Chapter 11, Problem 11.63P

A recuperator is a heat exchanger that heats air used ina combustion process by extracting energy from theproducts of combustion. It can be used to increase the efficiency of a gas turbine by increasing the temperature of air entering the combustor.

Consider a system for which the recuperator is a cross-flow heat exchanger with both fluids unmixed andthe flow rates associated with the turbine exhaust and theair are ${\stackrel{\dot{}}{m}}_h=6.5\text{ kg/s}$ and ${\stackrel{\dot{}}{m}}_c=6.2\text{ kg/s}$ , respectively.The corresponding value of the overall heat transfer coefficient is $U=100{\text{ W/m}}^2\cdot \text{K}$ .
(a) If the gas and air inlet temperatures are $T_{h,i}=700\text{ K}$ and $T_{c,i}=300\text{ K}$ , respectively, what
heat transfer surface area is needed to providean air outlet temperature of $T_{c,o}=500\text{ K}$ ? Boththe air and the products of combustion may beassumed to have a specific heat of $1040\text{ J/kg}\cdot \text{K}$ .
(b) For the prescribed conditions, compute and plotthe air outlet temperature as a function of the heattransfer surface area.