Help setting up heat transfer equation

In summary, to cool a material from 350F to 290F, water must be sprayed at a hot flowing material. The equation to solve for the mass flow rate of water required is MFRwater*Cwater*(TwaterOUT-TwaterIN) + Lwater*MFRwater - MFRmaterial*Cmaterial*(TmaterialOUT-TmaterialIN).
  • #1
William12
8
0
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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  • #2
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?
 
  • #3
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
 
  • #4
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
 
  • #5
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
 
  • #6
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
 

FAQ: Help setting up heat transfer equation

What is the heat transfer equation?

The heat transfer equation is a mathematical formula that describes the transfer of thermal energy (heat) between two or more objects. It takes into account factors such as temperature, material properties, and surface area to determine the rate of heat transfer.

How do I set up a heat transfer equation?

To set up a heat transfer equation, you first need to identify the type of heat transfer involved (conduction, convection, or radiation), determine the relevant physical properties of the objects involved (such as thermal conductivity), and use the appropriate formula to calculate the rate of heat transfer.

What is the difference between conduction, convection, and radiation?

Conduction is the transfer of heat through direct contact between two objects, convection is the transfer of heat through the movement of a fluid (such as air or water), and radiation is the transfer of heat through electromagnetic waves.

How does the surface area affect heat transfer?

The larger the surface area, the more heat can be transferred between two objects. This is because a larger surface area allows for more contact points and more efficient heat exchange. Therefore, increasing the surface area can increase the rate of heat transfer.

What are the units of measurement for heat transfer?

The units of measurement for heat transfer depend on the type of heat transfer being considered. For conduction, the unit is typically watts per meter kelvin (W/mK), for convection it is watts per meter squared kelvin (W/m²K), and for radiation it is watts per meter squared (W/m²).

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