Membrane based clarification and concentration of fruit juice has become a popular unit operation in modern fruit juice processing industries. The well known membrane modules used for this purpose are tubular and spiral wound modules. Therefore, design of these modules is of utmost industrial importance. The key parameter for design of membrane modules is mass transfer coefficient. Most of the fruit juices have non-Newtonian rheology, e.g., power law, ellis fluid, etc. Till today, the mass transfer coefficient for such systems used is approximated from the corresponding relations developed for Newtonian fluids. Hence, a detailed fluid flow modelling with non-Newtonian rheology is urgently warranted. In the present work, this aspect is attempted. The expressions of the mass transfer coefficients are derived from the first principles for laminar, non-Newtonian fluid flow in a porous conduit. The effects of the permeation are incorporated quantitatively in the mass transfer coefficient from a theoretical basis. The analysis is carried out for various non-Newtonian rheologies. Effects of the operating conditions, i.e., Reynolds number, permeate flux, etc. on mass transfer coefficient are also investigated. Two flow geometries are considered. Flow through a tube and that through a rectangular thin channel, which are useful for the design of the tubular and spiral wound cross flow membrane modules. The developed relations of mass transfer coefficients would be of tremendous help to the design engineers.