The quality of sapphire single crystals used as substrates for LED production is largely influenced by two defects: dislocation density and bubbles trapped in the crystal. In particular, the dislocation density has a higher value in sapphire grown by the Czochralski (CZ) method than by other methods. In the present study, we predict a decreased value for the convexity and thermal gradient at the crystal front (CF) through the use of an additional heater in an induction-heated CZ system. In addition, we develop a solute concentration model by which the location of bubble formation in CZ growth is calculated, and the results are compared with experimental results. We further calculate the location of bubble entrapment corresponding with the use of an additional heater. We find that sapphire crystal growth with an additional heater yields a decreased thermal gradient at the CF, together with decreased CF convexity, improved energy efficiency, and improvements in terms of bubble formation location.