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.