#$2.(25)$ Two different fluids are contains in the concentric cylinders: fluid $1$ for inner side, $2$ for outer side. We know that the outer cylinder is rotating at ${}_2.$ Assuming steady incompressible flow, answer the following questions:

a$)$ Write down the governing equations and set the appropriate boundary conditions

b$)$ If the viscosity ratio $\frac{v_2}{v_1}=k>1,$ get the velocity profile, $u_1(r)$&$u_2(r)$