The T-Spherical Fuzzy set (T-SPHFS) is one of the core simplifications of quite a lot of fuzzy concepts such as fuzzy set (FS), intuitionistic fuzzy set (ITFS), picture fuzzy set (PIFS), Q-rung orthopair fuzzy set (Q-RUOFS), etc. T-SPHFS reveals fuzzy judgment by the degree of positive membership, degree of abstinence, degree of negative membership, and degree of refusal with relaxed conditions, and this is a more powerful mathematical tool to pair with inconsistent, indecisive, and indistinguishable information. In this article, several novel operational laws for T-SPFNs based on the Schweizer–Sklar t-norm (SSTN) and the Schweizer–Sklar t-conorm (SSTCN) are initiated, and some desirable characteristics of these operational laws are investigated. Further, maintaining the dominance of the power aggregation (POA) operators that confiscate the ramifications of the inappropriate data and Heronian mean (HEM) operators that consider the interrelationship among the input information being aggregated, we intend to focus on the T-Spherical fuzzy Schweizer–Sklar power Heronian mean (T-SPHFSSPHEM) operator, the T-Spherical fuzzy Schweizer–Sklar power geometric Heronian mean (T-SPHFSSPGHEM) operator, the T-Spherical fuzzy Schweizer–Sklar power weighted Heronian mean (T-SPHFSSPWHEM) operator, the T-Spherical fuzzy Schweizer–Sklar power weighted geometric Heronian mean (T-SPHFSSPWGHEM) operator, and their core properties and exceptional cases in connection with the parameters. Additionally, deployed on these newly initiated aggregation operators (AOs), a novel multiple attribute decision making (MADM) model is proposed. Then, the initiated model is applied to the City of Penticton (British Columbia, Canada) to select the best choice among the accessible seven water reuse choices to manifest the practicality and potency of the preferred model and a comparison with the proffered models is also particularized.

The aim of this article is to investigate the effect of mass and heat transfer on unsteady squeeze flow of viscous fluid under the influence of variable magnetic field. The flow is observed in a rotating channel. The unsteady equations of mass and momentum conservation are coupled with the variable magnetic field and energy equations. By using some appropriate similarity transformations, the partial differential equations obtained are then converted into a system of ordinary differential equations and are solved by Homotopy Analysis Method (HAM). The influence of the natural parameters are investigated for the velocity field components, magnetic field components, heat and mass transfer. A direct effect of the squeeze Reynold number is observed on both concentration and temperature. Moreover, increasing the magnetic Reynold number shows an increase in the fluid temperature, but in the case of concentration, an inverse relation is observed. Furthermore, a decreasing effect of the Dufour number is observed on both concentration and temperature distribution. Besides, in case of the Soret number, a direct effect is observed on concentration, but an inverse effect can be seen on temperature distribution. Different effects are shown through graphs in this study and an error analysis is also presented through tables and graphs.

In this paper, the 3-D squeezing flow of viscous incompressible fluid between two parallel plates rotating at the same rate is investigated. The flow is observed under the influence of the varying magnetic field. The flow phenomena are modeled by utilizing the basic governing equations, i.e., equation of continuity, coupled Navier Stokes, and Magnetic Field equations. Using appropriate similarity transformations, the resultant partial differential equations are then transformed into a system of ordinary differential equations. The computational technique is developed via the Homotopy Analysis Method (HAM) to obtain the solution of transformed systems of ordinary differential equations. The influence of several engineering fluid parameters, such as squeeze Reynolds number, magnetic field strength parameter, and magnetic Reynolds number, on velocity and magnetic field components, are observed from different graphs. It has been investigated that by increasing the squeeze Reynolds number, fluid velocity in the y and z directions will be increased as well. On the magnetic field component along the y-axis, an increasing influence of squeezing Reynolds number is also noticed. Similarly, raising the magnetic Reynolds number increases the velocity along the y-axis, whereas the inverse relationship is found for magnetic field components. Furthermore, for each flow phenomenon, an error analysis is also presented.

