A fluid is sheared between two parallel plates as we saw in Chapter 4. If the gap between the plates is small and the shearing rate is high, friction between the fluid molecules will generate heat....

A fluid is sheared between two parallel plates as we saw in Chapter 4. If the gap between the plates is small and the shearing rate is high, friction between the fluid molecules will generate heat. Energy will flow by conduction in the y direction from the hot plate toward the cold plate. As we will see later in Chapter 10, the heat generation rate will be given by:

a. For a fluid of viscosity, μ, a gap width between the plates of δ, and an upper plate velocity of v0, what is the heat generation rate within the fluid?

b. If the upper surface of the plate is held at a temperature of T0 and the lower surface at a temperature of T1, what is the temperature profile between the plates?

c. For the parameters:

μ = 0.25 Ns/m2 δ = 0.001 m

v0 = 1 m/s T0 = 325K T1 = 300K

 evaluate the heat generation rate and the temperature profile.