Rakhmatulin's Filtration Equation for Describing Blood Flow with Stenosis | Chapter 8 | Research Updates in Mathematics and Computer Science Vol. 3

 The study is devoted to the nature of blood flow with stenosis. The stenosis is modeled as a porous medium in order to apply the Rakhmatulin filtration model. Based on the penetrating model, considering the movement of particles immobile (immobile particles form stenosis), an equation describing the movement of blood with stenosis was obtained. Outside of stenosis, the equations turn into the Navier-Stokes equation. The resulting equations were solved numerically using the control method.The influence of the Reynolds number and the degree of stenosis on the nature of the flow on the behavior of blood is investigated.

Author(s) Details:

Umurdin Dalabaev,
University of World Economy and Diplomacy, Uzbekistan.

Please see the link here: https://stm.bookpi.org/RUMCS-V3/article/view/14039

Study on a Solution of the Navier-Stokes Problem for an Incompressible Fluid with Viscosity | Chapter 8 | Research Trends and Challenges in Physical Science Vol.3

 The methods of integral transformations in the theory of partial differential equations are well recognised for allowing the solution of numerous problems and the clarification of the physical significance of some important laws and phenomena in fluid mechanics. In this sense, this chapter looks at the Navier-Stokes system, which explains the flow of a viscous incompressible fluid. Furthermore, the developed method is used to convert the original problem to a system of second-order integral equations, and the theory of these systems is used to prove the existence and uniqueness of the solution of the non-stationary Navier-Stokes problem in the special space, which was introduced in this chapter. The discovered pressure distribution law, which is explained by a Poisson type equation and plays a crucial role in the theory of Navier-Stokes systems in generating analytic smooth (conditionally smooth) solutions, was also obtained in an analytical form.

Author(S) Details

Taalaibek D. Omurov
Kyrgyz National University named after Jusup Balasagyn, Kyrgyzstan.

View Book:- https://stm.bookpi.org/RTCPS-V3/article/view/4505