# How to calulate heat transfer though multiple layers?

1. Apr 2, 2015

### Erik S

I am setting up a hydraulic system on a cable laying machine. We dont have much space for the tank, and I am thinking of constructing it on the "wall" og a big 1m^3 stainless steel sand holder. That would make the tank With 5 faces in open air, 1 face With sand on the opposite side.

I am wanting to calculate the heat loss I can expect though the steel wall to the sand mass. Specifically if this will be better or worse than being Oil/wall/air

I have heat transfer values for the materials, I just dont know how to set up the an Equation for multiple layers..

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2. Apr 2, 2015

### BiGyElLoWhAt

Well, start with the first layer, and use the heat transfer as a function of time and temperature to come up with an equation for the temperature of layer 2 as a function of time and the outside temperature. Repeat, and ultimately you will end up with the sand temperature as a function of time and temperature of the outside as well as the transfer rates of the layers in between.

3. Apr 2, 2015

### Staff: Mentor

I don't quite understand the geometry. My understanding is that you have a 1 m^3 tank filled with sand, and heat transfer takes place at one wall of the tank; all the other walls of the tank are insulated. What I don't get yet is what layers of materials are present outside that wall (and how thick)? (I don't need to know the details of the application).

Chet

4. Apr 3, 2015

### Erik S

Hi chet.

There is no insulation, oil against stainless steel against sand.

Surface area of each "wall" that transfers the heat is 0.42m^2

I am trying to calculate if the sand will conduct more heat away than open air, or if it will have an opposite, insulating effect

The sand is slowly replaced so the rate of heat transfer plays a big role on deciding if it is a better solution.

5. Apr 3, 2015

### davenn

I suspect you will find that sand will be a very good insulator and will not conduct much heat away
a quantity of sand is very porous .... lots of air gaps, therefore heat conduction will be very low

you would be better off if the steel plate was just much bigger/thicker. and even better would be the use of
a thick finned block of aluminium which is lots lighter and has a much lower thermal resistance

Dave

6. Apr 3, 2015

### Staff: Mentor

Sorry. Still don't follow. It looks like davenn has figured out what the setup looks like and is being helpful, so I'm withdrawing.

Chet