Z. Angew. Math. Phys. (2017) 68:93
2017 Springer International Publishing AG
Zeitschrift f¨ur angewandte
Mathematik und Physik ZAMP
Eﬀect of electrical conductivity and magnetization on the biomagnetic ﬂuid ﬂow over
a stretching sheet
M. G. Murtaza, E. E. Tzirtzilakis and M. Ferdows
Abstract. The biomagnetic ﬂuid ﬂow (blood) over a stretching sheet in the presence of magnetic ﬁeld is studied. For the
mathematical formulation of the problem both magnetization and electrical conductivity of blood are taken into account and
consequently both principles of magnetohydrodynamics (MHD) and ferrohydrodynamics (FHD) are adopted. The physical
problem is described by a coupled, nonlinear system of ordinary diﬀerential equations subject to appropriate boundary
conditions. This solution is obtained numerically by applying an eﬃcient numerical technique based on ﬁnite diﬀerences
method. The obtained results are presented graphically for diﬀerent values of the parameters entering into the problem
under consideration. Emphasis is given to the study of the eﬀect of the MHD and FHD interaction parameters on the ﬂow
ﬁeld. It is apparent that both parameters eﬀect signiﬁcantly on various characteristics of the ﬂow and consequently neither
electrical conductivity nor magnetization of blood could be neglected.
Mathematics Subject Classiﬁcation. 76W05, 76D99, 76Z99.
Keywords. Stretching sheet, Biomagnetic ﬂuid, Ferrohydrodynamics, Magnetohydrodynamics, Ferroﬂuid, Magnetic ﬂuid,
Biomagnetic ﬂuid dynamics (BFD) is a relatively new area of ﬂuid mechanics. Numerous applications have
been proposed in bioengineering and medical science, and some of them include cancer tumor treatment
by using magnetic hyperthermia or development of magnetic devices for cell separation [1–3].
BFD is the study of the eﬀect of an applied magnetic ﬁeld on biological ﬂuid ﬂow. An initial model
of BFD was developed by Haik et al.  and is actually based on the principles of Ferrohydrodynamics
(FHD). According to this formulation, blood is considered as an electrically non-conducting magnetic ﬂuid
and the ﬂow is aﬀected by the magnetization of the ﬂuid in the magnetic ﬁeld. Thus, the arising force is
due to magnetization and depends on the existence of a spatially varying magnetic ﬁeld. However, blood
also possesses properties of an electrically conducting ﬂuid due to the ions in the plasma. The ﬂowing
ions produce a slight electric current which interacts with magnetic ﬁelds. The formulation of electrically
conducting ﬂuids is made by adopting the principles of the well-known magnetohydrodynamics (MHD)
which in contrast to FHD ignores the eﬀect of polarization and magnetization . In order to formulate
the entire magnetic properties of blood, i.e., electrical conductivity along with polarization an extended
BFD model was developed. This model is consistent with the properties of MHD as well as with those of
FHD and also includes the energy equation .
The shear-driven ﬂow over a stretching sheet constitutes a classical physical problem ﬁrst studied by
Crane in 1970 for a Newtonian ﬂuid . Later, Anderson derived an exact similarity solution for velocity
and pressure of the magnetohydrodynamic ﬂow past a stretching sheet . The study of MHD ﬂow over
a stretching sheet still constitutes a topic of current ongoing research. The radiation eﬀects on the MHD
ﬂow near the stagnation point of a stretching sheet were studied by Jat and Chaudhary andPopetal.