  An Omnimagnet is an electromagnetic device that enables remote magnetic
manipulation of devices such as medical implants and microrobots. It is
comprised of three orthogonal nested solenoids with a ferromagnetic core at the
center. Electrical current within the solenoids leads to Joule heating,
resulting in undesired temperature increase within the Omnimagnet. If the
temperature exceeds the melting point of the wire insulation, device failure
will occur. Thus, a study of heat transfer within an Omnimagnet is a necessity,
particularly to maximize the performance of the device. For the first time, a
transient heat transfer model, that incorporates all three heat transfer modes,
is proposed and validated with experimental data for an Omnimagnet with maximum
root mean square error equal to 8${\%}$ (4$^{\circ}$C). This transient model is
not computationally expensive. It is relatively easy to apply to Omnimagnets
with different structures. The accuracy of this model depends on the accuracy
of the input data. The code is applied to calculate the maximum safe
operational time at a fixed input current or the maximum safe input current for
a fixed time interval. The maximum safe operational time and maximum safe input
current depend on size and structure of the Omnimagnet and the lowest melting
point of all the Omnimagnet materials. A parametric study shows that increasing
convective heat transfer during cooling, and during heating with low input
currents, is an effective method to increase the maximum operational time of
the Omnimagnet.The thermal model is also presented in a state-space equation
format that can be used in a real-time Kalman filter current controller to
avoid device failure due to excessive heating.
