Hi, are you sure that your problem leads to a system of ODEs. The heat transfer is usually modelled by a system of PDEs.
Can you show us the system which you wish to solve? Richard is correct in general, but if your flow is of boundary layer type and if the boundary layer approximation applies, then you will be likely to have an ODE boundary value problem to solve. For that, the typical method of choice will be the shooting method allied with something like a Runge-Kutta scheme.
Dear Ali, in your case of heat and mass transfer model, probably as note by Richard you need PDE equation, but if your model is time dependent or there is a variable respect to which model has only first order partial derivative, you can apply lines method which translate PDE problems into ODE systems. This system can then be solved using standard method as Euler forward/backward or Runge-Kutta. In the following reference you can find description of this technique using Mathematica applied to heat equation. Gianluca
http://reference.wolfram.com/language/tutorial/NDSolveMethodOfLines.html
Thanks for all for their answer. My system is a boiling flow in vertical channel. Where I want to simulate 5 parameters such as void fraction, liquid and vapor velocity , pressure and temperature as a function of time and length.
Dear Rasikh Tariq, Yes my system is time dependent. In addition I have 5 parameter as explained above. Thanks for your interesting and your help. usually ode15s (Gear method) maybe the favorite in this systems?
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