MECH E4320 (Fall 2024): Homework #5

Please turn in your homework through Courseworks by the scheduled time. Please show and explain your work clearly and completely in order to earn full credit.

1. Write down the conservation equations for mass, species, and sensible enthalpy derived in class (before the simplification to a one step reaction which led to the nondimensional forms). What do each of the terms correspond to physically? What assumptions/approximations were used in their derivation? (50 points)

2. Starting from the conservation equations for Yi and hs derived in class (that correspond to Eqs. 5.6.1-5.6.2 in Combustion Physics), write down the definitions for Yi, hs, and T and then show and explain all the intermediate steps necessary to derive Eqs. 5.6.3-5.6.10 for the completely nondimensionalized conservation equations. (Note that there is a typo in Eq. 5.6.5: T in Eq. 5.6.5 should be a t which is a nondimensional time—not to be confused with the nondimensional temperature, T) Would this choice of nondimensionalization be appropriate for flowing systems of a given velocity, v0? Why or why not? (50 points)