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Dusty Casson fluids and tetra-hybrid nanofluids are complex phenomena that find their extensive uses in engineering and industrial applications. For instance, dusty fluids are used in gas-freezing systems and nuclear power reactors. The main objective of this article is to focus on the characterization of generalized two-phase free convection magnetohydrodynamic flow of dusty tetra-hybrid Casson nanofluid among parallel microplates: dusty Casson fluid and tetra-hybrid nanofluid exhibit free movement and electrical conductivity. The Caputo–Fabrizio fractional derivative recently discovered generalizes the partial differential equations governing the flow. Highly accurate temperature and velocity distributions can be obtained using finite sine Fourier and Laplace transform together. This study examines the relationships between temperature, dust particle velocity, and Casson fluid velocity, along with the effects of magnetic parameter, Grashof number, dusty fluid parameter, Peclet number, Reynold number, and particle mass parameter. The Mathcad-15 software provides Casson, dusty, and temperature profiles graphically. The Nusselt number and skin friction are also examined for the tetra-hybrid nanofluid. The fractional Casson fluid model is more accurate than the classical model in terms of velocity, temperature, heat transfer, and skin friction. Graphical results conclude that the fractional Casson fluid model describes a more realistic aspect of both (fluid and dust particle) velocities and temperature profiles, heat transfer rate, and skin friction than the classical Casson fluid model. Furthermore, the heat transfer rate enhanced from 0 to 39.3111% of the tetra-hybrid nanofluid.

This paper investigates the flow of a second‐grade viscoelastic fluid with dust particles under hydromagnetic effects between vertical plates. This study investigates the effects of the left plate's oscillations, which induce fluid motion, on heat and mass transfer, and particle temperature. The study also considers the variable temperature and concentration. Mathematical models are developed using partial differential equations to represent the flow regime. To generalize energy and concentration Fick's and Fourier's laws are employed. Laplace and finite Fourier‐Sine transforms are then used to solve the resulting system of dimensionless equations. Finally, Zakian's numerical technique is used in MATHCAD software to compute the Laplace inverse and obtain the final solution. The research concludes that the fractional approach is more realistic and practical than the classical approach. Changes in mass and heat transfer rates, as well as skin friction on the left plate, are observed over time across various physical parameters. Additionally, dust particles can be employed in various applications, including agriculture. In this sector, they can be mixed with water to create a dust suspension, which is subsequently sprayed over crops to enhance the effectiveness of pesticide application. [ABSTRACT FROM AUTHOR]

There are several applications for electro-osmotic MHD flow of hybrid Ferrofluid in the present era, notably in the biochemical as drug delivery systems, microfluidic devices, biomedical diagnostics, microscale systems and medical industries. The electro-osmotic MHD flow of a hybrid Ferrofluid containing Cobalt Ferrite, magnetite nanoparticles via a vertically inclined microchannel is investigated in this study. In furthermore, the perpendicular magnetic field is considered. Investigations are also carried into the effects of mass and heat transfer in this moving fluid. Partial differential equations provide as a representation for the aforementioned physical phenomenon, using suitable dimensionless nondimensional variables. Also, the classical system is fractionalized using the generalized Fourier and Fick's law. Generalizations are made based on the account of the Caputo derivative. The solution for the velocity, concentration, and temperature outlines is developed by using the Fourier and Laplace techniques. Moreover, the parametric impact of many physical factors as the Brinkman parameter, the temperature, velocity, concentration and stress parameters (Schmidt, Grashof, and Prandtl numbers). Graphs and discussions of concentration distributions is also discussed. The Sherwood number, rate of heat transmission, and skin friction are calculated and summarized. Since the fractional models are more accurate, they also provide a broader variety of possible solutions. Considering the relevant data, these solutions could be the best. Additionally, the heat transfer rate is higher as compare to nanofluid and regular fluid. The Hybrid Ferrofluid having capability to control velocity boundary layer rapidly as compare to nanofluid and regular fluid. [ABSTRACT FROM AUTHOR]

Fractional calculus gets more attention in applied and pure science from the last two decay due to their valuable contribution. Due to extensive applications of fractional derivatives, the main aim of this article is focused on the multi fractional comparative study of entropy generation of magnetohydrodynamic (MHD) flow of Casson nanofluid with slipping and ramped wall heating effect on the plate. Set of partial differential equations forms governing equation and by using constant proportional–Caputo hybrid (CPC), Atangana–baleanu (AB) and Caputo Fabrizio (CF) fractional derivative generalized the model. Using the Laplace transform approach, a closed form of the solution is attained. Entropy production for Casson nanofluid is explored and compared using triple fractional modelled and for four different nanoparticles. Furthermore, the Bejan number is compared for the previously mentioned fractional derivatives. The graphs depict the effect of several parameters on the minimization and maximisation of multi generalised entropy generation. Instead of Atangana–baleanu and Caputo Fabrizio fractional operators, the newly proportional Caputo hybrid operator has a strong memory effect. It is concluded that CPC fractional model is more realistic then other two fractional model in case of ramped wall temperature while in case of isothermal wall temperature the results are vice versa. [ABSTRACT FROM AUTHOR]

Couple Stress Fluid (CSF) incorporates a new material constant whose, in contrast to a Newtonian fluid, regulates both couple stress and lubricant viscosity. Due to the fourth‐order spatial derivative term that this material constant introduces into the momentum equation, this fluid (CSF), even for classical fluid problems, has received limited research. The aim of this article is to examine the joint impact of heat transmission and magnetic field on a time‐fractional model of two‐phase free convection flow of dusty fluid that is electrically conducting. Among parallel plates, one of which is stationary and the other of which is oscillating with constant velocity, the CSF is supposed to flow. Heat is transferred by free convection and buoyant force, which generates the flow. Furthermore, all spherical dust particles are uniformly dispersed through the fluid. The flow is modeled mathematically in terms of PDEs. The provided derived system of PDEs is generalized by applying a recently invented fractional derivative, the Caputo‐Fabrizio fractional derivative. Finite sine Fourier and Laplace transformations are jointly applied to handle the problem. The velocity and temperature profiles have closed form solutions. The CSF outcomes for stimulating fluid parameters are shown in numerous graphs for CF time fractional derivatives. Additionally, the influence of various parameters has been discussed. Mathcad‐15 is used to plot the graphical outcomes for the CSF, dust particle, and temperature profiles. Furthermore, the skin friction and Nusselt number are calculated. Table 1 demonstrates how the rate of heat transmission reduces as the Peclet number's value rises. Similarly, Table 2 demonstrates that the skin friction increases as the magnetic parameter and couple stress parameter are raised. Table 3 and 4, shows the Regression analysis that the variation in the velocity for Couple stress and dusty fluid parameter are statistically significant. By increasing the couple stress parameter λ, retarde the both velocities profile. [ABSTRACT FROM AUTHOR]

Leadership is the key driver for the success of any organization. When we talk about educational organization, then its importance further increases. This study examines the impact of ethical leadership on the faculty job satisfaction of the higher education institutions of Balochistan. Furthermore, this study also explains how this relationship is channelized by self-efficacy, organizational commitment, and psychological empowerment. A purposive sampling technique was used to collect data from the 386 faculty of the higher education institutes across the Balochistan province of Pakistan. The data was gathered via a closed-ended questionnaire and was analyzed via SmartPLS. The findings of this study show that ethical leadership plays a significant role in the job satisfaction of the faculty members of the higher education institutes of Balochistan. Furthermore, this study also found that this relationship is channelled by self-efficacy, organizational commitment, and psychological empowerment. [ABSTRACT FROM AUTHOR]