Free growth properties of the smectic B liquid crystalline phase into the supercooled nematic have been investigated in quasi-twodimensional geometry. Different orientation combinations of the two phases have been achieved experimentally and the interfacial patterns have been studied and analysed as a function of undercooling. The angular dependence of the surface tension has been deduced From the shape of the interface in thermal equilibrium The experimentally determined surface tension anisotropy has been incorporated into computer simulations based on the phase-field model. The simulations have reproduced qualitatively the rich variety of morphologies observed in the experiments for a given set of undercoolings in three geometries. Anisotropic heat diffusion on the nematic side, relevant to our experimental system has also been introduced. Both in the experiments and in the simulations we find that the growth is faster in the lower heat diffusion direction.