An anisotropic heat diffusion coefficient is introduced in order to study some interfacial growth phenomena. This anisotropy has been incorporated in a phase field model which has been studied numerically to reproduce some fundamental solidification situations (needle crystal growth) as well as the dynamics of a nematic–smectic-B interface. As a general result, we find that dendrites grow faster in the lower heat diffusion direction. Simulation results are compared with experiments with remarkable qualitative agreement.