Dear all,
e-NTU equation can be written as follows:
e = {1-exp[-NTU(1-CR)]} / {1-CR*exp[-NTU(1-CR)]};
To simplify above, we can write it as follows:
e = 1-exp[C*(1-X)] / 1-X*exp[C*(1-X)]
Can we linearize e , given that X is a variable in both the numerator and denominator?
Hi Parag Patil
Mathematically, it it linearizable. But there is a singularity at certain point of x (depending on the value of C, as in your case). The graph has a similar form of reciprocal functions.
Thank you Yew-Chung Chak for your answer. This will work for steady-state calculations. However, I wanted to see if this function ( the linearized one) can be used for optimization. But since the optimization will not always take the values of 'x' nearer to x0, while doing a search, I think using this form will not be very efficient. In fact, I can use this , but then I have to have some idea about my solution ( which should be nearer to x0).
I was looking for relaxation, such as McCormick's , which is good for bilinear terms.
Thank you for your answer.
It seems to me, here we have to problems.
1. To parametrize a process description. For solving it could be used non-linear regression analize, if you have not enougt efficient software, you could to elaborate your own software as a non linel optimization procedure (using parametres as variables.
2. Solving non-lineal optimization task using the available process description: onces again a non-lineal optimization problem arise
So, it seems to me you do not need to linerize. Would be enought to solve non-lineal optimization tasks
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