Convective contamination of self-diffusion experiments with an applied magnetic field is considered using a two-dimensional axisymmetric model. Constant, uniform, and an additional non-uniform heat fluxes are imposed along the sidewall of the cylinder while constant heat loss occurs through the top and bottom. In this model, due to a very small thermal Péclet number, convective heat transfer is neglected, and the flow is steady and inertialess. Time-dependent concentration is solved for various values of the mass Péclet number, Pe m, (the ratio between the convective transport rate and the diffusive transport rate) and different magnetic field strengths represented by the Hartmann number Ha. Diffusivities are obtained using the same algorithm used to extract diffusivity values from the actual experimental data. Normalized values of these diffusivities vs. effective Pe m are presented for different imposed temperature profiles. In all cases, the diffusivity value obtained through the simulated measurement increases as the effective Pe m increases. The numerical results suggest that an additional periodic flux, or "hot" and "cold" spots, can significantly decrease the convective contamination in our geometry. The number of periodicity in temperature does not have a significant impact on the diffusivity results. Keeping the top wall slightly warmer than the bottom wall has no effect on the diffusivities for this model.