We report mass transfer coefficient correlations, at low Reynolds numbers for a novel cross-corrugated membrane reactor, which is being developed for a number of processes, most notably phase-transfer catalysed reactions. The presence of Tollmien-Schlichting (T-S) waves saw a noticeable enhancement in mass transfer, giving characteristics usually only found in turbulent flow. Correlations for the channel wall and the channel corrugations are given in terms of dimensionless Sherwood numbers: Sh(CW) =0.0209Re(0.7675)Sc(0.333) (200 < Re < 2300), Sh(COR) =0.2477Re(0.489)Sc(0.333) (200 < Re < 2300).