Application of the differential transformation method in the study of blood flow in human arteries Radhika TSL1,*, Rani T Raja2, Brindha S1 1Department of Mathematics, Birla Institute of Technology & Science, Pilani, Hyderabad, Telangana, 500078, India 2Department of General Studies, Military Technological College (MTC), Portsmouth University, UK *Corresponding Author: Dr. (Mrs) Radhika TSL, Assistant Professor, Department of Mathematics, Birla Institute of Technology & Science, Pilani, Hyderabad, Telangana, 500078, India, E-mail: radhikatsl@hyderabad.bits-pilani.ac.in
Online published on 16 January, 2018. Abstract In this paper, we applied the differential transformation method to solve the mathematical model developed for the study of blood flow in human arteries. In our model, we have assumed power law fluid model for human blood and the blood flow as a pulsatile flow. This model resulted in a non-linear, unsteady partial differential equation (PDE) in terms of the fluid (or blood) velocity. This PDE with appropriate initial-boundary conditions was solved using the differential transformation method. The differential transformation method is an iterative method that generates a recurrence relation involving lower order approximations of the velocity function, zeroth approximation being the initial approximation. We then, obtained an expression for the velocity of blood flow and used this expression to predict the flow velocity in the radial artery of the human. Data required for this prediction i.e data related to radial artery, values of the parameters in the power law model and also data for simulating pulsatile flow are taken from published results. Through the velocity plots, we could observe a natural mechanism of the human circulatory system: Decrease in the volume of the blood flow increases the heart rate which is to compensate the deficiency in the supply of required amount of blood to the various parts of the body. We also presented and discussed other results. Top Keywords Non-linear PDE, Differential Transformation method, non-Newtonian fluid, Power law fluid. Top |