Heat Transfer in Metal Tank: Time to Drop from θ2 to θ1

[Thatrandomdudeacross]

I'm trying to find a heat transfer equation that includes time. Metal tank, partially filled with liquid. I need to find the time it would take for the temperature on the outside of the tank to drop from θ2 to θ1, given thickness, metal and liquid's properties, and tank dimensions

 

[anorlunda]

The most important parameters are surface area of the tank, temperature difference in and out, and heat transfer coefficient.

The heat transfer coefficient is small for well insulated walls, and large for no insulation and thin walls. It is very difficult to calculate. Typically, you would need to measure it by experiment, or to get a value from the manufacturer of the tank.

 

[Thatrandomdudeacross]

The most important parameters are surface area of the tank, temperature difference in and out, and heat transfer coefficient.

The heat transfer coefficient is small for well insulated walls, and large for no insulation and thin walls. It is very difficult to calculate. Typically, you would need to measure it by experiment, or to get a value from the manufacturer of the tank.

Thank you for the reply
The tank is not purchased; it was made in our student machine shop. Assuming I have the coefficient, how would I go on from there?

 

[gmax137]

Any introductory heat transfer textbook, look for: "unsteady" or "transient" one-dimensional heat transfer; Biot number; Heisler charts.

This problem can be solved approximately or in any amount of detail as needed.

 

[Thatrandomdudeacross]

Any introductory heat transfer textbook, look for: "unsteady" or "transient" one-dimensional heat transfer; Biot number; Heisler charts.

This problem can be solved approximately or in any amount of detail as needed.

Thank you!

 

[sophiecentaur]

Assuming I have the coefficient, how would I go on from there?

There is not really a single "coefficient" for this because the problem is very complex. You need to know the effect of convection inside the tank, conduction through the walls of the tank and convection of the air outside the tank. You should be aware of this before you look for a simple answer to your problem.
Try this link and a textbook about thermal physics. The best way to an answer would be to do experimental measurements. These would not be too hard if the tank is not too big and if you have a supply of water at various temperatures - and plenty of time.