A double pipe parallel flow heat exchanger is to be used to control temperature of the cold fluid $($diesel$)$ at $m^{}=1\mathrm{.}0k\frac{g}{sec}$ to an exhaust temperature of $te=35C,$ see Figure $1.$ The cold fluid inlet temperature is $ti=-5C.$ The hot fluid is water with $Ti=90C$ and $m^{}=2\mathrm{.}0k\frac{g}{sec}$

Assume the following: $1)$ Heat Exchanger Outer Wall is Insulated. $2)$ Inner pipe has neglible wall thickness and high thermal conductivity. $3)$ No Fouling Factors. $5)$ Use fluid properties as shown in Figure $1.$

a$)(2$pts$)$ What is the heat transfer rate for this heat exchanger?

b$)(2$pts$)$ What is the best temperature difference to use between these fluids?

c$)(2$pts$)$What Re# number should be utilized for each of these fluids?

d$)(2$pts$)$ What is the average convection coefficient $h$ for each of these fluids and the overall heat transfer coeff. $U?$ for each of these fluids?

e$)(2$pts$)$What is the length of heat exchanger that needs to be used for this design and is it reasonable for this application?

Extra Credit $(1$pt$)$ What is the effectiveness, $,$ and NTU# for this heat exchanger?