Help setting up heat transfer equation

[William12]

Water is being sprayed at a hot flowing material to cool it from 350F to 290F. Let's 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?

Assumptions
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 = 212FThis is how I set up the equation...

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

MFR_water*C_water*(T_waterOUT-T_waterIN) + L_water*MFR_water - MFR_material*C_material*(T_materialOUT-T_materialIN) = 0

Now, solving for MFR_water ...

MFR_water = [MFR_material*C_material*(350-290)] / [C_water*(212-75) + L_water]

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?

 

[tech99]

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?

 

[Chestermiller]

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?

Yes. Just divide the temperature changes by 1.8.

Chet

 

[William12]

Yes. Just divide the temperature changes by 1.8.

Chet

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?

I thought that when dealing with a temperature difference, you didn't have to convert? That's why I left the temperatures in Fahrenheit

 

[Chestermiller]

I thought that when dealing with a temperature difference, you didn't have to convert? That's why I left the temperatures in Fahrenheit

Not with the latent heat term in there.

Chet

 

[William12]

wow... I completely blanked out on that thank you. As far as setting up the equation, did I miss anything tho? I am sure the temperature change is going to change my answer