Entropy production during the ultrafiltration of a solution in a membrane tube is investigated. It is shown that the entropy production is minimum at an optimum diameter of the membrane tube provided that the mass flow rate is constant. The rate of the entropy production is minimum at an optimum Reynolds number when the membrane tube diameter is fixed. There exists a relationship between concentration polarization and the rate of entropy production. It is being suggested that in order to minimize the concentration polarization in an ultrafiltration process, the optimum diameter and the Reynolds number should be calculated before tube diameter and fluid conditions are set.