Z. angew. Math. Phys. 54 (2003) 551–565 0044-2275/03/040551-15 DOI 10.1007/s00033-003-1100-5 c  2003 Birkh¨auser Verlag, Basel Zeitschrift f¨ ur angewandte Mathematik und Physik ZAMP Biomagnetic fluid flow over a stretching sheet with non linear temperature dependent magnetization E. E. Tzirtzilakis and N. G. Kafoussias Abstract. The flow of a heated ferrofluid over a linearly stretching sheet is studied in the pres- ence of an applied magnetic field due to a magnetic dipole. It is assumed that the applied magnetic field is sufficiently strong to saturate the ferrofluid and the variation of magnetization with temperature can be approximated by a non linear function of temperature difference. By introducing appropriate non dimensional variables the problem is described by a coupled and non linear system of ordinary differential equations with its boundary conditions which is solved numerically by applying an efficient numerical technique based on the common finite difference method. The obtained results are presented graphically for different values of the parameters entering into the problem under consideration and the dependence of the flow field from these parameters is discussed. A comparative study, with a similar problem which has already been solved and documented in literature, is also made wherever necessary, emphasizing the impor- tance of the non-linear variation of magnetization with temperature. Emphasis is also given in the obtained results for Prandtl number equal to 21 and critical exponent δ =0.368 which are important and interesting in Biomagnetic Fluid Dynamics. Mathematics Subject Classification (2000). 76D05 , 34A34 , 76M20 , 76W 05 , 76Z99 Keywords. Biomagnetic fluid flow, magnetic dipole, magnetization, numerical solution. 1. Introduction A ferromagnetic fluid consists of a stable colloidal dispersion of subdomain mag- netic particles in a liquid carrier. The properties of the ferrofluid are profoundly affected by the thermal Brownian motion of the suspended particles and the fact that each subdomain particle is permanently magnetized [1]. A particularly at- tractive feature of the ferrofluids is the dependence of the magnetization upon the temperature and this thermomagnetic coupling makes ferrofluids useful in various practical applications. So, in recent years an extensive work has been done on the ferrofluid dynamics in the presence of magnetic field [2]-[6]. The behavior of a ferrofluid, under the action of an applied magnetic field, is also of fundamental importance in the development of Biomagnetic Fluid Dynam- ics (BFD) in which the blood is investigated as a magnetic fluid. It was found that