Magnetohydrodynamics (MHD) is the study of a charged fluid flowing through a magnetic field. In this case, the working fluid is a plasma, and the magnetic field is constant, uni-directional. Determining original conductivity of the fuid can be helpful in arcing-prevention, and thus desirable. Coupling Maxwell's equations, and electronmagnetic constitutive laws and genralized Ohm's law results in a set of non-linear PDEs. Making several cylindrical-based physical assumptions for simplification purposes, a further reduction of the model is seen. Numerical differentiation is then applied, particularly central-difference in space and forward difference in time, to determine the solution moving forward. Boundaries in the system are considered to be the two opposing ends of the channel, the outer wall, and the origin. Using simulated numerical data generated from a model, assuming that conductivity at the time 0 can be given. Minimization of residual function is achieved using non-linear least squares. Accuracy of estimated σ is then compared with the relative noise of the true (simualted) data, implying that these coupled equations may not be well-conditined or even well-posed.