Problem X$6(80$ points$)$ For textbook Example $6\mathrm{.}2$

$(10$ Points$)$ Derive equations for the inlet mass fractions of fuel and oxidizer.

$(15$ points$)$ Derived three specie conservation equations $($for fuel, oxidizer and products$)$ and one energy conservation equation. Combine them together to get one equation for the unknown system temperature.

$(30$ points$)$ Write a computer program using MATLAB or some other framework to find the system temperature for a range of flow rates and equivalence ratios.

$(10$ points$)$ For an equivalence ratio of $=1,$ use the program you wrote in the last part to calculate the product mixture outlet temperature and mass fractions versus mass flow rate. Enter them in the table below, and plot them. Determine the blowout flow rate $($where the outlet temperature is the same as the inlet$).$ Compare your results to those in Fig. $6\mathrm{.}7.$

$(15$ points$)$ Repeat the last part for $=0\mathrm{.}8$ and $0\mathrm{.}6.$ Add these data to the table below and the plot. Find the blowout mass flow rates at these lower equivalence ratios. Compare your results with those in Fig. $6\mathrm{.}8.$

$*$

$\backslash$table$[[$Mdot$,,$Temp,$Y_{fu},Y_{ox},Y_{pr}$

$6\mathrm{.}2$ Show that

$\frac{d(v_{x}A)}{dx}=0=\frac{1}{}\frac{(d)}{(d)x}+$cdots, etc.

$($see Eqn. $6\mathrm{.}43).$

Problem X$6(80$ points$)$ For textbook Example $6\mathrm{.}2$

$(10$ Points$)$ Derive equations for the inlet mass fractions of fuel and oxidizer.

$(15$ points$)$ Derived three specie conservation equations $($for fuel, oxidizer and products$)$ and one energy conservation equation. Combine them together to get one equation for the unknown system temperature.

$(30$ points$)$ Write a computer program using MATLAB or some other framework to find the system temperature for a range of flow rates and equivalence ratios.

$(10$ points$)$ For an equivalence ratio of $=1,$ use the program you wrote in the last part to calculate the product mixture outlet temperature and mass fractions versus mass flow rate. Enter them in the table below, and plot them. Determine the blowout flow rate $($where the outlet temperature is the same as the inlet$).$ Compare your results to those in Fig. $6\mathrm{.}7.$

$(15$ points$)$ Repeat the last part for $=0\mathrm{.}8$ and $0\mathrm{.}6.$ Add these data to the table below and the plot. Find the blowout mass flow rates at these lower equivalence ratios. Compare your results with those in Fig. $6\mathrm{.}8.$

$*$

$\backslash$table$[[$Mdot$,,$Temp,$Y_{fu},Y_{ox},Y_{pr}$