Spatio-temporal evolution of magnetohydrodynamic blood flow and heat dynamics through a porous medium in a wavy-walled artery.

BACKGROUND AND OBJECTIVE: In a healthy body, the elastic wall of the arteries forms wave-like structures resulting from the continuous pumping of the heart. The systolic and diastolic phases generate a contraction and expansion pattern, which is mimicked in this study by considering a wavy-walled arterial structure. A numerical investigation of the spatio-temporal flow of blood and heat transfer through a porous medium under the action of magnetic field strength is conducted. METHOD: The governing equations of the blood flow in the Darcy model are simulated by applying a vorticity-stream function formulation approach. The transformed dimensionless equations are further discretized using the finite difference method by developing the Peaceman-Rachford alternating direction implicit (P-R ADI) scheme. RESULTS: The computational results for the axial velocity, temperature distribution, flow visualization using the streamlines and vorticity contours, isotherms, wall shear stress and the average Nusselt number are presented graphically for different values of the physical parameters. CONCLUSIONS: The study shows that the axial velocity increases with an increase in the Darcy number, and a similar phenomenon is observed because of an amplitude variation in the wavy wall. Both temperature and wall shear stress decreases with an increase in the Darcy number. The average Nusselt number increases with the magnetic field strength, while it has a reducing tendency due to the permeability of the porous medium.

Fractional order model of thermo-solutal and magnetic nanoparticles transport for drug delivery applications.

We examine the capturing efficiency of magnetic nanoparticles bound with drug molecules infused into the blood stream and monitored them by the application of an external magnetic field. We analyzed the motion of the nanoparticles along with the blood velocity through a porous medium vessel under the effect of periodic vibration. The thermo-solutal transport with Caputo-Fabrizio fractional-order derivative is modeled with non-Newtonian biviscosity fluid, Soret and Dufour effect, thermal radiation, and linear variation of the chemical reaction. The Laplace transform, finite Hankel transform and their inverse techniques are used to find analytical solutions. The study shows that both the velocity of blood and nano-particles increase with the increase of particle mass and the concentration parameter, while the opposite behaviour is observed with increasing the fractional parameter, magnetic field effect, and thermal radiation. The heat and mass transfer rates at the wall are enhanced with an increase in the Peclet number and the metabolic heat source. Thermal radiation effect signifies the higher rate of heat transfer at the vessel wall. The study bears potential applications in drug delivery with magnetic nanoparticles at the targeted region.

Fractional order model for thermochemical flow of blood with Dufour and Soret effects under magnetic and vibration environment.

We examine the effect of the Caputo-Fabrizio derivative of fractional-order model on the flow of blood in a porous tube having thermochemical properties under the magnetic and vibration mode. Blood is considered as the biviscosity non-Newtonian fluid having thermal radiation and chemical reaction properties to observe its impact on energy flux and mass flux gradients. We provided analytical solution via the Laplace, finite Hankel transform, and the corresponding inverse techniques. The study shows that blood velocity and temperature both decrease in ascending values of the fractional-order parameter as memory effect. The permeability of blood flow medium resists to drive the fluid fast. The chemical reaction causes an increase in wall shear stress. Dufour effect influences to rise in the Nusselt number. Thus the study may help to explore further information about the fractional-order model, adsorption of nutrients and their strong correlation with the surface chemistry and applied them in pathology.

Mathematical model to verify the role of magnetic field on blood flow and its impact on thermal behavior of biological tissue for tumor treatment.

The numerical computation has been performed to study the effects of static magnetic field on thermal behavior of tumor surrounded by living biological tissues and blood vessels. A small rectangular shaped tumor enclosing the blood vessel surrounded by healthy tissue is considered. The model consists of two-layer composite system in which the microvessel for blood flow is considered as a fluid layer and the living biological tissue including tumor as a solid layer. The wave bioheat transfer equation in the tissue layer together with energy transport equation for blood flow layer has been used in the cylindrical polar coordinates. The analytical expression for blood velocity in the presence of magnetic field has been used from Gold's solution. The computational work has been performed by employing the Crank-Nicolson finite difference method. A comparison has been made to validate our numerical results with the previous solution by setting some parameters. The temperature profiles have been plotted at different locations of the axial tissue length for various values of the Hartmann number, Prandtl number, Womersley number and Reynolds number. It is observed that the application of magnetic field increases heat transfer rate within tumor tissues which in turn attribute to an enhancement of temperature about 316 K or above for hyperthermic treatment in cancer therapy.

Joule heating and zeta potential effects on peristaltic blood flow through porous micro vessels altered by electrohydrodynamic.

In most of the medical therapies, electromagnetic field plays important role to modulate the blood flow and to reduce the pain of human body. With this fact, this paper presents a mathematical model to study the peristaltic blood flow through porous microvessels in the presence of electrohydrodynamics. The effects of Joule heating and different zeta potential are also considered. Darcy law is employed for porous medium. The mathematical analysis is carried out in the form of electroosmosis, flow analysis and heat transfer analysis. Velocity slip conditions are imposed to solve momentum equation and thermal energy equation. Time dependent volumetric flow rate is considered which varies exponentially. Closed form solutions for potential function is obtained under Debye-Hückel approximation and velocity and temperature fields are obtained under low Reynolds number and large wavelength approximations. The influence of Hartmann number, electroosmotic parameter, slip parameters, Zeta potential, and couple stress parameter on flow characteristics, pumping characteristics and trapping phenomenon is computed. The effects of thermal slip parameters, Joule heating parameter, and Brinkman number on heat transfer characteristics are also presented graphically. Finally, the effect of Brinkman number on a graph between Nusselt number and Joule heating parameter is examined.