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Help setting up heat transfer equation

  1. Mar 17, 2015 #1
    Water is being sprayed at a hot flowing material to cool it from 350F to 290F. Lets assume that steam is produced when the water hits the hot material. How would I set up the heat transfer equation to solve for the mass flow rate of water required to cool it from 350 to 290?

    Specific Heat of Water = 4.186 KJ/Kg-K
    Specific Heat of Hot Material = 2.177 KJ/Kg-k
    Mass Flow Rate of Hot Material = 1.512 Kg/s
    Latent Heat of Vaporization = 2260 KJ/Kg
    Temperature of Water = 75F
    Evaporation Temperature of Water = 212F

    This is how I set up the equation....

    Energy absorbed by Water + Latent Heat of Vaporization - Energy released by Hot Material = 0

    MFRwater*Cwater*(TwaterOUT-TwaterIN) + Lwater*MFRwater - MFRmaterial*Cmaterial*(TmaterialOUT-TmaterialIN) = 0

    Now, solving for MFRwater ...

    MFRwater = [MFRmaterial*Cmaterial*(350-290)] / [Cwater*(212-75) + Lwater]

    When I plug in the numbers, I get a REALLY small answer. Am I missing a part of the equation? Is my algebra wrong? Am I using the right value for the specific heat of water, later heat of vaporization, and evaporation temperature of water? Or did I do everything correctly?
  2. jcsd
  3. Mar 17, 2015 #2


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    Gold Member

    I think C is the Specific Heat. You seem to specify it in degrees K but you use degrees F in the equation. Why not convert to Celsius or Kelvin throughout?
  4. Mar 17, 2015 #3
    Yes. Just divide the temperature changes by 1.8.

  5. Mar 17, 2015 #4
    I thought that when dealing with a temperature difference, you didn't have to convert? That's why I left the temperatures in Fahrenheit
  6. Mar 17, 2015 #5
    Not with the latent heat term in there.

  7. Mar 17, 2015 #6
    wow.... I completely blanked out on that thank you. As far as setting up the equation, did I miss anything tho? Im sure the temperature change is going to change my answer
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