The idea of optimization of electromagnetic coil for levitation under terrestrial conditions using analytical approach or numerical simulations seems attractive, yet, formulation of such problem is not straightforward. As a first step toward it, analytical and numerical modeling for the real electromagnetic inductor are performed using 2D and 3D presentation of the latter with analysis for the equilibrium position of samples of various sizes, their temperature and the symmetry of the fluid flow. Results obtained numerically are compared with experimental observations.