Let vec$(v)=(v_x,v_y,v_z)$ be the velocity profile of a fluid flowing between two plates. The flow is

unidirectional in the direction of $x.$ The upper plate is moving at a constant velocity of $v_p$ in the

x$-$direction. Assume that there is no pressure drop, so the fluid motion is solely a result of the

upper plate movement.

a$.$ Start with the continuity equation and the equation of conservation of momentum $($pick

the right direction$),$ simply the equations by eliminating all zero$-$valued terms.

b$.$ Now assume that there is a heating coil generating heat at $3sin(x)\frac{J}{m^{3}K}.$ Start with the

conservation of energy equation, simply the equation by eliminating all zero$-$valued

terms, and solve for the temperature profile.