It is desired to heat cold ethanol in a double$-$pipe heat exchanger using hot water. Data are as follows.

$\backslash$table$[[$parameter$,\backslash$table$[[$cold ethanol$],[$inside pipe$]],\backslash$table$[[$hot water$],[$outside pipe$]]],[$inner diameter $(cm),5\mathrm{.}250,7\mathrm{.}793],[$outer diameter $(cm),6\mathrm{.}0325,8\mathrm{.}89],[$inlet temperature $(C),20,80],[$outlet temperature $(C),40,50],[$flow rate $(k\frac{g}{s}),1\mathrm{.}26,-],[$heat capacity $(\frac{J}{k}g*K),2500,4200],[$thermal conductivity,,$],[,(\frac{W}{m}*K),,]]$

The double$-$pipe heat exchanger operated in countercurrent flow mode is illustrated as follows.

a$.$ Calculate the hot water flow rate?

b$.$ What is the best flow configuration and the log mean temperature difference $($LMTD$)?$

c$.$ What is the inside convective heat transfer coefficient?

d$.$ What is the overall heat$-$transfer coefficient and exchanger area based on the outside area of the inner tube? Neglect inner tube wall heat transfer and assume the best flow configuration found in part $b.$