Question

Consider the two-dimensional, incompressible flow with constant properties in the entry region of a horizontal channel shown in the figure below To- a) Write the ful equations for conservation of mass and of momentum in the r and y directions, and the equation of thermal energy. (10) (b) Simplify the equations, as they apply to this case. Explain your simplifications. (10) (c) Nondimensionalize the simplified governing equations, defining your nondimensional pa- rameters. (10) (d) Simplify the nondimensional equations for the limiting cases of RePe → 0 and RePe → 00 Note: Pe- Re Pr) Explain your simplifications. Name the type of resulting flows. (10) (e) Write the simplified form of the mass and momentum equations for the downstream region of the channel, after the flow becomes fully developed. Explain your assumptions and simplifications. (10, (f) Consider a long domain starting at the beginning of the channel and extending to the fully developed region. Propose Boundary Conditions for each variable (u, v, T) in each boundary side. (5,)

Answer 1

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