This paper addresses the problem of multichannel audio source separation in under-determined convolutive mixtures. We target a semi-blind scenario assuming that the mixing filters are known. The convolutive mixing process is exactly modeled using the time-domain impulse responses of the mixing filters. We propose a Student's t time-frequency source model based on non-negative matrix factorization (NMF). The Student's t distribution being heavy-tailed with respect to the Gaussian, it provides some flexibility in the modeling of the sources. We also study a simpler Student's t sparse source model within the same general source separation framework. The inference procedure relies on a variational expectation-maximization algorithm. Experiments show the advantage of using an NMF model compared with the sparse source model. While the Student's t NMF source model leads to slightly better results than our previous Gaussian one, we demonstrate the superiority of our method over two other approaches from the literature.