In a particular application involving fluid flow at a rate m` through a circular tube of length L and diameter D, the surface heat flux is known to have a sinusoidal variation with x, which is of the form q″s(x) = q″ₛ,ₘ sin(πx/L). The maximum flux, q″ₛ,ₘ, is a known constant, and the fluid enters the tube at a known temperature, Tₘ,ᵢ.
Assuming the convection coefficient to be constant, how do the mean temperature of the fluid and the surface temperature vary with x? i. e. determine the equation for Tₘ(x) and Tₛ(x).

Two microscope slides are placed horizontally, one on top of the other, with a drop of a dishwashing liquid between them. the gap between the slides is 1 mm. a machine pulls the top slide to the right with a velocity of 0.15 millimeters per second while the bottom slide is held stationary. a stress gage indicates that a shearing stress of 0.5 pa is required to pull the top slide with this velocity. if the dishwashing liquid adheres to both slides during this process, what is the viscosity of the liquid? specify whether your answer is dynamic or kinematic viscosity, and use appropriate units.