This numerical investigation reports the unsteady MHD pulsatile flow of couple stress Non-Newtonian fluid. In the fluid, the effect of non-uniform wall temperature and concentration as a result of periodic heat and mass input at the heated wall was taken into consideration. Also, the influence of a uniform external magnetic field between two parallel plates was considered. The pressure driven fluid was analysed using Eyring-Powell Non-Newtonian fluid model. The non-linear dimensional partial differential equations, under some assumptions, are transformed into a set of dimensionless equations. The solution to the dimensionless equations is obtained using spectral relaxation techniques (SRM). Graphical results are provided for different values of fluid parameters.
In order to increase the drug potency and cancer treatment effectiveness, hyperthermia therapy is an adjuvant procedure in which perfused bodily tissues are heated to extreme temperatures. While certain types of hyperthermia treatments rely on thermal radiations from single-sourced electro-radiation measures, conjugating dual radiation field sources is being discussed in an effort to enhance the delivery of therapy. The thermal efficiency of a combined infrared hyperemia with nanoparticle recirculation near an applied magnetic field on subcutaneous strata of a model lesion as an ablation technique is investigated computationally in this research. To tackle the equation of linked momentum and thermal equilibrium in the blood-perfused tissue domain of a spongy fibrous tissue, an intricate Spectral relaxation method (SRM) was developed. The well-known Roseland diffusion approximation was used to define thermal diffusion regimes in the presence of external magnetic field imposition and to outline the effects of radiative flux inside the computational domain. Utilizing pore-scale porosity mechanics, the contribution of tissue sponginess was studied in a number of clinically relevant circumstances. Our findings demonstrated that magnetic field architecture could govern hemodynamic regimes at the blood-tissue interface across a significant depth of spongy lesion while permitting thermal transport across the depth of the model lesion. This parameter-indicator could be used to regulate how much hyperthermia therapy is administered to intravenously perfused tissue.
In this paper, results of $\omega$-order preserving partial contraction mapping generating a quasilinear equation of evolution were presented. In general, the study of quasilinear initial value problems is quite complicated. For the sake of simplicity we restricted this study to the mild solution of the initial value problem of a quasilinear equation of evolution. We show that if the problem has a unique mild solution $v\in C([0,T]: X)$ for every given $u\in C([0,T]:X)$, then it defines a mapping $u\to v=F(u)$ of $C([0,T]:X)$ into itself. We also show that under the suitable condition, there exists always a $T',\ 0<T'\leq T$ such that the restriction of the mapping $F$ to $C([0,T']:X)$ is a contraction which maps some ball of $C([0,t']:X)$ into itself by proving the existence of a local mild solution of the initial value problem.
In this paper, we present results of $\omega$-order preserving partial contraction mapping generating a wave equation. We use the theory of semigroup to generate a wave equation by showing that the operator $ \begin{pmatrix} 0 & I\\ \Delta & 0 \end{pmatrix}, $ which is $A,$ is the infinitesimal generator of a $C_0$-semigroup of operators in some appropriately chosen Banach of functions. Furthermore we show that the operator $A$ is closed, unique and that operator $A$ is the infinitesimal generator of a wave equation.
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