a novel energy transfer device for heating water that uses the viscous dissipation effect. A highly viscous fluid is contained in the space between two cylinders as shown below. The outer cylinder (radius R ) moves at 0 radians per second and is insulated to prevent any transfer of energy to the outside. The inner cylinder (at r=KR ) is fixed and contains the water to be heated. The inner cylinder temperature is a constant Ti . The often-mad professor has proposed using worker mice to turn the outer cylinder to supply hot water to the oligarch mice that he controls. You are to solve the energy balance equation for this system to obtain the temperature and energy flux profiles for the viscous fluid for a previously determined viscous dissipation rate that was obtained by solving the mass and momentum balance equations - You DO NOT have to solve those equations. Just use the following result (constant, maximum dissipation rate term)

=B0/R2

where is the fluid viscosity, B0 is a rotation rate constant for the outer tube (length/time units). You can assume steady state, Newtonian fluid, constant physical properties, laminar flow vr=0,vx=0,v=v(r) only), -symmetry, no z dependencies.

Determine the Temperature and heat flux profile for this system.

B0=(1k2)l0ke,aconstonf viscous fluid (blee shede)