This paper starts with an introduction to the concept of momentum current. It is followed by a discussion of its strength and density with the aid of several analogies made between momentum current and electric current. Based on the novel concepts of thermal charge and its quantity (entropy), the analogies are extended to entropy current. The broadened analogies cover the driving force and resistance of each current, the effects that the strength or density of each current has on their conductors, and the relationships between the above three currents and energy current, etc, which involve practical problems such as industrial safety, human thermal sensation, process control parameters as well as energy carriers and energy transport.