1. Using the change of variables from cylindrical coordinates to the radial coordinate, eta, how does one get equations (5)-(7) ? I am always getting some additional terms and different signs. If anyone finds the same final equations, please let me know.
2. Also, when they do a numerical analysis of the system, they use Ode45, which is a Runge-Kutta method (iterative) to solve ODEs. While the system is a set of PDEs, thez perform the numerical analysis in a similar manner to ODEs. There is no change of variable that could convert the PDEs to ODEs in the defined range in the mentioned article. What justifies the reason for the use of the same?
Addressing your first question, I have attached derivation of the axial component of momentum in terms of the transformed variables. There seems to be a typo .You can use my notes to check the other equations.
Please see the work of my team which is pretty clear.
1.A.K.Politis et al ,Numerical Modelling of Simulated blood flow in idealised composite arterial coronary grafts: Steady state simulations. J. of Biomechanics 40(5),pp1125-1136,2007 and the Transient simulations J. of Biomechanics 41(1),pp25-39,2008.
2.A.K.Politis et al J. of Biomechanics,39,S402,2006
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