**4. Conclusion**

**Figure 6(a)** and **(b)** show a 3D and 2D view of the radial temperature field within the malignant tissue for different values of the frequency of the magnetic field. It was considered a small value of both Qv and the tissue porosity in order to analyze a temperature field with

**Figure 5.** The influence of the parameter—zeta potential ξp on the radial dependent volume fraction of the particles (a)

**Figure 7(a)** shows the values of the main parameters Qv and f which determines the same temperature on the radial direction. **Figure 7(b)** shows the isothermal surfaces for different

**Figure 6.** The evolution with the frequency of the magnetic field of the temperature field on radial direction Qv = 10 μl/min;

strong non-uniformity (and implicitly high thermal gradients).

values of values of the main parameters Qv and f.

and the temperature field (b).

316 Numerical Simulations in Engineering and Science

ɛ<sup>1</sup> = 0.2 and ξ<sup>p</sup> = −30 mV. (a) 3D view and (b) 2D view.

The model developed in this paper analyzes the essential role of the ferrofluid infusion rate in the radial MNP distribution after their injection within a malignant tissue. Analytical correlations between the following parameters: (i) the particle velocity, (ii) the pressure developed in geometry during the ferrofluid infusion and (iii) the particle concentration were done in order to understand and predicts the temperature field within tissues when an external magnetic field is applied. The temperature field is concentrated within the malignant tissue. The temperature on the tumor border (approximately 38–39°C) not affects the healthy tissue.

The thermal energy deposited within the malignant tissue provides from the MNP distributed as result of convection-diffusion-deposition of the particles after their injection inside tissue. The ferrofluid infusion rate influences significantly the radial distribution of the particles and consequently the temperature field.

The temperature field within the malignant tissues can be controlled by the control of the ferrofluid infusion rate Qv during the infusion process. The particles having higher velocity moves on larger distances on radial direction from the injection site within tumor. As a result, the particles which not remain in the vicinity of the injection site are distributed in the tumor volume. This important effect determines a temperature field with small temperature gradients. The model developed in this paper can be used as a planning tool to compute the temperature field for different parameters.
