Narrow Results

The study of the blood flow through arterial walls is an important subject due to different chemical reactions and magnetohydrodynamic having an impact on the arterial walls during the treatment of cancer, malignant tumors, drug targeting and endoscopy. So, this paper aims to present a comprehensive investigation of the blood bioconvective flow of Carreau–Yasuda (C–Y) nanofluids in an arterial. Variable velocity conditions near the walls are considered. The flow domain is filled by a porous medium and a time-dependent magnetic field is assumed. The impacts of an exponential chemical reaction are considered and the viscous dissipation in the case of the C–Y model is formulated and examined. The fully implicit finite difference method is applied to solve the dimensionless governing system. The case of the shear thinning $(n=0.5)$ and shear thickening $(n=1.5)$ are analyzed for the variations of the governing parameters such as Weissenberg $(0.001\le \mathrm{\text{We}}\le 0.1)$ and parameter of the porous medium $(0\le \beta \le 2)$. The major outcomes revealed that the friction coefficient is improved as the C–Y parameter is raised. Also, values of heat and mass transfer are higher in the case of the shear thinning compared to the shear thickening.

Anomalous Reaction-Sub-diffusion equations play an important role transferred in a lot of our daily applications in our life, especially in applied chemistry. In the presented work, a modified type of these models is considered which is the Reaction-Sub-diffusion equation of variable order, the linear and nonlinear models and we will refer to it by VORSDE. An accurate technique depends on a mix of the finite difference methods (FDM) together with Hermite formula is introduced to study these important types of anomalous equations. Regarding the analysis of the stability for the mentioned, it is done using the variable Von-Neumann technique; also the convergent analysis is introduced. As a result of the previous steps, we derived a stability condition which will be held for many discretization schemes of the variable order derivative and some other parameters and we checked it numerically.

This paper aims to look into the determination of effective area-average concentration and dispersion coefficient associated with unsteady flow through a small-diameter tube where a solute undergoes first-order chemical reaction both within the fluid and at the boundary. The reaction consists of a reversible component due to phase exchange between the flowing fluid and the wall layer, and an irreversible component due to absorption into the wall. To understand the dispersion, the governing equations along with the reactive boundary conditions are solved numerically using the Finite Difference Method. The resultant equation shows how the dispersion coefficient is influenced by the first-order chemical reaction. The effects of various dimensionless parameters e.g. Da (the Damkohler number), α (phase partitioning number) and Γ (dimensionless absorption number) on dispersion are discussed. One of the results exposes that the dispersion coefficient may approach its steady-state limit in a short time at a high value of Damkohler number (say Da ≥ 10) and a small but nonzero value of absorption rate (say Γ ≤ 0.5).

In this paper, an efficient numerical method is introduced for solving the fractional (Caputo sense) Fisher equation. We use the spectral collocation method which is based upon Chebyshev approximations. The properties of Chebyshev polynomials of the third kind are used to reduce the proposed problem to a system of ODEs, which is solved by the finite difference method (FDM). Some theorems about the convergence analysis are stated and proved. A numerical simulation is given and the results are compared with the exact solution.