On some fixed point results using CG simulation functions via w-distance with applications.

Based on the notion of class of CG simulation functions, we launch the concept of (ρ,ϑ)-ZG-contraction on the setting of w-distance mappings. We employ our new concept to formulate and prove several fixed point results over the complete metric spaces. Also, we provide some concrete examples to show the usability of the obtained results. Furthermore, we study the existence of a unique solution of nonlinear fractional differential equations, nonlinear integral equations and spring-mass system problems. The results presented in this manuscript generalize many of the results known in the literature.

Unsteady micropolar nanofluid flow past a variable riga stretchable surface with variable thermal conductivity.

In this study, we considered the flow of a micropolar fluid over a vertical Riga sheet. The non linear stretching sheet is considered. The effects of variable thermal conductivity and radiation on the Riga sheet are taken into account. Additionally, we also debated the Brownian motion and thermophoretic. To simplify the partial differential equations, we converted them into dimensionless ordinary differential equations using suitable similarity variables and solved dimensionless system numerically using the bvp4c function. The impact of some intended parameters on the dimensionless velocity, microrotation, temperature, and concentration distributions graphically are presented and the numerical outcomes of physical quantities like skin friction, Nusselt number, Sherwood number, and couple stress have been presented in tabular form. The micropolar parameter increased which increased the couple stress and friction at surface. Because, the fluid rotation increased which increased friction at surface and also increased the couple stress. The transfer of mass decayed and transfer of heat heightened by larger values of variable thermal conductivity. Thermal conductivity improved which improved the heat transfer phenomena, so transfer of heat at surface becomes larger while also reducing the transfer of mass.

Thermodynamic flow of radiative induced magneto modified Maxwell Sutterby fluid model at stretching sheet/cylinder.

A steady flow of Maxwell Sutterby fluid is considered over a stretchable cylinder. The magnetic Reynolds number is considered very high and induced magnetic and electric fields are applied on the fluid flow. Joule heating and radiation impacts are studied under the temperature-dependent properties of the liquid. Having the above assumptions, the mathematical model has been evolving via differential equations. The differential equations are renovated in the dimensionless form of ordinary differential equations using the appropriate transformations. The numerical results have been developed employing numerical techniques on the ordinary differential equations. The impact of involving physical factors on velocity, induced magneto hydrodynamic, and temperature function is debated in graphical and tabular form. The velocity profile is boosted by thicker momentum boundary layers, which are caused by higher values of the magnetic field factor. So, the fluid flow becomes higher velocity due to enlarging values of the magnetic field factor. Heat transfer factor and friction at surface factor boosted up for increment of [Formula: see text] (Magnetic field factor). The [Formula: see text](Magnetic field factor) is larger which better-quality of heat transfer at surface and also offered the results of friction factor boosting up in both cases of stretching sheet/cylinder. The [Formula: see text](Magnetic Prandtl number) increased which provided better-quality of heat transfer at surface.

Heat and mass transfer of generalized fourier and Fick's law for second-grade fluid flow at slendering vertical Riga sheet.

In this analysis, the generalized Fourier and Fick's law for Second-grade fluid flow at a slendering vertical Riga sheet is examined along with thermophoresis and Brownian motion effects. Boundary layer approximations in terms of PDE's (Partial Differential Equations) are used to build the mathematical model. An appropriate transformation has been developed by using the Lie symmetry method. PDE's (Partial Differential Equations) are transformed into ODE's (Ordinary Differential Equations) by implementing the suitable transformation. A numerical method called bvp4c is used to explain the dimensionless system (ODE's). Graphs and tables are used to interpret the impact of the significant physical parameters. The curves of temperature function declined due to enchanting the values of the thermophoresis Parameter. The temperature is produced at a low level due to enchanting the values of thermophoresis because this force transports burn at a low 10 µm diameter so the temperature becomes lessor. Increments of thermophoresis parameter which enhanced the values of concentration Function. As the concentration boundary layer increased which declined the mass transfer due increment in thermophoresis. The curves of temperature function are increasing due to enhancing the values of the Brownian parameter because addition in the Brownian motion, improved the movement of particles ultimately increasing the kinematic energy of fluid which improved the heat transfer phenomena. Increments of Brownian parameter which declined the values of concentration function. Physically, the kinematic energy improved which declined the mass transfer rate near the surface.