise. In a two-dimensional system, the antisymmetric disturbance case is found to be more unstable than the corresponding symmetric disturbance situation. Some characteristics, such as Wabe number, Ohnesorge number, and electric field, have destabilizing effects, whereas others, such as porosity, medium permeability, viscoelasticity parameter, gas-to-liquid viscosity ratio, and dielachic constants, have stabilizing effects. Finally, it is discovered that the gas-to-liquid velocity ratio plays a dual role in the stability condition depending on whether the gas-to-liquid velocity ratio U ≶ 1. In the past, we have only found evidence of very few previous studies.

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