Design Portable Container for Medicine at 4 °C for 12 Hours

[karmatic]

Homework Statement

Design a portable container that will keep medicines at around 4 degrees celcius for at least 12 hours.

Homework Equations

Fouriers law, q=kA(T₁-T₂/L)
Thermal Resistance=L/kA

q=heat transfer rate (in W)
K=thermal conductivity (W/M*degrees C)
A=cross sectional area normal to heat flow (m²)
T₁-T₂=temperature difference across the material of L thickness (degrees C)
L=material thickness (m)

The Attempt at a Solution

I am completely lost with this, in my text it gives me the definition of the terms in the equation but I'm not sure what it means by cross sectional area normal to heat flow, is that just the surface area? and if so it would be the outside surface area correct? I am also not sure where the concept of time comes into this equation. So far all I have is the values for the temperature gradient which would be 28^o-4^o.

Is anyone able to point me in the right direction please?

 

[Quinzio]

You're not told the maximum ambient T. Do you have to guess it ?
What is the box is left at the sun light ? :)
A hot summer day can be 45°C
Can you put a block of ice into the box ?

The problem is really poorly explained.

 

[karmatic]

the only guidelines for the design are the duration it has to stay below the max temp. I was just going to use 28 degrees C as a starting off point, and then once I can show the relationship between the material used and dimensions of the box on the temperature within the box, come up with a variety of options to display in a graph. I'm just not sure how the time factor comes into fouriers law, I'm guessing it has something to do with the units of thermal conductivity which is in Watts correct? I need to find my other textbook...

 

[Quinzio]

I'm just not sure how the time factor comes into fouriers law,

The temp inside the box will eventually reach the ambient temperature after a long (infinite) time. The shape of T versus time is an exponential curve, like the RC discharge curve, if you're familiar with electric circuits.
You should define a thermal capacity of the inside in J/kg.

 

[karmatic]

I have absolutely no experience with anything to do with electric circuits! How would I go about calculating a thermal capacity?

Also, I still don't know what is meant by "A=cross sectional area normal to heat flow (m2)"

edit* and isn't thermal capacity measured in Joules per Kelvin?

 

[karmatic]

okay attempt at solution so far. I decided on a cube shape, sides of 0.5m and a thickness of 0.02m made of glass. The glass has thermal conductivity of 1.4 W/m*k, at a room temperature of 34^oC.

q=kA(T₁-T₂/L)
q=(1.4W/m*k)(1.5m²)(30^oC/0.02)
q=3150W=3150J/s

So that gives me the heat transfer rate, 3150J/s? But now I don't know how to use that information to solve the problem, and when working out the heat transfer rate of the air within the box do I simply add that to the heat transfer rate of the glass to get a total amount?

edit* adding the heat transfer rate calculation for your criticism, I'm unsure of the value for L that I used...

q=(0.0263W/m*k)(1.2696m²)(30^oC/0.46)
q=2.17764W=2.17764J/s

 

[karmatic]

I'm now trying to calculate the specific heat of the box using E_thermal=mc(T_final-T_initial), and for some reason I'm getting a higher value for glass than for air, which seems wrong because from what I have read in my textbook gases are meant to have a lower level of heat transfer than solids. I can't work out what I'm getting wrong here, I've obviously got the wrong idea about something. Can anybody please help me?

 

[karmatic]

can anyone help at all? I have to try to complete a 15 page report on this by the end of the day, and I can't even start writing it without the correct science behind it all =(