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Unformatted text preview: h, 1998). We will assume that the y can be expressed as: k d , j = f ( d , j , q m , j , c , i ,.....) k 0
k a , j = f ( a , j , q , j , c , i ,.....) k m 0 This yields 2N more relationships. Finally, the dispersio n coefficient can be expressed as: d p u 0 = 0.2 + 0 011 e 0 . 48 . R
Finally, the dispersio n coefficient can be expressed as: d p u 0 = 0.2 + 0 011 e 0 . 48 . R
a. How would you classify this system o f equations? Why? b. How many variables are there? How many equat ions (relationships)? What is the number of degrees of freedo m? c. Is this system underdetermined or overdetermined? Why? d. What addit ional relat ionships, if necessary, can you suggest to reduce the degrees of freedo m to zero? Solution: a. This model should be classified as a nonlinear, distributed model. Distributed models provide relat ionships for state variables as funct ions of both space and t ime, whereas a nondistributed (lumped) model will only depend on t ime. It is also nonlinear as one can see the terms invo lving mult iplicat ion of state variables. b. For N components, we have c j and q j as the state variables. One can al...
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