A time fractional model of hemodynamic two-phase flow with heat conduction between blood and particles: applications in health science

The magnetogasdynamics effect on a two-phase (blood and magnetic particles) flow in a cylindrical vessel is represented. The blood is taken as a non-Newtonian (Casson) fluid. The temperature equation for blood and particles is also considered with the Concentration equation. The mathematical model for the flow is formulated in terms of partial differential equations. The classical time model is then generalized to the fractional time model by using Caputo fractionalorder derivatives. By using appropriate dimensionless variables the generalized model is then non-dimensionalized. After dimensionalization, the equations are solved by the joint application of Laplace and Hankel transforms. It is worth noting that the blood and particle velocities decreased by enhancing values of magnetic parameter H which is beneficial to control the blood flow during magnetic therapy (for treating pain, such as the back, foot) and bleeding during surgeries. The fractional parameter alpha not only controls the velocities of both blood and particle and temperature of blood but also control the temperature of particles and concentration of blood. Therefore a maybe a tool to control the blood and particle velocities, temperatures, and concentration of blood during cure by using the suitable values of alpha and regulating the velocities and temperature of blood and particles.

Automated summary

This study investigates the magnetogasdynamics effect on a two-phase flow of blood and magnetic particles in a cylindrical vessel. The non-Newtonian behavior of blood is considered, and a mathematical model is formulated with partial differential equations. By using fractional time derivatives, the classical time model is extended. The model is then non-dimensionalized using appropriate dimensionless variables. The study reveals that increasing the magnetic parameter H reduces the velocities of blood and particles, which is beneficial for controlling blood flow and bleeding during magnetic therapy and surgeries. The fractional parameter alpha controls the velocities, temperatures, and concentration of both blood and particles.