Prior space experiments have suggested that the defect (twin and dislocation) density can be dramatically reduced if the crystal is grown without wall contact. Techniques have been proposed to promote wall detachment during solidification by Larson, Duffar, and Wilcox. In this paper, we adopt an ampoule with a soft-finned carbon inner wall, which can arrange for growth essentially free from wall contact. An integrated numerical model for detached solidification has been developed to combine a global heat transfer model of a Bridgman system with a meniscus model near the wall. The global model accounts for heat transfer in a multiphase system (solid, liquid and gas), convection in the melt, and interface dynamics. The meniscus model accounts for meniscus dynamics over a finned structure, and a force balance at the three-phase boundary. The effects of the finned carbon wall on the temperature gradients and the interface shape will be investigated. The integrated model will be used to design apparatus and find the optimal geometry for detached solidification of CdTe growth in space and on the ground.