Radial Variations in Viscosity

Variable viscosity in laminar tube flows is an example of the coupling of mass, energy, and momentum transport in a reactor design problem of practical significance. Elaborate computer codes are being devised that recognize this 

Consider axisymmetric flow in a circular tube so that Vg = 0. Two additional assumptions are needed to treat the variable-viscosity problem in its simplest form  

The momentum of the fluid is negligible compared with viscous forces. 

The radial velocity component Vr is negligible compared with the axial component Fz. 

The first of these assumptions drops the momentum terms from the equations of motion, giving a situation known as creeping flow. This leaves Vr and coupled through a pair of simultaneous, partial differential equations. The pair can be solved when circumstances warrant, but the second assumption allows much greater simplification. It allows to be given by a single, ordinary differential equation  

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