Invariant vorticity and thermal state of the creeping flow of a fluid through a permeable membrane

A new class of stationary creeping flows of a viscous fluid is presented in complience of external resistance force. An example of an invariant vorticity of a fluid flow is studied through the permeable membrane and capsular system. The influence of capsular morphology on the entropy production is mastered. An important role of the correlation “velocity vortex - viscous dissipation of energy” in forming the thermal field of a fluid is discovered.