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Question 1 (35P). Consider a shaft and housing for the shaft as shown in the following figure, inner shaft rotates at the velocity of w (u) and the housing rotates of W. (u.) in the opposite direction to the shaft. Where w is angular velocity and u is linear velocity, respectively. Incompressible fluid is located between shaft and housing. The clearance between shaft and housing is given by H that is very small compared to the radius of the shaft ri: shaft radius Wo ro: housing radius H fo Win -fluid Consider steady, two-dimensional, incompressible flow between the shaft and the housing, no gravitational effect Couette flow). Find the followings. a) Velocity profile between the shaft and housing, u = f(y), draw the velocity profile b) Temperature distribution between the shaft and housing (consider viscous dissipation), T=f(y) c) Heat transfer coefficient (h) d) Location where the velocity changes the direction