Reference no: EM132409307
Exercise - Mathematical Modeling Of Differential Equation
Consider the equation for the scaled absolute temperature in an exothermic oxidation reaction with λ = 2.2,
σ dθ/dt = 2.2e-1/θ - (θ - θα)
It's worth noting that the model assumptions listed in pag 262 of the textbook have been used.
(a) For each of the three values θα = 0.11, 0.19 and 0.27 generate a plot that allows you to determine the number of equilibrium solutions. Does the number of equilibrium solutions change with θα? If the number of equilibrium solutions changes, interpret this change in terms of bifurcation theory.
(b) Show that if θαc is a critical ambient temperature where a bifurcation occurs then the equations
θc = 2.2e, θαc = θc - θc
must be satisfied. In these equations θc is a critical scaled absolute temperature at which bifurcation occurs.
(c) Use the equations in (b) to graphically estimate the critical ambient temperature θαc above which spontaneous ignition occurs. Give the numerical value of this estimation.
Note - Use matlab code in the book maybe you need to do some modification of the code in the book. Must follow the standard of book Explain step and justify answer.
Textbook - MATHEMATICAL MODELLING WITH CASE STUDIES - Using Maple and MATLAB, Third Edition by B. Barnes and G. R. Fulford.