How long to cool a hot cube in a cold room?

[seasar]

I need to calculate to a reasonable degree of accuracy how long it will take to cool a cube (about 3 ft in each dimension) of hot honey in a tote in a cold room.
I have the particulars for the honey, specific heat, thermal conductivity.
At the start the temperature of the honey is uniform (120f), when placed into a room at 35F I need to know how long before the center of the cube reaches 110F.

I had planned on simply calculating the heat transfer along an assumed 1D adiabat from the outside of the tote to the center along the shortest route (I also know the particulars for tote's construction). Then I questioned whether this would be an accurate representation. I thought about using a technique I remembered from heat transfer in college and setting up a 2D grid for the tote and use a finite difference method.
The only tools I have available are pen/paper/calculator and Excel along with my reference books.

Thoughts on how to set this up? Thanks!

 

[IRstuff]

"reasonable degree of accuracy" numerically means what?

How is the room maintained at 35°F? Does the AHU drive it below 35°F?

What is the air flow?

What is the emissivity of the honey and the walls of the room? Radiation at the temperatures stipulated is nearly triple that of free convection.

There is a downloadable HT text:

http://web.mit.edu/lienhard/

http://www/ahtt.html

You should consider whether you need a 3D model, using a lumped sum approach.

TTFN

FAQ731-376

 

[Compositepro]

Viscosity is one of the main factors. With viscosity below about 100 poise convection will be your main mode of heat transfer through the honey. Cool honey at the top and walls will sink as it cools so the temperature of the whole container will drop fairly evenly until viscosity increases to the point that convection stops. Conduction alone will be one or two orders of magnitude slower. Cooling the walls to too low a temperature can freeze the material at the walls and slow down the cooling. I don't know anything except CFD (Computational Fluid Dynamics) that can actually calculate what you want and you would have to run experiments to collect data for that to work.

Cooling from 120F to 110F seem a rather trivial practical problem. You can do it almost instantly by mixing in some cool honey.

 

[seasar]

What is the lumped sum approach?

The requirement for the timeline to cool the honey is based on needing to know how long the tote will stay above 110F not trying to attain 110F.
The desired accuracy in this timeline would be something like within 20% of actual. The room is very large and the heat given off the tote will not appreciably affect the surroundings. The velocity of the air near the tote will be close to zero.

 

[IRstuff]

Then the cheap answer is relatively easy. Determine the maximum heat transfer by convection and radiation, and divide that into the thermal mass change of the honey for the 10°F drop. The result will be the fastest possible cooling of the honey.

Assume that all exposed sides of the honey are vertical, and max free convection would be about 189 W/m^2 (4 W/m^2-K. Radiation would be about 286 W/m^2, assuming 100% emissivity. So a total of about 475 W/m^2.

TTFN

FAQ731-376

 

[IRstuff]

For added conservatism, you might consider, as CompositePro alluded, the effect of non-circulation, since the outer surface will cool substantially faster than the interior. You might consider limiting the thermal mass to something like the outer 4 inches, and assume no heat from from the interior.

TTFN

FAQ731-376

 

[dvd]

If you are doing engineering work for a honey producer, they most likely have all of the materials required to perform a study (honey and container). Buy a couple of thermocouples (or thermowells) and insert into the container at key locations and collect data on a datalogger. You won't have to make too many assumptions. You could spend a lot of hours calculating results and not know if they are correct.

 

[chicopee]

An interesting problem because about 40 years ago I had a pop quiz on how long it would take to cool down a full beer can from room temp. to 50f when place in a freezer.

To keep it simple, assume bottom of tote insulated then Hc*A*DT1=m*Cp*DT2/Dt where Hc = effective convective HT coefficient which must take into consideration the Hc's outside and inside the tote and the k value of the tote; A= total surface area of tote; DT1 is the temp difference between the room and the bulk temp of 110ft. m=mass of honey;Cp specific heat of honey;DT2 is the temp difference between initial and final bulk temp. of honey; Dt is time which you want with an error of+- 50%.