A 2-dimensional analytical and numerical theory for linear induction drives (LIDs) using hot seawater from coolant systems of nuclear reactors as a driving medium has been presented. This work suggests its use in nuclear submarines as it could be considered an important application on how to utilize the coolant output from nuclear reactors in nuclear submarines to generate energy that can be used in nuclear submarine and supercarriers as silent propulsion systems. In this paper, the stepped distribution of the 3-phase winding of the LID has been presented by Fourier integrals. The boundary value problem of the LID has been solved using Fourier transform techniques. The force and seawater input power expressions of the LID have been given in Fourier integral forms, which permit studying the effect of the design parameters of the LID to get the optimum performance. The effect of changing the conductivity of seawater due to the change in seawater temperature has been studied, showing the necessity of injecting hot water from the coolant system of the nuclear submarines or supercarriers, into the LID to improve their performance. The paper shows that the duct size, the conductivity, and the frequency are crucial factors for controlling the silent speed of these machines. For the same length of the machine, the paper shows that decreasing the number of poles and increasing the pole pitch improves the performance than increasing the number of poles and decreasing the pole pitch.