This paper is concerned with the double diffusive convection due to the melting of a horizontal ice cylinder into a calcium chloride aqueous solution inside a cylinder cavity. It appears a quiescent layer between an upper concentration convection and a lower thermal convection in the melt liquid. The thickness of the layer gradually increases during the melting process due to the decay of the both convections. The present numerical results predicts well the mean Nusselt number at the melting front.