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Recover esign formula

In this screencast, we're going to design a heat exchanger network based on information we collected in a previous screencast with the transfer of energy between two hot streams and two cold streams, and utilities that we designated also in the last screencast. So a little background first on defining this pinch point, and how we would go about starting to design our heat exchanger network. So if we look at a heat exchanger between a hot stream and a cold stream, we've designated our cold stream as C, so we have our inlet cold temperature, and our cold outlet, we have our hot inlet, and our hot outlet. We have some heat transfer, Q, and a temperature difference between the hot inlet and cold outlet as delta T2, the same on the other side, we designate it delta T1, and then the values Ch and Cc are the specific heat flow rates, and the units on this is given as an energy per temperature. So if we write out our equation for our heat transfer, it's just going to be for the hot stream our Ch times the temperature difference between the outlet and the inlet, and we can do the same for the other side. So we can rearrange these equations to get the following. Now hopefully what you see here is that if we subtract the two equations, these two groups form our delta T2 and these two groups form our delta T1. This means that we get the following result, where delta T2 minus delta T1 is equal to the heat transfer, Q, times Cc minus Ch over Cc times Ch. So what does this mean? This means that when we're designing our two heat exchanger networks, one on the hot side and one on the cold side of the pinch point, we're going to examine them in the following manner. First, we use this equation to say that if we're designing on the hot side, then delta T1, this is for the hot side of the pinch, delta T1 is going to be our designated minimum approach temperature. This leaves us with a delta T2 equaling delta Tmin plus the value on the right side. Now, to ensure that our delta T2 here is going to be greater than our approach temperature, this value on the right side has to be positive. Now Q is positive and our heat capacity flow rates are positive, so that means Cc has to be greater than or equal to Ch. Now the following is going to be true if we're looking at the cold side: We set delta T2 equal to delta Tmin, we rework this equation, this time there's going to be a negative sign. Now for this to be true and to make our delta T1 is going to be greater than delta Tmin, our Ch has to be greater than or equal to our Cc. So we use these two guidelines when we're designing our...