# How to solve coupled steady laminar diffusion flame jet problem? [closed]

I am trying to solve governing equations of laminar diffusion flame jet for steady state case. In the next step, I will solve for unsteady case.

I have non-dimensional continuity, axial momentum, mixture fraction and energy equations. Axial momentum, mixture fraction, and energy equations have same form and boundary conditions. Since density ($\rho$) is function of mixture fraction ($mf$), I have to solve Eqns. 1.1, 1.2, and 1.3 together.

I haven't solve any PDEs in Matlab before, and I don't know much about solution methods of coupled PDEs. So far I was able to find some finite volume methods to solve PDE, and I discovered NAG Toolbox for MATLAB and FiPy: A Finite Volume PDE Solver Using Python. I couldn't find so far an example that is dealing with coupled PDEs with variable coefficients that is dependent on one of the solved variables.

Mass diffusivity ($D$), exit axial velocity($u_{\text{exit}}$), and jet radius at the exit($R_N$) are constant in the governing equations. • What's your specific question? What have you tried so far? – Bill Barth Aug 11 '14 at 11:51
• I don't know how to approach this problem. What would you do first to solve this problem and what would be a good solution strategy for this PDE set? As I said, I am newbie regarding solving PDEs; I am open to any suggestion. – Murat Ates Aug 11 '14 at 15:39
• Unfortunately, there are whole books on this subject. Whole libraries, even. It's a reasonable question, but not for this site. I would suggest that you talk to your advisor or other colleagues. – Bill Barth Aug 11 '14 at 15:41
• Could you recommend any book? Thank you for the suggestion. – Murat Ates Aug 11 '14 at 15:46

• Thank you for the advise @Geoff Oxberry. One of my advisors recommended solving transient scheme instead of steady state with adaptive RK4 method. I hope Strikwarda's book can help me get there. Also, I don't feel comfortable with writing finite differences of PDE terms having different dependent variables i.e. $d/dr(r*\rho*v*mf)$. Would Strikwerda's book help me on this or is there any introductory book that you could recommend that works on these issues? Thanks! – Murat Ates Aug 13 '14 at 20:10