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Need Help Solving Set of Coupled ODEs

  1. Nov 19, 2016 #1
    1. The problem statement, all variables and given/known data
    Liquid nitrogen is in a dewar connected to a vacuum pump. Initial pressure in a dewar is 1atm and saturated with gaseous nitrogen. If the vacuum pump started, it removes gas in it and the pressure in a dewar will be reduced under the saturation pressure of the liquid nitrogen. Then evaporation rate will be increased and the temperature of the liquid nitrogen will be decreased due to the latent heat. And when the temperature of the nitrogen closed the phase change temperature, liquid nitrogen will be solidified. I have to set up a model to calculate the time for the solidification.

    2. Relevant equations
    1) The evaporation rate can be defined as m dot = hA(Pv-Ph) where h is boiling coefficient, Pv and Ph is saturation pressure and environment pressure respectively.
    2) Temperature change of liquid nitrogen : cm_ln*dT/dt = m dot*hfg where c is specific heat, m_ln is mass of liquid nitrogen, hfg is latent heat.
    3) Vapor pressure change : dPv/dt = -m dot*R*Tk/(Mn2*Vf) where, Tk is the temperature of a dewar, Mn2 is nitrogen's molecular weight and Vf is free volume in a dewar.
    4) Time to reach P=p2 from p1 : tp=(V/Ss)ln[(p1-pu)/(p2-pu)] where Ss is system pumping speed, pu is the ultimate pressure.

    3. The attempt at a solution
    I have hard time combining upper mentioned equations. Also it is to complicate to solve.
     
  2. jcsd
  3. Nov 19, 2016 #2
    Please read the tutorial on LaTex text editor and rewrite you equations using LaTex. As the equations are written, they are very hard to understand mathematically. Also, I have moved your thread to a math forum where you may get more of a response.
     
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