Capture the rayleigh line between mach number 02 to 40

Question

We have an air flow inside a frictionless duct with heat transfer. At location 1, flow has pressure, p₁ = 1 atm., T₁ = 288 K and M₁ = 0.2. Capture the Rayleigh line between Mach number 0.2 to 4.0 initially by adding heat q in small increments taking the flow to M = 1 at location 2, there after removing heat until you achieve M = 4. Use the differential equations from lecture 7 to get new Mach number, M after adding heat q, then use the newly calculated M in differential equations to compute entropy s and thereafter T. Once you compute M, you can compute ratios like p/p*, T/T* etc.

(1) Plot Rayleigh line (T-s plot) between M = 0.2 to 4.

(2) Plot T0/T0^*, p/p*, Ρ/Ρ*, T/T*, u/u*, p₀/p₀* (keep y axis range 0 - 4)

(3) Find T, when M = 1/sqrt(γ) (i.e. when dT/ds = 0) and M = 1 (i.e. when ds/dT = 0)

(4) Verify that you achieve same T at M = 1, when you hand calculate starting from M₁ = 0.2 and M₁ = 4 using lecture 6 material and tables in the text.

You can assume s₁ = 0 to start with. For air C_p = 1004.5 J/kg.K, γ = 1.4. Using MATLAB solve the ODEs using any method (Euler's Method or RK method). Submit script of your code in the project report.