A mathematical framework on relaxation losses of heating of magnetite nanoparticles synthesized with Polydimethylsiloxane (PDMS) gel encasement is presented. Numerical solution of the mathematical model showed explicit dependence of the temperature rise of the device on frequency and amplitude of the external applied field, relaxation time and volume fraction of the nanoparticles. Hyperthermia therapeutic temperature of 41 - 46oC can be achieved with an external field of frequency and amplitude in the ranges 2.16 - 2.19 kHz and 9.77 - 9.89 kA/m respectively. Also, viscosity and volume...