A Mistake in Kern's Heat Transfer

Chemical engineers must be familiar with this set of equations, for designing a shell & tube heat exchanger.
The third equation for F_T then plotted in some figures, corresponded to type of shell & tube exchanger flow. for example in the figure below. This set can be found in any reference that talk about shell & tube heat exchanger, and I think all of that refer to the main source, Kern's "Heat Transfer".

Let's check these cases out...

< case 1 >A stream 90 °C is going to be cooled to 70 °C using cold stream 30 °C, which its temperature will rise to 50 °C. We'll find, the value of R will be 1. Use this value in the equation for F_T & LMTD. The value will be indefinite. So we cannot calculate the first equation.
< MyOpinion >The temperature differences are equal in both sides (T1-t2 = T2-t1), thus we can assume that the weighted/average temperature difference in this system is the same of those temperature differences, so we could use one of those. We can replace the F_T.LMTD in the first equation with TD, which TD=T1-t2=T2-t1. We can see the similar condition in the system which use latent heat in both streams.

< case 2 >A stream 90 °C is going to be cooled to 60 °C using cold stream 30 °C, which its temperature will rise to 70 °C. In this system, we can calculate the value of LMTD, but not for the F_T (it will be indefinite), so we cannot calculate the first equation for Q.
< MyOpinion >Examine the system, we will find that there will be cross temperature difference there. So, we cannot apply the combination of parallel-countercurrent (1-2, 1-4, 1-6, 1-8) to this system. We must use the fully countercurrent (with 1-1 exchanger) to this system, and replace the F_T.LMTD with LMTD only, in the first equation.

Those are my opinions. I hope there will be other opinions, or comments. I'm affraid, perhaps i missunderstood the problem, then please send comment, or tell me the truth....thanks :)