Group method analysis for blood‐Mn‐ZnFe2O4 flow and heat transfer under ferrohydrodynamics through a stretched cylinder

Abstract

In this paper, a steady, viscous, incompressible, and electrically non‐conducting laminar flow of biomagnetic fluid, namely, the flow of blood with magnetic particles over a stretched cylinder in the presence of magnetic dipole, is studied. Since magnetic particles with low cytotoxicity can carry away unwanted reactive oxygen species and provide safeguard for biomedical applications, this study has immense applications in medical and bio‐engineering sections like cancer treatment, drug delivery, and magnetic resonance imaging (MRI). The problem is first analyzed by applying group theoretical method, namely, one parameter group method. The invariance property of system of partial differential equations (PDEs) under one parameter group method transformations yields the weeny generators. By using the basic theorem of one parameter group method including invariance conditions, the set of PDEs is converted into ordinary differential equations (ODEs), and consequently, the number of independent variables is reduced into one variable. Afterwards, the resulting coupled nonlinear set of ODEs is numerically solved by introducing an efficient numerical technique that based upon common finite difference with central differencing, a tridiagonal matrix manipulation, and finally, an iterative procedure. A comparative graphical analysis of velocity, temperature profiles, skin friction coefficient and rate of heat transfer for blood‐Mn‐ZnFe2O4 magnetic fluid has been carried out for various physical parameters such as ferromagnetic interaction parameter and magnetic particles volume fraction etc. The important findings from the present investigation are that the temperature of blood is enhanced for larger values of magnetic particles volume fraction and more effectively than pure blood. It is also found that blood velocity is increased as the ferromagnetic number increases. The skin friction coefficient is enhanced 132.22%, and the rate of heat transfer is increased by 5.86% by the application of magnetic field; whereas for particles volume fraction, skin friction decreases about 0.61%, and rate of heat transfer declines about 4%. Additionally, this study also discloses that the application of group theoretical method is justified in biomagnetic fluid dynamics especially research on blood flow and heat transfer, where the blood flow significantly influenced by the ferromagnetic number. A comparison has been also performed, and the results are found in excellent agreement with previous published in literature. The present study could be considered for magnetic driving of biologically suitable magnetic particles filled with medicine.