Consider fully developed Couette flow—flow between two infinite parallel plates separated by distance h, with thetop plate moving and the bottom plate stationary as illustrated in Fig. P7–56. The flow is steady, incompressible, and two-dimensional in the xy-plane. Use the method of repeating variables to generate a dimensionless relationship for the xcomponent of fluid velocity u as a function of fluid viscosity μ, top plate speed V, distance h, fluid density rho, anddistance γ, Show all your work.

1in2 processor chip can be modelled as an isothermal plane wall of silicon, isothermal on both sides. the power input to the bottom of the plane wall, or the processing power of the chip, often called the thermal design power (tdp), is 100w. assume the periphery is adiabatic. the silicon is 400 microns thick. the temperature at the junction, or in this case on the bottom of the isothermal plane wall, is 85°c. what is the top surface temperature, assuming that the only mode of heat transfer is conduction