Consider the two-dimensional shallow liquid in Fig. P2.1. The sides of the con- tainer at x = 0 and x = / are at temperatures T and T, so that T > T. In steady state, the thermocapillary effect results in a circulatory flow as shown in the figure. T,o de X Gas P Figure P2.1. Shallow liquid film in Problem 2.1. H dP dx U (y) = Liquid Assume constant liquid properties and negligible gas viscosity, and assume negligible inertial effects so that the momentum equation in the x direction reduces to +HL dU dx Prove that the following expressions apply: 1 0 = 01 +3PL (H-H). = 0. 2L 27 T20 do dx H2