# Zlámal Seminar

Summer semester 2017/18

ZLÁMAL SEMINAR takes place in the Seminar room 1842 in the 18th floor of A1 building Faculty of Mechanical Engineering BUT, Technická 2. The seminar in the Summer semester will start on Wednesday April 4th, 2018 at 13:00.

**Program:**

- Wednesday April 4th, 2018

*Prof. RNDr. Ing. Tomáš Březina, CSc.*

(Institute of Mathematics FME BUT)

**Three examples of semi-symbolic computation (in Czech)** - Wednesday April 11th, 2018
**(at 10:00 – 12:00)**

*10:00 Prof. Eugenia N. Petropoulou*

(University of Patras Department of Civil Engineering)

**A nonstandard “discretization” technique for the solution of ODEs**

Abstract: A nonstandard “discretization” technique for the solution of ordinary differential equations (ODEs) will be presented. This technique is based on the transformation of the original ODE into an equivalent difference equation, through an operator equation of an abstract Banach space. The technique will be demonstrated by applying it to initial or boundary value problems regarding the Duffing equation, the Duffing-van der Pol equation, the logistic equation and the Blasius equation. The obtained computed solutions are both real and complex.

*11:00 E.E. Tzirtzilakis*

*(Department of Mechanical Engineering, Technological Educational Institute of Western Greece, Patras, Greece)*

**Modelling of Biomagnetic Fluid Flows and Applications**

Abstract: We will present the mathematical formulation of Biomagnetic Fluid Dynamics (BFD). The mathematical model is consistent with both principles of ferrohydrodynamics (FHD) and Magnetohydrodynamics (MHD). Blood is considered as a homogeneous non isothermal Newtonian fluid and is treated as an electrically conducting magnetic fluid which simultaneously exhibits polarization [1].

As an application we consider two basic configuration physical problems. The BFD stretching sheet flow and the BFD fully developed flow in a 3D rectangular channel. The first physical problem of BFD stretching sheet flow, 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 [2]. The second physical problem is that of the BFD flow in a 3D rectangular channel. The flow is considered as laminar, incompressible, three–dimensional, fully developed, taking place in a straight rectangular duct. The numerical results are obtained using a finite differences numerical technique based on a pressure–linked pseudotransient method on a collocated grid [1, 3].

The obtained results for both physical problems 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.

[1] E.E. Tzirtzilakis, A mathematical model for blood flow in magnetic field, Physics of Fluids, Vol. 17, 077103, 2005.

[2] M.G.Murtaza, E.E. Tzirtzilakis and M. Ferdows, Effect of electrical conductivity and magnetization on the biomagnetic fluid flow over a stretching sheet, ZAMP, 68:93, DOI 10.1007/s00033-017-0839-z, (15 pages), 2017.

[3] E.E. Tzirtzilakis, V.D. Sakalis, N.G. Kafoussias, P.M. Hatzikonstantinou, Biomagnetic Fluid Flow in a 3D Rectangular Duct, International Journal for Numerical Methods in Fluids, Vol 44, pp. 1279–1298, 2004.

All interested are cordially welcomed.