A double pipe parallel flow heat exchanger is used to heat a cold fluid $($diesel$)$ at $m^{}=0\mathrm{.}5k\frac{g}{sec},$ see Figure $1.$ The cold fluid inlet temperature is $t=-5C.$ The hot fluid is water that enters at $Ti=80C$ and leaves at $Te=50C$ at a rate of

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 $h$ and the overall heat transfer coefficient $U$ 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$)$: How does the convection coefficient vary with the outside pipe diameter?, a plot is fine.