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The impact of Hall current on the multiphase thermal transfer of an incompressible electrically conductive Jeffrey flow over an infinitely vertical plate when heat absorption and chemical reaction are present has been examined. Partial differential equations have been used to describe the process, accounting for heat and mass transfer effects. This study uses extended Fourier's and Fick's laws together with the recently announced constant proportional Caputo (CPC) fractional operator. The fractional model is converted into a nondimensional form by applying some appropriate quantities. The nondimensional produced fractional model for momentum, heat, and diffusion equations based on the CPC fractional operator has been calculated semi‐analytically by applying the Laplace method. The Mathcad 15 software to sketch the graphs for several factors, like the Grashof number, mass Grashof number, Schmidt number, Prandtl number, Hall, and magnetic field parameters, is used to describe the velocity profile. Additionally, a graphical explanation is provided for the influence of the appeared parameters, particularly the effect of the fractional parameters. It is concluded that the result of the fluid model developed by the generalized constitutive relations is more accurate and generalized than the results of the artificially contracted fractional model. A fractional derivative is therefore the ideal option to achieve controlled concentration, temperature, and velocity. The current study is immediately relevant to geophysical, cosmically fluid dynamics, medical, biological, and any other processes that are significantly enhanced by a low gas density and a high magnetic field. [ABSTRACT FROM AUTHOR]

AbstractA study is conducted on the unsteady motion of a free convective flow of second grade fluid, energy transfer, and Darcy’s law over an oscillatory smooth vertical plate. The study compares two different approaches in developing a fractional model: the Caputo-Fabrizio operator with nonsingular kernel and the constant proportional Caputo fractional operator with Fourier’s and Fick’s laws. By applying the Laplace method and transforming the provided set of equations into nondimensional form, we obtained semi-analytical results and presented these results through graphical analysis. The study examines how different flow parameters, including the fractional parameters, affect the velocity, mass, and heat profiles of the physical system. The results suggest that the physical model using constant proportional Caputo derivative leads to higher temperature, stronger concentration, and increased velocity compared to the Caputo-Fabrizio model. This highlights the importance of selecting an appropriate fractional model when studying complex physical systems. It is also depicted from the whole analysis that field variables with novel hybrid fractional derivative constant proportional Caputo exhibits a more effective and declining tendency than Caputo-Fabrizio. [ABSTRACT FROM AUTHOR]

A fractional technique is used to evaluate the temperature, mass, and velocity flow of single and double wall CNTs over a vertical plate. Slip boundary conditions and applied magnetic force are addressed. Human blood is used to examine how base fluid behaves. Applying the proper dimensionless variables results in the dimensionless formulation of initial and boundary conditions related to the governed dimensional concentration, momentum, and energy equations. The Laplace transform technique is used to resolve the dimensionless governing partial differential equations and get the solutions. The constant proportional Caputo (CPC) time-fractional derivative is a unique class of fractional model used in the simulation technique. The fundamental definitions are used to support the said model first. Using MWCNTs and SWCNTs in comparison to the flow characteristics, a thermal and mass study is given. The heat and mass transfer processes for single-walled carbon nanotubes (SWCNTs) have been shown to typically be progressive. The momentum profile decreases as the fractional variables rise. Multi-walled carbon nanotubes (MWCNTs) show more progressive velocity control as a result of the magnetic parameter. Graphs demonstrate the influence of embedding factors on the velocity, energy, and concentration profiles. [ABSTRACT FROM AUTHOR]

The localisation of a network is the process of gaining access to a node's precise location or position. Using this technology, it is possible to determine the exact position of each network node in terms of a select few nodes within a subset. The locating set of a network is this subset, and the locating number of a network is its lowest cardinality. While the edge locating number is the same concept but on the bonds instead of nodes. In this work, we discussed some resolvability parameters such as locating number, edge locating number, fault-tolerant locating number and partition locating number of honeycomb rectangular torus. The honeycomb rectangular torus is very effective and innovative structure in chemical graph theory. This type of structure is being used in image processing, cellular phone base stations, computer graphics and more in mathematical chemistry. [ABSTRACT FROM AUTHOR]

The generalized magnetohydrodynamics (MHD) free convection flow of a Casson fluid through a channel immersed in a porous media with mass and heat transfer is considered. With heat generation, the contribution of concentration gradient is taken into account for heat flux (Dufour effect), and chemical reaction of order first for species balance is also considered. Initially, governing equations of flow model are reduced to nondimensional equations and then solved analytically. The transformed solutions for concentration, temperature, and velocity are written in summation form to invert by Laplace transform easily. The closed form solution of field variables has been plotted graphically due to different parametric variations to analyze the behavior of concentration, temperature, and flow fields against the physical parameters. Furthermore, comparisons among fractionalized and ordinary concentration, temperature, and velocity fields are made to see the effect of parameter α. It is concluded that concentration, temperature, and velocity obtained with fractional derivative are smaller than that obtained by ordinary derivative. Therefore, fractional derivative is the best choice to obtain controlled concentration, temperature, and velocity. [ABSTRACT FROM AUTHOR]

Unsteady flow of fractionalized Jeffrey fluid over a plate is considered. In addition, thermo diffusion and slip effects are also used in the problem. The flow model is solved using Constant proportional Caputo fractional derivative. Initially, the governing equations are made non-dimensional and then solved by Laplace transform. From the Figs., it is observed that Prandtl and Smith numbers have decreasing effect on fluid motion, whereas thermodiffusion have increasing effect on fluid motion. Moreover, comparison among fractionalized and ordinary velocity fields is also drawn. [ABSTRACT FROM AUTHOR]

The purpose of this paper to explain the role and importance of fractional derivatives for mass and heat transfer in Casson nanofluids including clay nanoparticles. These particles can be found in water, kerosene, and engine oil. The physical flow phenomena are illustrated using PDE and thermophysical nanoparticle properties, and this paper addresses the Casson fractional fluid along with chemical reaction and heat generation. The heat and mass fluxes are generalized using the constant proportional Caputo fractional derivative. The present flow model are solved semi-analytically using the Laplace transform. We generated several graphs to understand how various flow factors affect velocity. The acquired results reveal that fractional parameters have dual behavior in velocity profiles. Velocity and temperature are also compared to previous studies. Compared to the other fractional derivatives results, field variables and proposed hybrid fractional derivatives showed a more decaying trend. Furthermore, significant results of clay nanoparticles with various base fluids have been obtained. [ABSTRACT FROM AUTHOR]