Validation of Equation 1

[rwsasser1]

Wattage required to heat material:

Weight of material (lbs) x Specific Heat (Btu/lb °F) x Temperature rise (°F)/3.412 btu/watt hr. x Heat-up time (hr.)

= Watts

I found this on a website, does this fly with you guys? My heat transfer book has nothing on this.

 

[IRstuff]

And how does this equation address the heat losses during heating?

TTFN

 

[rwsasser1]

It doesnt I guess, but thats ok, for my needs I can use a worst case scenario. So you agree with this equation(assuming no heat loss during heating)?

 

[rwsasser1]

let me rewrite the equation

(W*Cp*Delta T)/(3.412*Time)

 

[IRstuff]

By ignoring losses, you don't have "worst case scenario"

TTFN

 

[rwsasser1]

I am trying to figure out the maximum temperature increase in the material. So If I assume no heat is lost then wouldnt that give me the maximum temperature increase possible?

 

[rwsasser1]

Ok, I just found this in my thermo book, Q=mCp(Ti-Tf)/time

so I believe it now.

 

[JStephen]

You've got the time multiplied instead of divided in your original post.

 

[IRstuff]

Energy/time = power

TTFN

 

[25362]

In the original formula, time is indeed multiplied, but it is in the denominator. Parenthesizing it would have clarified the imbroglio.

Heat/(surface[×]time) = heat flux.

 

[jrhols]

You have to be real careful with this calculation.
The literature starts with Laplace's famous diffusion equation that diffusivity in square meters per second is equal to the quantity conductivity K divided by specific heat (thermitivity c) in joules per kilogram per degree C or K divided by density.

But research since that time, including Einstein has shown other variables are involved. It is an oversimplification.
Moisture and geometry are huge influences. When you say to heat a plate for instance, this equation assumes you heat it from both sides. It all changes when you heat from one side, and that is just for a slab or thin film with constant K coefficient, no wave or drop in surface temperature or emissivity or reflection or....

 

[jrhols]

To summarize, Laplace said Power=diffusivity* area * temperature change.
Einstein in his Kinetic Theory of Matter said that calories are a measure of heat energy, time to heat being proportional to the capacity of the molecules to contain the heat. Temperature is the 1/2 Mass times velocity squared. The english system has the same units for heat energy values, that is 1BTU is 1 calorie, it is only for converting between them that we need .293 times BTU's to get a calorie. For a long time dimensionless factors were used for losses. Now that is changing. See

http://www.thermcoat.com.

Also you often see 1.73 used to convert between watts and btu conductivity. Actually, that is 1.73 BTU's per foot converted to watt per foot. This is only a lengthwise heat path with no diffusion or sideways movement of heat. So, you don't see this factor in the downloaded model, just so you know it goes beyond simple conversion factors. Also when you say maximum, that usually means that there is some efficiency factor, as used often in injection molding calculations of how much heat to use to heat so many pounds of plastic so many degrees in so much time. Again, that is a dimensionless model to simplifiy the physics.

 

[chicopee]

A time rate of increase or decrease either in mass or in the temperature is missing. Cp is assume constant for a temperature range.
Equat. s/b q=(1/3.412)*M*Cp*dT/dt or (1/3.412)*dM/dt*cp*dT.

 

[25362]

Which validates the formula by rwsasser1.

To chicopee, your comment is right. However, we shouldn't forget (1/3.412) is not an all-embracing factor since it only applies when converting Btu to watt-hour.