Exact Symmetric Solutions of MHD Casson Fluid Using Chemically Reactive Flow with Generalized Boundary Conditions

Dynamic analysis of magnetic fluids with the combined effect of heat sink and chemical reactions based on their physical properties demonstrates strong shock resistance capabilities, low-frequency response, low energy consumption, and high sensitivity. Therefore, the applied magnetic field always takes diamagnetic, ferromagnetic, and paramagnetic forms. The influence of radiation is considered in the temperature profile. This manuscript investigates an analytic solution of incompressible and magnetic Casson fluid in Darcy’s medium subjected to temperature and concentration dependence within a porous-surfaced plate with generalized boundary conditions. The substantial mathematical technique of the Laplace transform with inversion is invoked in the governing equations of the magnetic Casson fluid. The analytic results are transformed into a special function for the plate with a constant velocity, a plate with linear velocity, a plate with exponential velocity, and a plate with sinusoidal velocity. Graphical illustrations of the investigated analytic solutions at four different times are presented. Our results suggest that the velocity profile decreases by increasing the value of the magnetic field, which reflects the control of resistive force. The Nusselt number remains constant at a fixed Rd and is reduced by raising the Rd value.

Investigation of the Fractional Strongly Singular Thermostat Model via Fixed Point Techniques

Our main purpose in this paper is to prove the existence of solutions for the fractional strongly singular thermostat model under some generalized boundary conditions. In this way, we use some recent nonlinear fixed-point techniques involving α-ψ-contractions and α-admissible maps. Further, we establish the similar results for the hybrid version of the given fractional strongly singular thermostat control model. Some examples are studied to illustrate the consistency of our results.

Functional Application of G-Functions of Lorenzo and Hartley on the Free Convection Flow of Oldroyd-B Fluid with Ordinary and Fractional Techniques

In this article, free convection flow of an Oldroyd-B fluid (OBF) through a vertical rectangular channel in the presence of heat generation or absorption subject to generalized boundary conditions is studied. The fractionalized mathematical model is established by Caputo time-fractional derivative through mechanical laws (generalized shear stress constitutive equation and generalized Fourier’s law). Closed form solutions for the velocity and temperature profiles are obtained via Laplace coupled with sine-Fourier transforms and have been embedded with regards to the special functions, namely, the generalized G-functions of Lorenzo and Hartley. Solutions of the known results from recently published work (Nehad et al. Chin. J. Phy., 65, (2020) 367–376) are recovered as limiting cases. Finally, the effects of fractional and various physical parameters are graphically underlined. Furthermore, a comparison between Oldroyd-B, Maxwell and viscous fluids (fractional and ordinary) is depicted. It is found that, for short time, ordinary fluids have greater velocity as compared to the fractional fluids.

On a Riemann–Liouville Type Implicit Coupled System via Generalized Boundary Conditions

We study a coupled system of implicit differential equations with fractional-order differential boundary conditions and the Riemann–Liouville derivative. The existence, uniqueness, and at least one solution are established by applying the Banach contraction and Leray–Schauder fixed point theorem. Furthermore, Hyers–Ulam type stabilities are discussed. An example is presented to illustrate our main result. The suggested system is the generalization of fourth-order ordinary differential equations with anti-periodic, classical, and initial boundary conditions.