A thermokinetic model for the concentration u and temperature q of a mixture consists of the...

 

Transcribed Image Text:

A thermokinetic model for the concentration u and temperature q of a mixture consists of the following equations (Gray and Scott 1994): du dt dq = -ki-kzuek, = k4uek39-k5q. dt The initial conditions are u = = 0 and q = 0 at t=0. (a) What are the dimensions of each of the ki's? (b) Explain why the rule of thumb for scaling used in the projectile problem does not help here. (c) Find the steady-state solution, that is, the solution of the differential equations with u' = 0 and q' = 0. (d) Nondimensionalize the problem using the steady-state solution from (c) to scale u and q. Make sure to explain how you selected the scaling for t. A thermokinetic model for the concentration u and temperature q of a mixture consists of the following equations (Gray and Scott 1994): du dt dq = -ki-kzuek, = k4uek39-k5q. dt The initial conditions are u = = 0 and q = 0 at t=0. (a) What are the dimensions of each of the ki's? (b) Explain why the rule of thumb for scaling used in the projectile problem does not help here. (c) Find the steady-state solution, that is, the solution of the differential equations with u' = 0 and q' = 0. (d) Nondimensionalize the problem using the steady-state solution from (c) to scale u and q. Make sure to explain how you selected the scaling for t.