Thermo problem!

[Purplehaze]

Need to check my calculation.

I have a cheese (mozzarella) that has optimal melting
characteristics when a heat capacity of 675 J/g is
supplied.
I need to find out the amount (mass) of steam required to melt the cheese at this optimal point. Cp of steam is 2009 J/kgC.
assumptions may me made where appropriate.
we know: q = m * (T2-T1) * Cp

your help is appreciated...

 

[quark]

PurpleHaze!

For that you don't require heat capacity but latent heat of fusion. Latent heat of evaporation of steam is 550 kCal/Kg.

if Mc is the mass flow rate of cheese and Hc is its latent heat then steam flow rate you require is Ms = McHc/550.

Regards,

 

[Purplehaze]

now what about if I were to use water to heat the cheese instead of steam.
I would use:
q=m*deltaT*Cp

right?

 

[quark]

Yes. You are right. For cheese part it again depends whether you want to heat it or melt it. For melting you have to use latent heat.

Regards,

 

[poetix99]

The equations above will provide the MINIMUM required amount of steam or water - accurate for direct contact heat exchange, but not very good for your mozzarella.

 

[Purplehaze]

quark - thanks.

poetix99 - would you suggest a different method/equation(s) for this problem?

 

[poetix99]

I was being a little bit sarcastic, but the obvious question is: what is the physical arrangement for melting the cheese?

Without knowing the second thing about food-processing, I can imagine various melting schemes which would have some amount of heat loss to the surroundings. There is not necessarily another method; you might want to get a handle on the accuracy of these equations for your application.

If this is a well-insulated, jacketed vessel, without a lot of air moving along with the cheese, then the simple heat balances that "quark" gave you will be good estimates. If those "criteria" aren't met, you might have to make some accounting for these losses.

How much air is "a lot of air"? If the process does NOT use air to "fluidize" the cheese (for example if it is gravity fed or a "batch" process), my seat-of-the-pants guess is that you could ignore the incidental flow of air.
Otherwise, add

(air mass flow)*(air specific heat)*(T:steam - T:ambient air)

to

(cheese mass flow)*(cheese heat of fusion)

and adjust your steam flow accordingly.

 

[Purplehaze]

The cheese we want melted is submerged in hot water (this water is heated using steam injection)....so there is direct
contact between the cheese and water itself. No outstanding losses of heat transfer should be evident for this application.

cheese <----- directly heated by hot water (which is heated to the desired temperature by steam injection)

what would be your suggestion on the easiest method to determine the amount of steam require to heat the water
(in order to melt the cheese)?
*how's that for a scenario *

Thanks.

 

[poetix99]

OK, so ignore all that &quot;hot air&quot; about fluidized mozzarella, etc.

The answer is as nearly &quot;quark&quot; indicated in his first post, with the following refinement: you should add the sensible heat gain of the cheese as well as the latent heat of fusion (melting).

Q = (chs.mass flow)*[(chs.delta T)*(chs. specific heat) + (chs. latent ht.)]

This can be used to solve for the steam flow required.

*****

I'm still thinking about potential losses from your melter. Is hot water drained out of the melter along with the cheese? Is this made up with cold water? If so, this should be accounted for as well. In any event, you will get a good first approximation so long as you have properly identified the heat fluxes in this basic energy balance.

 

[abeltio]

A lot of heat will be lost to atmosphere trough the surface (I understand you are working with an open vessel). Also, is this a batch process? i.e. you want to melt a certain mass of cheese within a certain amount of time? OR is this a continuous process?
The equations will be completely different then...
See Process Heat Transfer by D.Q. Kern Chapter 18, Batch and Unsteady-State Processes.
Also, never thought pizza could become so complicated!!!
HTH
Saludos.
a.

 

[moich23]

Assuming there is no heat loss to the atmosphere and initially the water temp is below the cheese melting point.

Q1 + Q2 = Q3 + Q4 + Q5

Q1 = heat given by steam condensing
= m1*L1
Q2 = heat given by condensed water cooling from 100 deg.C
to T1
= m1*c1*(100-T1)
Q3 = heat taken by water (temp. increases from T2 to T1)
= m2*c1*(T1-T2)
Q4 = heat taken by cheese (temp. increases from T2 to its
melting point, say T3)
= m3*c2*(T3-T2)
Q5 = heat taken by melting cheese
= m3*L3

m1 = mass of condensed steam
m2 = mass of water in the tank
m3 = mass of the cheese
c1 = spec. heat capacity of water
c2 = spec. heat capacity of cheese
L1 = spec. latent heat of water (evaporation)
L3 = spec. latent heat of cheese (fusion)

This equation is just a guideline to ur problem. Since, lots of information is not available just as abeltio said, it(the eq.) can be modified to suit ur problem.

 

[PacificSteve]

Being a former Wisconsin Cheesehead, I find this subject near and dear to my heart, and am glad to see this is one of the most popular threads.

The situation appears to be a lot like steam injection into large dishware washing units. My experience with these is that a heck of a lot of energy is lost to atmosphere - i.e. the steam doesn't give all of its energy to the water. This can and should be attempted to be controlled, but some loss is unavoidable.

Are we really talking about a phase change in the cheese? My gut says no. I don't think that &quot;firm cheese&quot; is a solid and that &quot;flowing cheese&quot; is a liquid, they are just different temperature multi-component amorphous blobs. I think some time/temperature tranformation graphs could verify that theory.

Be careful what steam use use---any steam system treatment chemicals will need to be FDA approved. I assume there is direct contact between the cheese and water. No joke here.

PacificSteve

 

[Purplehaze]

hmmm.... I'm walking the edge here
so many answers given....

-this is a batch process (ie. 30,000kg in 2 hours <--not true, just an example)

-and I think you may be right Pacific Steve...(is this a phase change or not?)....I'm thinking no,..but I'm looking
at the heat required to take cheese from a solid block to
a flowable substance (so I believe heat of fusion comes into play)

moich23 - i believe your equation can be modified to suit
this application adequately....now, if I could just somehow
classify the heat loss to the atmosphere,etc. by the steam.

 

[Purplehaze]

 

[TD2K]

I don't think you have a phase change exactly as you heat up cheese. In my own experience (frying cheddar), you do have oil that comes out of the cheese. Now that portion I could see going through a phase change. But the milk solids are likely just sensible heat.

Funny, Perry's doesn't list any data on cheese :-0. I'll check my copy of CRC tables for applied engineering science when I get home, they have lots of 'different' data.

 

[Purplehaze]

i had that same problem finding info on cheese in PErry's..

 

[TD2K]

sorry, nothing on cheese in CRC either.

 

[Toronto]

Purplehaze, what is the melting point of your cheese? (Is this a propietary info?)

Have you done a DSC on it? The DSC trace should be able to tell you if you have melting point, glass transition, or what? That would be helpful for your energy balance, I think, since one of the terms deals with phase transition.

As usual, the literature data should be taken with a grain of salt... best is to run your own measurements if you have not done them already?

 

[EngineerDave]

DSC on cheese? Wow that would have been a fun experiment back in my materials engineering classes.

Has anyone noticed that alot of the big chains stopped using mozzarella? In case I'm totally mistaken some of them are using provolone (which I can only surmise is cheaper)