Very thick slurries and pastes sometimes move in channels almost as a solid plug. Thus, one can approximate the velocity profile by a constant value v0 over the conduit cross section. Consider the plug flow in a circular tube of radius R. For z<0, the slurry temperature is uniform at the inlet temperature T1. For z>0, there is a constant radial heat flux qr=-q0 at the wall. a) Reduce the appropriete energy equation on the attatched sheet to get a differential equation for T. List all the physical assumptions you made. Indicate beside each canceled term the corresponding assumption used. Each assumption must be a physical interpretation, not a mere mathmatical statement. For example, stating that the temperature does not depend on theta is not acceptable.
b) Recast the energy equation in dimensionless form using
c) Write the boundary conditions in dimensioned and dimensionless forms