A layer of concentrated polymer solution (thickness 8) is applied on a solid surface and the solvent is allowed to evaporate in air. Write down the governing equation for the solvent in polymer c_A and b, c, for the system assuming that atmosphere has no mass transfer resistance to the evaporating solvent. Assume now that small penetration approximation can be made. Solve the resulting equation when the initial amount of solvent in the polymer was c_Ao. On a cold vertical wall at T_0, saturated steam T_d condenses and the condensate runs down the surface under gravity in form of a thin liquid film (see Figure 14.7-1). Apply lubrication theory approximation. When the heat transfer is considered, only conduction perpendicular the wall is important. Hence show that the conduction into the wall from the film is given by k/delta(T_d - T_0) = gamma/A delta vector H_wrp where k is thermal conductivity of the condensate, gamma is the rate of condensation on the wall in mass/time, A is the area of the wall and delta vector H_wrp is the latent heat. (Obtain the governing equation for T, the temperature profile in the film in the direction perpendicular to the wall, y-coordinate) and b.c. Solve to get T, then do a balance to get the above.) Show that a material balance leads to din/dz = gamma/A where dot m is w/W in Eq. (2.2-21) and z-direction in down the wall in the direction of flow. Show that this equation is actually a differential equation in delta.