Two all-electric melting furnaces, 15t/d and 36t/d, were simulated and analyzed with the ANSYS FLUENT 14.0 software add-on MHD module. The electric power density distribution, temperature distribution, and velocity field in the glass furnaces of these two models were analyzed. Electric power density and temperature are found to increase initially and then decrease from the center of the furnace to the side wall in a horizontal direction. Similar trend is observed from top to bottom in a vertical direction. The temperature distribution causes the internal and external circulations in the all-electric melting furnaces. An unstable connectivity relation is proven to exist between the external circulation flow and the dog-hole of the 15t/d all-electric melting furnace. Experimental evidence of the relation is presented from the annular strip images of the corresponding glass pipe product samples. Our analysis revealed several design flaws in the working condition of the two types of furnaces. The simulation results of the two models were compared.