Cooling method for gas turbines. Refer to the Journal of Engineering for Gas Turbines and Power (Jan. 2005) study of a high-pressure inlet fogging method for a gas turbine engine, presented in Exercise 12.27

(p. 701). Recall that you fit a first-order model for heat rate (y) as a function of speed 1x12, inlet temperature 1x22, exhaust temperature 1x32, cycle pressure ratio 1x42, and air mass flow rate 1x52 to the data.

a. Researchers hypothesize that the linear relationship between heat rate (y) and temperature (both inlet and exhaust) depends on air mass flow rate. Write a model for heat rate that incorporates the researchers’ theories.

b. Use statistical software to fit the interaction model you wrote in part

a. Give the least squares prediction equation.

c. Conduct a test (at a = .05) to determine whether inlet temperature and air mass flow rate interact to affect heat rate.

d. Conduct a test (at a = .05) to determine whether exhaust temperature and air mass flow rate interact to affect heat rate.

e. Interpret practically the results of the tests you conducted in parts c and d.