Numerical simulations were carried out for microwave thawing of 2-D cylinders of pure materials with internal convection in the liquid regions. Enthalpy formulation of the energy balance equation was wed with a superficial mushy region around the melting-point. Electric field, energy and momentum balance equations were solved using the Galerkin finite-element method with the penalty finite-element formulation of the momentum balance equation. Microwave power absorption, temperature, and stream functions were studied for various cases. For samples of diameter D, thawing was contrasted between samples for 0.032 < D/D-p < 3. 73 and 0.10 < D/(m) < 1.58. These ratios were computed based on the liquid-phase penetration depth D-p and wavelength of microwave radiation in the medium (m). In all cases, Pr = 0.5 was used and the Rayleigh number varied from 1.067 x 10(3) for the smallest diameter to 1.33416 X 10(5) for the largest sample (D = 2 cm). Thawing was contrasted for MWs being incident from the top and bottom faces of the cylinder and with the thawing dynamics in the absence of convection in the liquid. Our simulations indicate that convection plays a small role for D/Dp much less than 1 and thawing is independent of the direction of MWs. At intermediate values of D/D-p where a strong maximum occurs in the power, the influence of convection with primary and secondary cell formation in the liquid regions was a strong function of the direction of incident microwaves. In the presence of multiple connected thawed regions convection was suppressed.