Help setting up heat transfer equation

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Discussion Overview

The discussion revolves around setting up a heat transfer equation to determine the mass flow rate of water needed to cool a hot material from 350°F to 290°F. Participants explore the assumptions and calculations involved in the heat transfer process, including the effects of steam production when water contacts the hot material.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant proposes an energy balance equation involving the energy absorbed by water, latent heat of vaporization, and energy released by the hot material.
  • Another participant questions the use of temperature units, suggesting that converting to Celsius or Kelvin might be beneficial for consistency.
  • There is a discussion about whether temperature differences can be used directly in Fahrenheit without conversion, with some participants asserting that conversion is not necessary for temperature differences, while others argue that the latent heat term complicates this.
  • A participant expresses uncertainty about whether their setup of the equation is complete or if they have missed any factors that could affect the mass flow rate calculation.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the necessity of unit conversion for temperature differences in the context of the heat transfer equation. There is also uncertainty regarding the completeness of the initial equation setup.

Contextual Notes

Participants express concerns about the appropriateness of specific heat values and the latent heat of vaporization, as well as the implications of temperature unit choices on the calculations. The discussion reflects a need for clarity on these assumptions and their impact on the results.

William12
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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

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?
 
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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?
 
tech99 said:
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
 
Chestermiller said:
Yes. Just divide the temperature changes by 1.8.

Chet
tech99 said:
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
 
William12 said:
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
 
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
 

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