The impact of heat source and chemical reaction on MHD blood flow through permeable bifurcated arteries with tilted magnetic field in tumor treatments

Abstract

In this research work, we investigate the influence of heat source and chemical reaction on electro-magneto-hydrodynamic (EMHD) blood flow through bifurcated arteries with external tilted magnetic field for treating tumor. The potential electric field applied along the bifurcated arterial wall, accurately described the Poisson-Boltzmann equation. We modeled the EMHD blood flow to obtain the non-dimensionalized form of the equations. We converted the modeled equations to ordinary differential equations by the use of suitable variables. Exact solutions of the converted equations are calculated by the method of undetermined coefficients and the results obtained with the aid of Mathcad software were simulated and presented graphically. From the graphical representation of results, we observed that increase in Joule heating and Eckert number, increases the temperature distribution in the affected tumor cells which prevent high thermal radiation exposure from killing the healthy cells within the tumor region. The curves of the wall shear stress seem to be greater in the converging region in comparison to the diverging region, but when the strength of magnetic field and thermal radiation parameters increase the wall shear stress decreases at the bifurcated wall where blockage may likely occur due to the development of boundary layers on the inner walls of the bifurcated region. By increasing the heat radiation parameter, we observed that the curves representing both velocity and temperature profiles increase rapidly from the origin and the velocity of blood flow varies directly for the converging, diverging and the tumor regions of the bifurcated arteries. Thus, thermal radiation effect is a result of the higher rate of heat transfer at the vessel walls. Further, combining the electromagnetic field and the heat radiation together gives new insights of the physical properties of blood flow in the body system network which is essential for health practitioners and clinicians.