A dilute polymer solution at 293K flows over a heated plane surface ( 250mm wide 500 mm long) maintained at 333K. The free stream velocity is 1.6m/s. The thermo-physical properties (except viscosity) are close to that of water at the same temperature. The rheological behavior of this solution can be approximated by a power-law model with n=0.45 and m (consistency coefficient) =0.33.3104TPasn where T is the temperature in K. Evaluate: (a) (5 points) The thermal and momentum boundary layer thickness at distances of 50 and 200mm from the leading edge, when the free-stream velocity is 1.6m/s. At 313K, the following properties of the dilute polymer solution can be assumed: =992kg/m3, Cp=4175J/kgK, and k=0.633W/mK. b) (5 points) The average Reynolds and Prandtl's number for the flow. c) (5 points) The convective heat transfer coefficient for the flow. (d) (3 points) The rate of heat transfer from the top side of the plate. (e) (7 points) the fluid velocity to increase the heat transfer coefficient by 25% while maintain the fluid and surface temperatures at the same value