The electrically conducting, incompressible and isothermal Newtonian fluid-flow in unsteady tank drainage is studied. The perturbation method is employed to obtain solution and results have been compared with those of obtained by adomian decomposition method result. The results of adomian decomposition method are same as those of perturbation method. The Newtonian fluid solution is worked out with substitution ? = 0. Explicit expressions on behalf of velocity field, flow rate, relationship however will the times vary with length, average velocity and time needed for complete drainage are acquired. Impacts of different developing parameters on velocity profile, vz, flow rate and depth of the tank, H(t), are exhibited graphically.

This article explores the influence of Joule heating and viscous dissipation on the unsteady three-dimensional squeezing flow of Newtonian fluid. The flow in a rotating channel with a lower stretched permeable wall is observed under the influence of a uniform magnetic field. The impact of thermal radiation is also considered. The effects of mass and heat transfer on the squeezing flow of Newtonian fluids are observed and modelled using the four fundamental governing equations of fluid flow: the mass equation, momentum equation, concentration equation, and energy equation. Using the appropriate similarity transformations, the resultant non-linear partial differential equations are then transformed into ordinary differential equations. The analytical strategy is developed using the homotopy analysis method to obtain the series solution. The influence of several physical parameters, including the squeezing parameter, the suction parameter, the magnetic number, the rotation parameter, the Eckert number, the Prandtl number, the Dufour number, the Soret number, the radiation parameter, and the Schmidt number, on the velocity profile, energy, and concentration are also discussed through graphs. Additionally, it is observed that enhancing the top plate’s squeezing impact causes a rise in the velocity profile while lowering the temperature and concentration distribution. It is also found that for the velocity field, increasing the magnetic number shows a decrease in the value of the velocity field along the y- and z-axis, whereas the velocity field along the x-axis exhibits dual behavior, such that it initially falls as the magnetic number intensifies but starts to rise in the upper region of the channel. The impact of the Dufour, Soret, and Eckert numbers on temperature and concentration distribution is also studied. It is found that while these numbers directly affect the temperature distribution, the mass distribution follows the opposite trend. Also, it is noticed that the thermal radiation parameter is an increasing function of temperature and mass distribution. Further, graphs and tables are presented to illustrate an error analysis.

This article explores the influence of joule heating and viscous dissipation on the unsteady three-dimensional squeezing flow of Newtonian fluid. The flow in a rotating channel with a lower stretched permeable wall is observed under the influence of a uniform magnetic field. The impact of thermal radiation is also considered. The effects of mass and heat transfer on the squeezing flow of Newtonian fluids are observed and modelled using the four fundamental governing equations of fluid flow: the mass equation, momentum equation, concentration equation, and energy equation. Using the appropriate similarity transformations, the resultant non-linear partial differential equations are then transformed into ordinary differential equations. The analytical strategy is developed using the homotopy analysis method to obtain the series solution. The influence of several physical parameters, including the squeezing parameter, the suction parameter, the magnetic number, the rotation parameter, the Eckert number, the Prandtl number, the Dufour number, the Soret number, the radiation parameter , and the Schmidt number, on the velocity profile, energy, and concentration are also discussed with the help of graphics and thorough discussion. Additionally, it is observed that enhancing the top plate’s squeezing impact causes a rise in the velocity profile while lowering the temperature and concentration distribution. It is also found that for the velocity field, increasing the magnetic number shows a decrease in the value of the velocity field along the y-and z-axis, whereas the velocity field along the x-axis exhibits dual behavior, such that it initially falls as the magnetic number intensifies but starts to rise in the upper region of the channel. The impact of the Dufour, Soret, and Eckert numbers on temperature and concentration distribution is also studied. It is found that while these numbers directly affect the temperature distribution, the mass distribution follows the opposite trend. Also, it is noticed that the thermal radiation parameter is an increasing function of temperature and mass distribution. Further, graphs and tables are presented to illustrate an error analysis.