The steady Marangoni convection in a bridgeman between two circular bars of different diameter is parametrically studied in a gravity-free space as well as in a gravitational field. Two melts of different Prandtl numbers, Pr=0.023(Si) and Pr=2.6($NaNO_3$) are considered. The effect of rotation of the bars on the Marangoni convection is studied for different rotational conditions of the crystal and feed bars:iso-rotation, single-rotation and counter-rotation. In the presence of bar rotation, Maragnoni convection was confined to a thin layer near the free surface of the bridgeman, whereas the forced convection due to bar rotation occupied the interior zones. The patterns of Marangoni convection in the present conical melt zone were considerably different from those in a cylindrical melt zone. The presence of bar rotation presented much more variaty in the flow patterns of Maragoni convection in the present conical melt zone than in the traditional cylindrical zone. This paper presents the flow patterns in a conical bridgeman.